# The study of key reactions shaping the post main-sequence evolution of
massive stars in underground facilities

Ferraro F. 1, Ciani G.F. 2,3, Boeltzig A. 3, Cavanna F. 4 and Zavatarelli S.
1,∗

###### Abstract

The chemical evolution of the Universe and several phases of the stellar life
are regulated by minute nuclear reactions. The key point for each of these
reactions is the value of cross sections at the energies at which they take
place in stellar environments. Direct cross-section measurements are mainly
hampered by the very low counting rate and by cosmic background, nevertheless
they have become possible by combining the best experimental techniques with
the cosmic silence of an underground laboratory. In the nineties the LUNA
(Laboratory for Underground Nuclear Astrophysics) collaboration opened the era
of underground nuclear astrophysics installing first a home-made
$50\,\mathrm{kV}{}$ and later on, a second $400\,\mathrm{kV}{}$ accelerator
under the Gran Sasso mountain in Italy: in 25 years of experimental activity,
important reactions responsible for hydrogen burning could have been studied
down to the relevant energies thanks to the high current proton and helium
beams provided by the machines. The interest to the next and warmer stages of
star evolution (_i. e._ post main sequence, helium and carbon burning) drove a
new project based on an ion accelerator in the MV range called LUNA-MV, able
to deliver proton, helium and carbon beams. The present contribution is aimed
to discuss the state-of-the-art for some selected key processes of post main
sequence stellar phases: the
${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ and the
${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fundamental for helium and carbon
burning phases, and ${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$
and ${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ that are
relevant to the synthesis of heavy elements in AGB stars. The perspectives
opened by an underground MV-facility will be highlighted.

##  1 Keywords:

Underground nuclear astrophysics, helium burning, carbon burning, gamma
spectroscopy, neutron spectroscopy

##  2 Introduction

The hypothesis that the energy which powers the Sun comes from thermonuclear
reactions seems to be mainly due to Eddington (1920) and Aston. After the
discovery of nuclear reactions by Rutherford in the twenties it became clear
that only the enormous amount of energy stored in the nuclei and released
during fusion reactions was able to support the sun luminosity for a time
period compatible with the geological datings (von Weizsäcker (1938), Bethe
and Critchfield (1938)): by fact, in order to properly understand the chemical
evolution and the stellar energy engine, it is fundamental to precisely know
how light nuclei are converted to heavier ones.

According to current theories, the first nuclei were formed through a network
of nuclear reactions in the Big Bang nucleosynthesis (BBN), a few minutes
after the Big Bang. BBN left our universe containing about 75% hydrogen, 24%
helium by mass, with some traces of lithium and deuterium. The composition of
the present Universe is not very different from the primordial one, with the
total mass elements heavier than hydrogen and helium (”metals” according to
the astronomers) at the level of a few percent. Stars fuse light elements to
heavier ones in their cores, up to iron and nickel in the more massive stars.

The most important stellar properties that determine the evolutionary fate of
a star are its mass and its composition (Rolfs and Rodney (1988), Iliadis
(2015)) : the larger the mass, the larger the temperature in the core. The
star composition influences which reactions dominate the burning processes.

When a low-mass star like the Sun runs out of hydrogen in the core, it becomes
a red giant star, fusing H to He via the CNO cycle in a shell surrounding an
inert He core. When the core temperature reaches 100 million K, the He nuclei
in the core have sufficient kinetic energy to fuse to C (helium burning),
forming ${}^{12}\mathrm{C}$ in a two-stage process. Subsequent fusion with
another helium nucleus produces ${}^{16}\mathrm{O}$ nuclei. This process, in
symbols ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$, is the main
source of the carbon and oxygen found in the Universe, including that in our
bodies and represents by fact the ”Holy Grail” of nuclear astrophysics since
the C/O ratio at the end of helium burning greatly affects the subsequent
evolution of the star. At some point, when the He in the core is exhausted,
the stars start to burn He in a shell surrounding the inert C/O core, in
addition to burning H to He in a shell surrounding the He burning region. This
phase, referred to as the asymptotic giant branch (AGB), is characterised by
thermal instabilities: at a given time the burning shells extinguish and the
low-mass star will end its existence as a white dwarf, consisting mainly of C
and O and supported by electron degeneracy pressure.

Massive stars evolve very differently from low-mass stars. After the end of a
burning phase, the core contracts gravitationally, and the temperature
increase can be sufficient to ignite the next and heavier nuclear fuel. In
case of masses larger that 11 $M_{\odot}$, after undergoing He burning, the
core experiences further burning episodes referred to as C-, Ne-, O- and Si-
burning. The duration of each subsequent nuclear burning phase decreases
significantly. There are two main reasons: the first is that each burning
phase releases by far less energy per unit mass with respect to the previous
phase; the second that an increasing fraction of energy is radiated away by
neutrinos. Therefore, while H burning may continue for many million years, C
burning typically lasts hundreds of days and Si burning may run out in just
one day. After the last advanced burning stage (Si burning) the core consists
mainly of iron isotopes: no more energy can be generated through fusion
reactions. The core contracts and when it exceedes the Chandrasekhar mass
limit, it collapses until the density of nuclear matter is reached. As a
consequence of the neutron degeneracy pressure, the core rebounds and produces
an outgoing shock wave. The wave heats and compresses the overlying layers of
the star, consisting of successive shells of Si, O, Ne and C thus more
episodes of nucleosynthesis, referred to as explosive Si-, O-, Ne- and
C-burning, take place.

The creation of elements heavier than iron occurs mainly through neutron
capture processes, eventually followed by beta decays in the so called s
(slow)-process (Käppeler et al. (2011a)) and r (rapid)-process. The r-process
dominates in environments with higher free neutrons fluxes and it produces
heavier elements and more neutron-rich isotopes than the s-process. Supernovae
explosions and neutron star mergers are potential sites for the r\- process.
The s-process is slow in the sense that there is enough time for beta decays
to occur before another neutron is captured: a network of reactions produces
stable isotopes by moving along the valley of beta-decay stable isobars. This
process primarily occurs within ordinary stars, particularly AGB stars, where
the neutron flux is sufficient to cause neutron captures to recur every 10–100
years, much slower than for the r-process, which requires 100 captures per
second.

The key point for each of these reactions is the value of cross sections at
the energies at which they take place in stellar environments. For most
stellar scenarios, the changes in the system are slower than the collision
time between the ions or atoms inside the stars, thus the temperature profile
is well-defined: the thermonuclear reaction rate depends on the Maxwell-
Boltzmann velocity distribution and on the cross section $\sigma$(E) energy
dependence (Rolfs and Rodney (1988)). Typical stellar temperatures for main-
sequence low-mass stars, correspond to peak energies of the Maxwell-Boltzmann
distribution of $k_{B}\,T\sim 0.9-90\,\mathrm{keV}{}$. In case of more massive
stars during advanced burning stages, peak energies can be as high as few MeV.
For charged particles induced reactions these energies are typically well
below the Coulomb barrier due to the nuclei electrostatic repulsion and the
nuclear reactions proceed via tunnel effect. As a consequence, the low values
of the cross sections, ranging from pico- to femto-barn and even below,
prevent their measurements in a laboratory at the Earth’s surface where the
signal to background ratio is too small mainly because of cosmic rays. The
observed energy dependence of the cross section at high energies is
extrapolated to astrophysically relevant energies leading to substantial
uncertainties. In particular, the reaction mechanism might change, or there
might be the contribution of unknown resonances which could completely
dominate the reaction rate at the stellar energies.

In the nineties the LUNA collaboration proved that the installation of the
experiments in a deep underground laboratory, the Gran Sasso National
Laboratory, is a successful approach: for the first time nuclear astrophysics
measurements with very small counting rates, down to few events per month
became a reality.

The high current hydrogen and helium beams provided by the 50 kV (Greife et
al. (1994)) and, later on, by the LUNA-400 kV accelerators (Formicola et al.
(2003)) allowed to investigate for the first time at stellar energies the most
important reactions responsible for the hydrogen burning in the Sun, such as
the ${}^{3}\mathrm{He}({}^{3}\mathrm{He},2p){}^{4}\mathrm{He}$ (Bonetti et al.
(1999)) and for the BBN such as the
${}^{2}\mathrm{H}(\mathrm{p},\gamma){}^{3}\mathrm{He}$ (Casella et al. (2002);
Mossa et al. (2020)).

Full descriptions of LUNA and of the several results obtained in 25 years of
experimental activity can be found in recent review papers (Broggini et al.
(2018); Cavanna and Prati (2018); Broggini et al. (2019)).

Such achievements have motivated two proposals for similar facilities in China
(Liu et al. (2016)) and in the United States (Robertson, Daniel et al.
(2016)).

The importance to extend such precise studies to the processes relevant to the
late and warmer stages of star evolution (post main-sequence phases, helium
and carbon burning) has motivated the LUNA collaboration to acquire a new and
more powerful 3.5 MV single-ended accelerator . The new machine will deliver
ion beams of H+, ${}^{4}\mathrm{He}$+, ${}^{12}\mathrm{C}$+ and
${}^{12}\mathrm{C}$++ in the energy range from 0.350 to 7$\,\mathrm{MeV}$ with
$100\,\mathrm{\mu{}A}$ \- $1\,\mathrm{mA}$ intensity currents, depending on
the ion species and on the energy value.

In the following sections, first we will focus on the technical aspects which
are important for an underground nuclear astrophysics experiment. Then, the
state of the art and the expected improvements from underground measurements
are presented for some selected key processes of post-main-sequence stellar
phases: in detail, the ${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$
and ${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$, that are
sources of neutrons for the s-process in asymptotic giant branch stars (AGB)
and during hydrostatic evolution of massive stars and the
${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ and the
${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reactions, key processes of helium and
carbon burning, respectively.

In the conclusions, the commissioning phase of the new accelerator will be
detailed, together with highlights about the exciting perspectives opened by
the new facility in a larger time window scenario.

##  3 The MV facility at Gran Sasso

The MV facility will be hosted in the north side of Hall B in the Gran Sasso
Laboratory and will consist of an accelerator room with concrete walls and a
multistory building housing the control room and technical facilities. The
concrete walls and ceiling (thickness of 80 cm) of the accelerator room will
act as neutron shielding.

Nuclear astrophysics experiments require both high beam currents and a well-
defined and stable beam energy: to perform reliable energy scans of the
targets the accelerator terminal voltage must be stable to
$<1\,\mathrm{keV}{}$ over many hours and to $<0.1\,\mathrm{keV}{}$ over one
hour. A precise energy value is mandatory because of the almost exponential
energy dependence of the cross section induced by the tunnel effect
probability: a small fluctuation of the beam energy would cause a large
uncertainty in the measured cross section value. Since for some reaction long
data taking times are expected, the ion source must be able to run stably
overnight without human intervention.

A 3.5$\,\mathrm{MV}$ linear DC accelerator was specifically developed by High
Voltage Engineering to meet the stringent requirements on beam intensity and
stability (Sen et al. (2019)). The machine will deliver ion beams into two
different beam lines via a 35∘ switching analyzing magnet. Two independent
target stations for solid and gas targets will be located at 2 m distance from
the analyzing magnet. The LUNA-MV accelerator is single-ended, _i. e._ it has
an ion source and an injector block located inside the accelerator tank in the
high-voltage terminal.

The need for high-intensity protons as well as carbon ions in the 2+ charge
state were the reasons to prefer an electron cyclotron resonance (ECR) ion
source for the accelerator.

The accelerator operates at a terminal voltage (TV) range of
$300\,\mathrm{kV}{}-3.5\,\mathrm{MV}{}$, while the ion source can operate at
$30\,\mathrm{kV}{}-40\,\mathrm{kV}{}$. In the present system, high-intensity
beam currents should be maintained over a large dynamic range: by considering
a 1 mA current capability in case of a proton beam, the beam power can be as
high as 3.5 kW. To guarantee voltage stability for longer time periods ($>$1
h) a high precision, low- temperature coefficient ($<$ 5 ppm
${}^{\circ}\mathrm{C}$) resistor chain is used to measure the terminal
voltage. Beam intensity on target for H, He and C ions are reported in Table
1. Compared to previous Singletron accelerators, the LUNA-MV has improved
specifications for terminal voltage stability and ripple ($10^{-5}$). Beam
energy reproducibility is in the order of $10^{-4}$. A detailed description
can be found in Sen et al. (2019).

Table 1: Beam intensity on target Ion Species | Current (e$\mu$A)
---|---
|  TV range: $3.5-0.5$$\,\mathrm{MV}$ ($0.5-0.3$$\,\mathrm{MV}$)
${}^{1}\mathrm{H}$+ | 1000 (500)
${}^{4}\mathrm{He}$+ | 500 (300)
${}^{12}\mathrm{C}$+ | 150 (100)
${}^{12}\mathrm{C}$++ | 100 (60)

For practical considerations, targets for direct measurements of nuclear cross
sections on stable nuclides are typically either in solid or gaseous state.
The basic aspects of such targets are similar for experiments underground and
on surface, but certain requirements are emphasized for experiments deep
underground to fully embrace the advantages of the location. In the case of a
solid target, the beam energy loss occurs in a relatively small volume. The
resulting power density, up to on the order of $10^{2}-10^{3}$ W/cm2 at LUNA
400 if the beam is stopped in the target, requires the target to be cooled to
avoid an increase of temperature that would damage the target or accelerate
beam-induced target degradation. For targets on an inert backing material,
such as those produced by evaporation, sputtering or implantation, water
cooling behind the target is often used to dissipate the heat. The maximal
power densities attainable on target will increase with the next generation of
underground accelerators, either because of higher beam energies at comparable
intensities (such as the MV facility at Gran Sasso), or due to further
increased beam intensities (cf. JUNA Liu et al. (2016)) compared to LUNA 400.
Efforts are underway to adopt and advance techniques from surface experiments,
such as cooling for high-powered targets (Wolfgang Hammer et al. (1986)) or
large-area reaction targets (Chen et al. (2020)), to overcome thermal
limitations on the beam intensity in future underground experiments. Even with
best efforts in cooling, the performance of solid targets degrades under beam,
which is seen for example in a reduction of target thickness or changes in the
target stoichiometry. In the regime of low-energy nuclear astrophysics
experiments, solid targets typically have to be replaced after an irradiation
corresponding to accumulated 100-101 (particle) Coulombs of beam on target.
This is an important practical aspect for the use of massive shielding against
environmental radiation in low-background measurement. Compared to experiments
on surface, where secondary cosmic radiation on shielding materials results in
diminishing returns beyond a certain thickness of shielding, much more massive
shielding setups of lead and copper have been used at LUNA 400 (Caciolli et
al. (2009)), where for experiments with solid targets, easy access to the
target had to be secured (Boeltzig et al. (2018)). More sophisticated, _i. e._
larger and multi-layered, shielding configurations are foreseen in the future,
as a consequence of an improved understanding of the relevant backgrounds and
allowed by the more spacious target station layout at the new MV facility.
Target access requirements will continue to be central in future experiments
with these setups that employ solid targets.

Figure 1: Differential pumping system schematic. The beam comes from the
accelerator on the left, passes through the apertures AP3, AP2 and AP1, enters
the target chamber and stops on the calorimeter.

The effects of target degradation may be avoided, wherever possible, by
choosing targets in gaseous form: a windowless gas target system offers
stability over the long data taking periods, up to several weeks, if needed.
Another advantage is the chemical purity. Solid targets are rarely made by an
element alone: possible changes in the stoichiometry should be continuously
monitored during the running time.

The gas target system presently in use at LUNA-400 accelerator is shown in
Figure 1. It consists of three differential pumping stages, the target
chamber, the gas pipeline and a recycling system (see Figure 1). Three pumping
stages produce a strong pressure gradient between the interaction chamber and
the beamline. A water cooled collimator is placed between adjacent pumping
stages, provides the correct gas flow and determines the pressure drop. The
gas target system can either recycle the gas or let it flow away.

The gas enters the interaction chamber close to the beam stop and flows into
the first pumping stage, where the 99.5% of the gas is pumped away through a
roots pump. Approximately 0.5% of the gas also goes in the second pumping
stage, where it is pumped by three turbo-molecular pumps. A few gas flows in
the third pumping stage through and is pumped away by a turbo-molecular pump.
A roots pump collects the gas from the previous pumps and is itself connected
to the roughing pump or the recycling pump, depending on the running mode.

The target volume, typically 10-40 cm long, is surrounded by the detectors and
is delimited by the chamber walls, the calorimeter and the target chamber
collimator. This latter does not only collimate the beam, but also makes the
pressure decrease steeply towards the first pumping stage.

The ionization of the target gas and the neutralization of the beam prevent
the electrical reading of the beam current and a power compensation
calorimeter with constant temperature gradient is used to monitor the beam
intensity (Ferraro et al. (2018)). For the proper characterization of a
windowless gas target, the density and the detectors efficiency profile along
the beam path must be known. The density profile is usually measured using a
mock-up scattering chamber equipped with measurement ports for capacitive
pressure gauges and thermoresistors. The efficiency profile is, in turn,
measured by moving radioactive sources along the beam line. Another method is
the resonance scan technique: the target system is filled with selected gases
such as ${}^{14}\mathrm{N}$ or ${}^{21}\mathrm{Ne}$ and their narrow, strong
resonances are excited with a proton beam of proper energy. The resonance
position is then moved along the target by changing the beam energy
accordingly. Gas target setups usually ask for heavier detector shielding
systems due to the larger dimensions.

The LUNA laboratory is protected by 1400 meters of dolomite rock from cosmic
ray induced effects. This rock overburden completely suppresses the hadronic
and the soft electromagnetic component of cosmic rays. Muons are able to
penetrate inside the mountain but their flux is mitigated by about six orders
of magnitude when compared with the Earth surface: this makes typically
negligible also muon induced radiations, such as spallation neutrons or
cosmogenic unstable nuclides. Long-lived radioisotopes such as the ones
produced by the natural ${}^{238}\mathrm{U}$ and ${}^{232}\mathrm{Th}$ decay
chains or ${}^{40}\mathrm{K}$ are present in any laboratory and do not depend
on depth, but rather on the radiopurity of rocks, buildings and detector
materials. The induced gamma radiations can be mitigated by a suitable passive
shielding surrounding the target and the detectors, usually consisting of
selected low-background lead and freshly refined electrolytic copper. For the
deep-underground setting of LUNA, a shielding of $15-25$ cm lead with low
${}^{210}\mathrm{Pb}$ content lined at the inside with 5 cm electrolytic
copper has been found to give excellent background capabilities as shown in
Figure 2. Impurities in the detector and target, on the other hand, must be
minimized by proper material selection.

Figure 2: $\gamma$-ray background spectra taken with a Hp-Ge detector in
surface laboratory (red line), at Gran Sasso (blue), and at Gran Sasso with 15
cm lead shield (green).

From the point of view of neutron background, the underground location allows
for a reduction of 3 orders of magnitude with respect to above-ground
measurements (Figure 3) even without any further shielding. To further
increase the sensitivity in view of neutron emitting reactions that are going
to be studied with the MV facility, a deep study devoted to selection material
was performed to reduce intrinsic background of detectors such as
${}^{3}\mathrm{He}$ counters. We remind that a typical counter consists of a
gas-filled tube with a high voltage applied across the anode and cathode: a
neutron passing through the tube will interact with a ${}^{3}\mathrm{He}$ atom
to produce tritium and a proton. These two particles ionize the surrounding
gas atoms to create charges, which in turn ionize other gas atoms in an
avalanche-like multiplication process.

Figure 3: (Colour online) Comparison of neutron background measured by means
of ${}^{3}\mathrm{He}$ counters: the black one is measured in a surface
laboratory. Red and blue spectra are measured in the LNGS underground
laboratory by means of counters with stainless steel and aluminum cases,
respectively.

Indeed, alpha particle decays, coming from impurities of uranium and thorium
in the counter cases, represent the main source of intrinsic background. By
selecting stainless steel cases instead of standard aluminum ones a reduction
of one order of magnitude was achieved as shown in Fig. 3: the blue and the
red spectra were measured in the Gran Sasso with stainless steel and aluminum
counters, respectively. The black spectrum is the background in a surface lab
with a stainless steel counter. As a matter of fact, the new MV facility
together with the extremely low gamma and neutron background achieved by the
LUNA collaboration provide a unique sensitivity to assess the key processes of
post main sequence stellar burning.

##  4 Neutron sources for the s-process

The basic idea of the s-process was born in the ’50s, with the famous paper by
Burbidge et al. (1957). It consists of a series of ”slow” neutron captures and
$\beta$ decays along the neutron-rich side of the valley of stability, close
to the stability line. This process is responsible for the production of about
half of the elemental abundances between iron and bismuth, as stated in
Käppeler et al. (2011a), the other part being produced by the rapid neutron
capture process (r-process) and to a lesser extent by the proton capture
processes.

The s-process takes place in a low neutron flux, where the neutron capture
rate is lower than the $\beta$ decay rate of the resulting unstable nuclei.
Such conditions are satisfied in the helium-burning shell of low-mass
thermally pulsing stars in the asymptotic giant branch (main s-process) or in
the helium-burning core of massive stars in the Red Giant Branch (weak
s-process). The main s-process is mostly responsible for the production of
elements with $90\leq A\leq 209$ (_i. e._ from zirconium to bismuth), while
the weak s-process contributes to elements in the range $56\leq A\leq 90$ (_i.
e._ from iron to zirconium).

It is well established that the
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ reaction
($Q_{\mathrm{value}}=2.216\,\mathrm{MeV}{}$) is the principal neutron source
for the main s-process, while the major neutron source of weak s-process is
the ${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reaction
($Q_{\mathrm{value}}=-0.478\,\mathrm{keV}{}$). The cross section of both these
reactions greatly depends on temperature, the existence of excited states
close to the reaction threshold and the initial abundances of the interacting
species.

###  4.1 The main s-process and the
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ reaction

Käppeler (1999) attributed the formation of the main s-process elements to
thermally pulsing stars in the asymptotic giant branch (TP-AGB) with mass
$1.5\,M_{\odot}<M\leq 3\,M_{\odot}$. More recently, Cristallo et al. (2018)
indicated a slightly broader mass interval, between $1.2$ and $4\,M_{\odot}$.

The structure of TP-AGB stars is organized in the following layers: a carbon
oxygen core, a He-burning shell, a He-rich inter-shell, a H-burning shell and
a H-rich envelope. While the H-burning shell produces helium, the core
contracts and heats up the basis of the He-burning shell, whose energy
production increases. Eventually, the energy produced by the He-burning shell
is not anymore radiated away efficiently and a thermonuclear runaway occurs,
known as ”helium shell flash” or ”thermal pulse”. This translates in an
expansion of the He-rich inter-shell and the cool-down of the H-burning shell,
which extinguishes. Also the He-burning shell is affected by the expansion and
cools down until extinction. A new contraction takes over and causes the
initial re-ignition of the H-burning shell and of the He-burning shell
afterwards, until another thermal pulse occurs. A reservoir of
${}^{13}\mathrm{C}$, produced via the
${}^{12}\mathrm{C}(\mathrm{p},\gamma){}^{13}\mathrm{N}(\beta^{+}\nu){}^{13}\mathrm{C}$
reaction chain, forms the so-called ${}^{13}\mathrm{C}$ pocket at the
interface between the He-rich inter-shell and the H-rich envelope. As of
today, the exact formation mechanism of such a pocket is still debated, as
stated by Cristallo et al. (2018). During this phase, which lasts some
$10^{4}$ years, the ${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$
reaction takes place and provides neutrons for the main s-process.
In the paper by Cristallo et al. (2018), the authors claim that, in the most
metal-rich stellar models with an almost solar composition, a small amount of
${}^{13}\mathrm{C}$ might survive and be engulfed into the convective zone
generated by the incoming thermal pulse. This scenario would affect several
branching points along the s-process path, and excesses of
${}^{60}\mathrm{Fe}$, ${}^{86}\mathrm{Kr}$, ${}^{87}\mathrm{Rb}$ or
${}^{96}\mathrm{Zr}$ are expected compared to the radiative (low neutron
density) ${}^{13}\mathrm{C}$ burst. The unburned ${}^{13}\mathrm{C}$ left at
the end of the interpulse and available to produce neutrons in the subsequent
pulse depends on the rate of the
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ reaction.
The relevant astrophysical temperature for this process is $\sim$ 0.1 GK
corresponding to a Gamow energy window between 140 and 250$\,\mathrm{keV}$.
Indeed, the energy range of interest could be even larger as discussed in the
paper by Kimura and Bonasera (2013), since the S(E) factor is energy
dependent. In Figure 4, the level scheme of
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ nuclear reaction
process is shown. The excited states of interest for AGB nucleosynthesis are
highlighted in green and red.

Figure 4: (Colour online) Schematic diagram adapted from Cristallo et al.
(2018) of the ${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ nuclear
reaction process, together with the competing exit channel
${}^{17}\mathrm{O}+\gamma$. The excited states of interest for AGB
nucleosynthesis are highlighted in green

In particular, green levels are broad states which must be taken into account
for any ${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ cross section
evaluation in the astrophysical region of interest. These are the (1/2)+ near
threshold state and the (3/2)+ at $E_{x}=7239\,\mathrm{keV}{}$.

It is important to mention that the energy level of the near-threshold state
is debated: Ajzenberg-Selove (1986) attributed to this state as a sub-
threshold energy of $E_{x}=-(3\pm 8)\,\mathrm{keV}{}$, while recently a study
by Faestermann et al. (2015) deduced a positive energy value at $E_{x}=(4.7\pm
3)\,\mathrm{keV}{}$.

####  4.1.1 State-of-the-art

A conspicuous number of measurements of the
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ cross section have
been carried out over the past 45 years.

In the following we focus the attention on crucial direct and indirect
measurements performed.

Among direct measurements:

  * •

Drotleff et al. (1993) measured the cross section of the
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ reaction in the
$370-1000$$\,\mathrm{keV}$ energy range with ${}^{3}\mathrm{He}$ proportional
counters embedded in a moderating polyethylene matrix. This is still the
dataset with the lowest point ever measured with a direct measurement. The
low-energy points reveal a S-factor enhancement, possibly due to a $1/2^{+}$
sub-threshold resonance mentioned by Ajzenberg-Selove (1986);

  * •

Brune et al. (1993) used ${}^{3}\mathrm{He}$ counters to measure the
resonances of the ${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$
reaction, at $E_{\alpha}=656$ and $802\,\mathrm{keV}$: the authors concluded
that the resonance strengths for these two states are too weak, compared to
the non-resonant contribution, to affect the stellar reaction rates;

  * •

Harissopulos et al. (2005) measured the
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ reaction absolute
cross section in an energy range $E=0.8-8\,\mathrm{MeV}{}$ in steps of
10$\,\mathrm{keV}$ with a setup similar to Drotleff’s one. The main aim of the
measurement was the geoneutrino background subtraction required by neutrino
experiments such as Borexino and Kamland as explained in the paper by Araki et
al. (2005). An overall uncertainty of 4% was achieved;

  * •

Heil et al. (2008) promoted a new study of the
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ cross section in the
energy range $E=420-900\,\mathrm{keV}$. Heil used a different approach,
employing a n-$\gamma$ converter consisting of a Cd-doped paraffin sphere
surrounded with 42 $\mathrm{BaF}_{2}$ $\gamma$ detectors. In the central hole
a neutron converter was installed. A detailed uncertainties analysis is
described in the paper. The authors recognized as the main source of
systematic error the change of target stoichiometry caused by the build up
during the beam irradiation. At higher energies overall uncertainties could be
reduced to the level of 5%;

  * •

Recent measurements at high energy are due to Febbraro et al. (2020), covering
the same energy range spanned by Harissopulos. They improved the precision and
accuracy by means of a setup sensitive to the neutron energies, measuring also
the excited state transitions via secondary $\gamma$-ray detection. With this
setup, they discriminated neutrons emitted from different energy groups and
they could measure the individual partial cross sections of the
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ reaction to the ground
state and second excited state of the ${}^{16}\mathrm{O}$ final nucleus.

At low energies, uncertainties of direct measurements are larger than 50%:
they are dominated by the low counting statistics caused by unfavorable S/N
ratio.
Moreover, going down in energy, direct measurements face limits of the fast
dropping of the cross section due to the Coulomb barrier and the increase of
the screening effect.

For this reason, complementary indirect studies have been developed to better
constrain the cross section of this neutron source in the relevant energy
region for astrophysics. These measurements were mostly aimed to determine the
spectroscopic factor and/or the asymptotic normalization coefficient (ANC) of
the 1/2+ level of ${}^{17}\mathrm{O}$ near threshold, that represents that
largest source of uncertainty at low energies. Kubono et al. (2003) evaluated
a spectroscopic factor $S_{\alpha}=0.01$, but data were reanalysed by Keeley
et al. (2003) indicating a factor of 40 larger contribution. The ANC method
was approached for the first time in the work by Johnson et al. (2006) that
used the ${}^{6}\mathrm{Li}({}^{13}\mathrm{C},\mathrm{d}){}^{17}\mathrm{O}$
sub Coulomb-transfer reaction. These results were recently revisited in the
paper by Avila et al. (2015).
Other indirect measurements were obtained with the Trojan Horse Method (THM):
in this approach projectiles (or targets) are selected and described as
clusters of two particles in quasi-free kinematics. One is involved in
reaction, while the other constituent cluster, called the spectator nucleus
”s”, is emitted without interacting with the system. For further information
on the method one could see e.g. Tumino, A. et al. (2018). Using this
technique, the
${}^{13}\mathrm{C}({}^{6}\mathrm{Li},\mathrm{n}\,{}^{16}\mathrm{O})\mathrm{d}$
reaction was studied in quasi-free kinematic conditions (the deuteron inside
the ${}^{6}\mathrm{Li}$ beam is considered as a spectator to the three-body
reaction), as described in La Cognata M. et al. (2013). This work covered an
energy range between $-0.3$ and $1.2\,\mathrm{MeV}{}$, and allowed to study
the near-threshold resonance at $E_{x}=6356\,\mathrm{keV}$. In general THM
results need to be normalized to selected direct data and their uncertainty
strongly depends on the choice of the reference direct measurements: in the
first THM analysis by La Cognata M. et al. (2013), data were scaled to the
astrophysical S-factor recommended by Heil et al. in the energy region between
$\sim$ 0.6 and 1.2$\,\mathrm{MeV}$. As a result, a THM S-factor was good in
agreement with the direct ones, but with a squared Coulomb-modified ANC
$(7.7\pm 0.3)\,\mathrm{fm}^{-1}$ not in agreement with independent assessments
of the ANCs, whose weighted average is $(3.9\pm 0.5)\,\mathrm{fm}^{-1}$. After
the new evaluation of the near-threshold resonance energy Faestermann et al.
(2015), setting its center at $4.7\,\mathrm{keV}{}$ above the
${}^{13}\mathrm{C}$–$\alpha$ threshold, data by THM where re-analyzed by O.
Trippella and M. La Cognata (2017) normalizing experimental data with respect
to the ANC parameter of the threshold resonance obtained by Avila et al.
(2015). Trippella obtained an ANC value of $(3.6\pm 0.7\,\mathrm{fm}{}^{-1})$,
in agreement with literature.
Data from most recent works (direct and indirect methods) are showed in Figure
5.

Figure 5: (Colour online) Selection of most recent
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ measurements. Among
the direct measurements the Drotleff and the Heil data are represented,
indicated by black triangles and red triangles, respectively. The solid red
curve indicates the R matrix extrapolation by Heil. The most recent indirect
measurement by THM by Trippella et al is indicated by the green squared area
and the central value is the green curve. In the plot the Gamow window for two
different stellar scenarios are drawn.

Both from direct measurements (high uncertainties at low energy and a large
scatter in absolute values among datasets) and from indirect measurements
(e.g. discrepancy in the spectroscopic factor evaluation, uncertain
normalization of THM) there is a clear indication that more direct data with
about 10$\%$ overall uncertainty are mandatory both at low and at high energy.

####  4.1.2 The LUNA direct measurement

Taking advantage from the low environmental background of LNGS and the highly
intense and stable alpha beam provided by the LUNA 400 accelerator, recently
the LUNA collaboration put huge efforts in the measurement of the
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ cross section at low
energy with the goal to reach an overall uncertainty near 10%. A detector
based on 18 ${}^{3}\mathrm{He}$ counters arranged in a polyethylene moderator
have been developed in order to maximise its efficiency. ${}^{13}\mathrm{C}$
targets used during the measurement at LUNA have been produced evaporating 99%
${}^{13}\mathrm{C}$ isotopically enriched powder on tantalum backing using the
evaporator installed at the nuclear institute of research Atomki (Debrecen,
Hungary). Hereby, the key points of the LUNA experiment are summarized. As
already said before, the installation of the accelerator in the LNGS
underground laboratory allows a neutron background reduction of 3 orders of
magnitude with respect to above-ground measurements. Moreover, a special
attention was paid to reduce the $\alpha$ particle intrinsic background from
detectors.
A further step for the background reduction was performed acquiring with Caen
V1724 digitizers raw preamplifier signals from detectors and rejecting alpha
signals with a pulse shape discrimination analysis described in the paper by
Balibrea-Correa et al. (2018). This allowed to reach an overall background in
the whole detector of about 1 count/h, 2 orders of magnitude lower than
previous experiments performed in surface laboratories as described in the
paper by Csedreki et al. (2019).
Possible beam induced background sources were investigated shooting alpha beam
on blank tantalum backings. The neutron detection rate was compatible with the
background measurement, making negligible the in-beam backgound.
The degradation monitoring under intense alpha beam is crucial during the
cross section measurement performed at LUNA. The well-known NRRA (Nuclear
Resonant Reaction Analysis) technique is not applicable, due to the lack of
resonances in the dynamic energy range of the accelerator. For this reason a
new method of analysis was developed.
Data taking at LUNA consisted in long $\alpha$-beam runs with accumulated
charges of $\approx 1\,\mathrm{C}$ per run, interspersed by short proton-beam
runs with moderator opened and HPGe detector in close geometry, with typical
accumulated charges of $0.2\,\mathrm{C}{}$ at most. During the last mentioned
proton run, the target degradation can be checked perfoming a gamma shape
analysis on the direct capture de-excitation to the ground state peak of
${}^{13}\mathrm{C}(\mathrm{p},\gamma){}^{14}\mathrm{N}$ reaction with the HPGe
detector.
Further information and details can be found in the paper by Ciani, G. F. et
al. (2020).
Thanks to the unprecedented background reduction for this kind of direct
measurement and the novel approach to monitor target degradation, it was
possible to measure experimental yield of the
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ reaction in an energy
range between 400$\,\mathrm{keV}$ down to 305$\,\mathrm{keV}$ in laboratory
system energy, 40$\,\mathrm{keV}$ lower than data in the literature: for the
first time LUNA collaboration measured with a direct technique cross section
inside the Gamow window reaching unprecedented overall uncertainty ($<20\%$).
Final results and astrophysical implication will be published within the end
of 2020.
The LUNA collaboration is planning to extend the measurement of the
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ at higher energies at
the new MV facility in the LNGS laboratory. This will give the unique
possibility to provide a complete data set over a wide energy range and to
avoid re-normalization to other datasets with unknown systematic
uncertainties.

###  4.2 The weak s-process and the
${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reaction

About half of the elements between iron and yttrium ($56\lesssim A\lesssim
90$) are produced via the weak s-process in massive stars with initial mass
$M>8M_{\odot}$ (Käppeler et al. (2011b)). In such stars, ${}^{22}\mathrm{Ne}$
is a by-product of He-burning starting from preexisting CNO isotopes.

The reaction ${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ has a
negative Q-value of $-478\,\mathrm{keV}$, and requires relatively high
temperatures to be ignited. At the base of the convective envelope around the
He core of massive stars, the temperature is sufficiently high ($>$ 0.25 GK)
to make this reaction a relevant source of neutrons for the weak s-process
until core He-burning extinguishes (Peters (1968); Couch et al. (1974); Lamb
et al. (1977); Prantzos et al. (1990); Raiteri et al. (1991a)) . Its
effectiveness as a neutron source, though, depends also on the cross section
of the competing reaction, the
${}^{22}\mathrm{Ne}(\alpha,\gamma){}^{26}\mathrm{Mg}$.

When core He-burning runs out, ${}^{22}\mathrm{Ne}$ is still rather abundant
(about 1% in mass as claimed in paper by Pignatari et al. (2010)) and the
reaction ${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ is
reactivated during shell C-burning (Raiteri et al. (1991b)) at a temperature
of about 1 GK. At this stage, the
${}^{12}\mathrm{C}({}^{12}\mathrm{C},\alpha){}^{20}\mathrm{Ne}$ process yields
$\alpha$ particles (Arnett and Truran (1969)) and even larger neutron fluxes
are provided as a consequence of the higher temperature.

Besides the broad interest as main neutron source in the weak s-process, it is
worth mentioning some contribution also to the main s-process in low mass
($M<3M_{\odot}$) AGB stars, during thermal pulses (Gallino et al. (1988);
Hollowell and Iben (1988)), and in intermediate mass
($4M_{\odot}<M<8M_{\odot}$) AGB stars (Bisterzo et al. (2014, 2015)), whereas
predicted abundances of ${}^{86}\mathrm{Kr}$, ${}^{87}\mathrm{Rb}$ and
${}^{96}\mathrm{Zr}$ are at variance with observations (Lugaro et al. (2003);
Garcia-Hernandez et al. (2006); Garcia-Hernandez, D. A. et al. (2007); Garcia-
Hernandez et al. (2009); van Raai, M. A. et al. (2012)).

####  4.2.1 State-of-the-art

Considering the weak s-process during core He-burning, the low-energy part of
the Gamow window of the
${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reaction extends
down to the boundary of the $(\alpha,\mathrm{n})$ threshold, located at
$E_{\alpha,\mathrm{lab}}=575\,\mathrm{keV}$. At such low energies,
measurements have so far suffered from low signal and high background,
especially because of the small cross section. For this reason, different
groups only succeeded to directly study the resonances down to
$E_{\alpha,\mathrm{lab}}=830\,\mathrm{keV}$. Other attempts to study the
resonances at lower energies by means of indirect methods, often obtained
inconsistent results. In the following we summarize the most relevant direct
studies of this reaction.

Figure 6: A subset of the previous measurements of the
${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reaction cross
section. Data retrieved from the EXFOR database version of October 8, 2020.
Blue circles are upper limits.

Back in the ’60s, Ashery (1969) discovered that it proceeds through many
resonances in the compound nucleus. Other experimental studies at about
1$\,\mathrm{MeV}$ and above are due to Haas and Bair (1973), Mak et al. (1974)
and Wolke et al. (1989).

Harms et al. (1991) investigated the energy range between
$E_{\alpha,\mathrm{lab}}=0.73$ and 2.10$\,\mathrm{MeV}$ with a windowless,
recirculating gas target system and two ${}^{3}\mathrm{He}$ ionization
chambers in close geometry. The resonance at
$E_{\alpha,\mathrm{lab}}=830\,\mathrm{keV}$ was clearly detected but it was
not possible to show the existence of resonances at lower energies. Soon
after, Drotleff et al. (1993) explored a lower energy range using the same gas
target and an improved 4$\pi$ detector including two concentric circles of
eight ${}^{3}\mathrm{He}$ counters in a polyethylene moderator. Despite of the
improved sensitivity, no new low energy resonances were observed in this
experiment.

Giesen et al. (1993) performed a direct measurement with implanted
${}^{22}\mathrm{Ne}$ targets to search for low-energy resonances. The
background from ${}^{11}\mathrm{B}(\alpha,\mathrm{n}){}^{14}\mathrm{N}$,
however, limited the sensitivity at lower energies. At the same time they
investigated the excited levels with natural parity in ${}^{26}\mathrm{Mg}$
thanks to an indirect technique, the $\alpha$-transfer.

Later, Jaeger et al. (2001) developed a new detector with twelve
${}^{3}\mathrm{He}$ counters arranged in an optimized geometry. This upgrade
allowed to achieve a sensitivity of $\sim$ 10 pb and to constrain the strength
of the $E_{\alpha,\mathrm{lab}}=830\,\mathrm{keV}$ resonance to
$\omega\gamma=(118\pm 11)\,\mathrm{\mu{}eV}$. The upper limit on the tentative
resonance at $E_{\alpha,\mathrm{lab}}=633\,\mathrm{keV}$ was significantly
lowered. Based on these results, Jaeger et al. (2001) calculated the reaction
rate under the assumption that the strength of the hypothetical resonance at
$E_{\alpha,\mathrm{lab}}=633\,\mathrm{keV}$ was at 10% of its observed upper
limit. However, the occurrence of such a resonance was ruled out by Longland
et al. (2009), who demonstrated that the corresponding excited state at
$E_{x}=11150\,\mathrm{keV}$ in ${}^{26}\mathrm{Mg}$ has unnatural parity.

At that time it was clear that only a very low-background setup in an
underground laboratory could have made possible a direct investigation of the
resonances at lower energies.

The focus then moved to the evaluation of the reaction rate and its
implications, mostly using direct cross sections measurements at relatively
high energy and indirect data.

Longland et al. (2012) used a sophisticated statistical approach to calculate
the ${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reaction rate,
including a careful treatment of the uncertainties. This led to a reduction of
the uncertainties on calculated rates and raised the need for new, more
precise and more sensitive measurements.

Bisterzo et al. (2015) estimated the impact of the
${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ uncertainty on the
isotopic abundances close to and within the branching of the s-path for main
s-process. They provided a new evaluation of the reaction rate that was a
factor of 2 higher than Longland et al. (2012). Even if this new rate was
still able to reproduce the contribution of s-only isotopes from the main
s-process within the solar uncertainties, Bisterzo et al. (2015) underlined
how a sizeable change could be caused by low-energy resonances.

In the following years several indirect studies attempted to improve the
knowledge of this reaction. A new experimental investigation by Talwar et al.
(2016) used $\alpha$ inelastic scattering to identify the important resonances
and the $\alpha$ transfer technique to indirectly measure their width. The
resulting ${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reaction
rate was close to the rate in Longland et al. (2012). Soon after, Massimi et
al. (2017) studied neutron capture reactions on ${}^{25}\mathrm{Mg}$ observing
several excited states of ${}^{26}\mathrm{Mg}$ and in particular at
$E_{x}=11.112\,\mathrm{MeV}$. In the same paper an R-matrix analysis was
developed to assign spin and parity values to the excited states in
${}^{26}\mathrm{Mg}$ without ambiguity and to calculate the upper limits on
the reaction rates of the
${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ and
${}^{22}\mathrm{Ne}(\alpha,\gamma){}^{26}\mathrm{Mg}$ reactions. In the same
work, Massimi et al. (2017) studied the impact of these new rates on the
evolution of stars with initial mass $M$ between 2 and $25M_{\odot}$. It was
observed that for a $25M_{\odot}$ star, the uncertainty of the
${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reaction rate was
responsible for large differences in the weak s-process abundances, up to a
factor of 50 in the Sr region. Noticeable changes were also found in
intermediate-mass AGB models (IMS-AGBs, $3<M/M_{\odot}<7$) with an increase of
$\sim 50\%$ in the abundances of Y and La.

The continued interest to this reaction is demonstrated by two very recent
experimental studies by Ota et al. (2020) and Jayatissa et al. (2020) with
$\alpha$ transfer reactions: Ota et al. (2020) studied the
${}^{22}\mathrm{Ne}({}^{6}\mathrm{Li},\mathrm{d}){}^{26}\mathrm{Mg}$ in
inverse kinematics, detecting outgoing deuterons and ${}^{25,26}\mathrm{Mg}$
in coincidence. In addition Jayatissa et al. (2020) studied the
${}^{22}\mathrm{Ne}({}^{7}\mathrm{Li},\mathrm{t}){}^{26}\mathrm{Mg}$ reaction.

The new evaluation of the reaction rate, based on spin-parity assignments by
Jayatissa et al. (2020) combined with data from Ota et al. (2020), resulted in
lower rates than previous evaluations, especially at low temperatures (see
Figure 7). The lower rate is also the result of excluding an excited state at
$E_{x}=11.112\,\mathrm{MeV}$, corresponding to
$E_{\alpha,\mathrm{lab}}=598\,\mathrm{keV}$, observed by Massimi et al. (2017)
and not observed in these studies.

In conclusion the thermonuclear reaction rate of this reaction is still
largely uncertain: several evaluations are present in the literature (see
Figure 7), based on theoretical considerations, direct and indirect
measurements, differing up to a factor of 5 in the temperature range relevant
to the s-process in core He burning.

Figure 7: A subset of the
${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reaction rate
evaluations, relative to Longland et al. (2012). Solid lines refer to the
evaluations reported in the JINA REACLIB database (Cyburt et al. (2010). In
particular: cf88=Caughlan and Fowler (1988), nacr=Angulo et al. (1999),
rath=Rauscher and Thielemann (2000), ths8=Cyburt et al. (2010), il10=Iliadis
et al. (2010), trc8=REFIT:Cyburt et al. (2010), li12=Longland et al. (2012).
Dashed lines: jae01=Jaeger et al. (2001), ota20=Ota et al. (2020).

The presence of low-energy resonances in the
${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reaction below
$E_{\alpha,\mathrm{lab}}=830\,\mathrm{keV}$ are expected, based on known
levels in ${}^{26}\mathrm{Mg}$, but no such resonances have been directly
observed, yet. Nevertheless they might contribute significantly to the
reaction rate around 0.2 GK and cause sizeable changes in the prediction of
weak s-process abundances.

The direct measurement of the
${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reaction cross
section will be carried out at the new MV facility at LNGS (Guglielmetti
(2014); Prati (2019)), using a windowless gas target (see Fig. 1) of enriched
${}^{22}\mathrm{Ne}$. Such experiment could provide precise and accurate cross
section measurements down to about $E_{\alpha,\mathrm{lab}}\sim
600\,\mathrm{keV}$. Most of the background is expected to be due to the
${}^{11}\mathrm{B}(\alpha,\mathrm{n}){}^{14}\mathrm{N}$ reaction, as already
reported by past experiments and therefore a proper reduction of contaminants
poses a crucial challenge, combined with the development of an optimized
detector setup.

SHADES (Scintillator-He3 Array for Deep underground Experiments on the
S-process) is an ERC starting grant (Grant agreement ID: 852016), recently
awarded to realize a new setup for the measurement of the
${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reaction at energies
of astrophysical interest. SHADES includes the development of a novel neutron
detector and a gas target to be used at LUNA. The detector combines an array
of ${}^{3}\mathrm{He}$ counters with their high detection efficiency and
liquid scintillators, which act as moderators for the reaction neutrons while
at the same time providing information on the neutron energy. The combination
of ${}^{3}\mathrm{He}$ tubes and scintillator, together with recently studied
signal processing techniques, see Balibrea-Correa et al. (2018), will be able
to limit backgrounds from external and internal sources as well as beam-
induced background to acceptable levels. The new detector will allow an
increase of at least two orders of magnitude in sensitivity, allowing for the
first time a measurement of the reaction cross section in the energy range
relevant to the s-process in core He burning.

##  5 The ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction

The reaction ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ competes with
the so-called triple-$\alpha$ process
(${}^{4}\mathrm{He}+{}^{4}\mathrm{He}\to{}^{8}\mathrm{Be}$ followed by
${}^{4}\mathrm{He}+{}^{8}\mathrm{Be}\to{}^{12}\mathrm{C}$) during stellar
helium burning (Burbidge et al. (1957)). The astrophysical rates of both
reactions influence the ratio of ${}^{12}\mathrm{C}$/${}^{16}\mathrm{O}$
produced during the helium burning phase, which in turn determines following
steps of stellar evolution. Due to the central role of these nuclides,
understanding their ratio in helium burning has been identified as a problem
of “paramount importance” Fowler (1984) for nuclear astrophysics. Compared to
the triple-$\alpha$ process, the cross section of
${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ is significantly less
well-known and, in spite of extensive experimental efforts, a better
understanding of this reaction remains desirable. A recent comprehensive
review on the state of understanding
${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ can be found in deBoer et
al. (2017).

Owing to the sharp drop of the charged particle reaction cross sections
towards the energy regions relevant for astrophysics, direct measurements in
the energy region of interest are not available, making extrapolations
necessary. Such extrapolations are challenging due to the nuclear structure of
the compound nucleus ${}^{16}\mathrm{O}$: the cross section in the energy
range of interest is characterized by the presence of broad resonances
(including sub-threshold states). It is crucial to study the interference
between states of the same Jπ, but also to account for angular effects from
the interference of processes with different $J^{\pi}$ (as outlined in deBoer
et al. (2017)). In particular, the E1 and E2 components of capture to the
ground state are of comparable strength in the energy range of interest, and
the extrapolated cross section is very sensitive to the interference of these
two components.

Different experimental approaches have been taken to directly study the
${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction: in normal
kinematics, a fixed ${}^{12}\mathrm{C}$ target (solid or gaseous) is bombarded
by $\alpha$ particles, detecting $\gamma$-rays from the reaction; inverse
kinematics employs a ${}^{12}\mathrm{C}$ beam impinging on a helium target.
Inverse kinematics experiments have been performed as measurements of the
$\gamma$-rays from the reaction, or detecting the ${}^{16}\mathrm{O}$ nuclei
in a recoil separator (Kremer et al. (1988); Schürmann et al. (2005); Matei et
al. (2006); Schürmann et al. (2011)). Studies of the inverse reaction
${}^{16}\mathrm{O}(\gamma_{0},\mathrm{p}){}^{12}\mathrm{C}$ at high-intensity
$\gamma$-ray facilities allow to infer information on the ground state
transitions. Other reactions to study the nuclear structure of
${}^{16}\mathrm{O}$ are used to constrain extrapolations of the reaction
${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ in frameworks such as _R_
-matrix theory. deBoer et al. (2017).

When measuring the $\gamma$-rays from reaction, angular distribution
measurements at multiple detector angles yield information to disentangle the
E1 and E2 components, whilst a total absorption spectroscopy setup, detecting
the total $\gamma$-ray energy, yields the total cross section with a large
detection efficiency. Figure 8 summarizes the current situation of direct
measurements, showing recent direct measurements of this reaction at low
energies for illustration. These measurements extend down to about 0.9 MeV
center of mass energy, but are characterized by increasing uncertainties when
approaching these low energies. As the cross section drops rapidly towards
these energies, backgrounds – environmental and beam-induced – are
increasingly relevant. For example experiments in normal kinematics are
affected by backgrounds from the reaction
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$, which has a cross
section that is of the order of $10^{6}$ times that of
${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$. Neutrons can produce
background signals directly in the detector, or through secondary radiation in
the environment of the detector. This background can be reduced by using
${}^{12}\mathrm{C}$ targets depleted in ${}^{13}\mathrm{C}$, or with the help
of bunched beams that allow to disentangle the prompt $\gamma$-ray signal from
neutron-induced backgrounds by time-of-flight.

Figure 8: Overview of recent experimental data (Kunz et al. (2001); Fey
(2004); Assunção et al. (2006); Makii et al. (2009); Plag et al. (2012)) for
the ground state capture in
${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$, with the results of
R-matrix fits from deBoer et al. (2017) for comparison. All data is unscaled.
The location of the Gamow window for a stellar temperature of 0.3 GK is shown
for reference.

Additional data at lower energies is desirable to better constrain the energy-
dependence of the extrapolation, and further experiments will aim to shed
light on it in the future. Direct measurements are expected to contribute to
this effort by pushing the lower limit for the available cross section data
further below 1 MeV center of mass energy. This includes promising
measurements with a recoil mass separator Fujita et al. (2015). On the side of
the new underground accelerator facilities, new exciting opportunities for the
study of this reaction will become available shortly. Measurements of
${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ are among the scientific
goals of the new MV facility at LNGS and the Felsenkeller shallow-underground
accelerator laboratory for nuclear astrophysics, Bemmerer et al. (2018). Both
accelerators will not only provide beams of $\alpha$ particles, but also of
carbon ions, allowing for underground measurements of this reaction in inverse
kinematics. The scientific program of JUNA at JPL, as outlined in Liu (2017),
includes the study of ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ as
well. To take full advantage of the high-intensity $\alpha$ beam and the deep
underground location of JUNA, the minimization of beam-induced backgrounds,
such as those created on ${}^{13}\mathrm{C}$, has been identified as crucial.

##  6  The ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reaction

At the end of the core helium burning, the central part of the star becomes
more massive, contracts and heats up. The contraction and the possible
consequent collapse can be halted by the ignition of carbon burning or by the
pressure of degenerate electrons. There are several factors preventing the
ignition temperature for carbon burning is reached prior to electron
degeneracy. For instance, plasma neutrinos are produced near the center of the
star and they cause a decrease of the central temperature while leaving it. In
addition, in the case of intermediate mass stars, the second dredge-up further
reduces the temperature of the star core, with the convective envelope
penetrating into the H-exhausted shell. Depending on the star mass, it may
attain the physical condition for C burning or become a carbon-oxygen white
dwarf. The minimum initial mass of a star able to experience a C-burning phase
is called $M_{\rm up}$. The value of $M_{\rm up}$ was proposed for the first
time by Becker and Iben (1980) who found $M_{\rm up}=9M_{\odot}$ for a star
with nearly solar composition. However, there are many uncertainties: those
affecting the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ and
${}^{12}\mathrm{C}+\alpha$ rates are the most important nuclear ones. As a
matter of fact, the value of $M_{\rm up}$ separates the progenitors of C-O
white dwarfs, novae and type Ia supernovae, from those of core-collapse
supernovae, neutron stars and stellar mass black holes. Finally, if the star
mass is slightly higher than $M_{\rm up}$, an off-center carbon ignition takes
place in degenerate conditions and the star may end its life as a O-Ne white
dwarf.

Stellar models predict that carbon burning, triggered by the
${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$, occurs for center of mass energies
between 0.9 and 3.4$\,\mathrm{MeV}$. The reaction can proceed through
different channels corresponding to the emission of a photon, a neutron, a
proton, one or two $\alpha$ particles or a ${}^{8}\mathrm{Be}$ nucleus. Among
these channels, the two most relevant are the
${}^{12}\mathrm{C}({}^{12}\mathrm{C},\mathrm{p}{}){}^{23}\mathrm{Na}$ and
${}^{12}\mathrm{C}({}^{12}\mathrm{C},\alpha){}^{20}\mathrm{Ne}$; alpha
particles can produce neutrons through
${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ and
${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ reactions. These
neutrons are fundamental for the synthesis of elements heavier than Fe through
the s-process.

The ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reaction rate at center of mass
energies $\approx 1.5\,\mathrm{MeV}{}$ also affects the physical conditions in
the SNIA explosion. In particular, carbon burning can be ignited in explosive
condition when material is accreted on the surface of a white dwarf in a close
binary system Bravo et al. (2011). A variation in the rate would modify the
extension of the convective core prior to the explosion, the degree of
neutronization and the temperature at the beginning of the thermonuclear
runaway. The knowledge of SNIA is fundamental in cosmology since these systems
allow the measurements of distances and of the expansion rate of high redshift
galaxies Tutusaus et al. (2019).

Unfortunately the Gamow window of the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$
reaction, $0.7-3.4\,\mathrm{MeV}{}$ depending on the astrophysical scenario,
is much lower than the height of the Coulomb barrier, $6.7\,\mathrm{MeV}{}$
approximately, making the direct measurement of the cross section extremely
difficult.

###  6.1 State-of-the-art

The two most relevant channels in the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$
reaction are the emission of protons and $\alpha$ particles, with a Q-value of
$2.24\,\mathrm{MeV}{}$ and $4.62\,\mathrm{MeV}{}$, respectively. The proton
and alpha channels can be measured either by detecting the charged particles
or the gamma decay. In particular, the largest branching is for the
dexcitation of the first excited state to the ground state of the
${}^{23}\mathrm{Na}$ or ${}^{20}\mathrm{Ne}$. Above 2 MeV, the first excited
state transition to the ground state accounts for approximately 50% of the
total cross section and produces photons of 440$\,\mathrm{keV}$ and
1634$\,\mathrm{keV}$ in the case of proton or alpha emission, respectively.

The challenge in obtaining a reliable measurement of the
${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ cross section at low energies, is
related to its exponentially falling behaviour which produces a very low
counting rate; in this scenario any natural or beam-induced background can
seriously affect the measurement. The latter is due to impurities in the
carbon target, manly hydrogen and deuterium, because they can form bonds with
carbon. The main background related to the gamma measurements comes from the
${}^{2}\mathrm{H}({}^{12}\mathrm{C},\mathrm{p}_{1}\gamma){}^{13}\mathrm{C}$
and ${}^{1}\mathrm{H}({}^{12}\mathrm{C},\gamma){}^{13}\mathrm{N}$ reactions,
as detailed in the experimental work by Spillane et al.. The Compton
background of the primary peaks could completely dominate the carbon fusion
$\gamma$-ray peaks Spillane et al. (2007). As far as the particle measurements
are concerned, it is kinematically impossible to find protons in the carbon
fusion region of interest, if the particle detectors are placed at backward
angles.

In the following the most recent papers focused on the
${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ cross section measurement at low
energies are summarized.

Jiang et al. (2018) have recently measured the
${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion cross section in the energy range
$2.5-5\,\mathrm{MeV}{}$. The authors studied the two main channels:
${}^{12}\mathrm{C}({}^{12}\mathrm{C},\mathrm{p}{}){}^{23}\mathrm{Na}$ and
${}^{12}\mathrm{C}({}^{12}\mathrm{C},\alpha){}^{20}\mathrm{Ne}$ at Argonne
National Laboratory using a Gammasphere array of 100 Compton-suppressed Ge
spectrometers in coincidence with silicon detectors. The measurement was
pushed down to $2.84\,\mathrm{MeV}{}$ and $2.96\,\mathrm{MeV}{}$ for the p and
$\alpha$ channels, respectively; the results are in good agreement with other
measurements using $\gamma$ Spillane et al. (2007) and charged particle
detection Zickefoose et al. (2018), but with smaller uncertainties.

Tumino et al. (2018) measured the cross section of the
${}^{12}\mathrm{C}({}^{12}\mathrm{C},\mathrm{p}{}){}^{23}\mathrm{Na}$ and
${}^{12}\mathrm{C}({}^{12}\mathrm{C},\alpha){}^{20}\mathrm{Ne}$ reactions
through the indirect Trojan Horse Method (THM). A $30\,\mathrm{MeV}{}$ beam
was delivered on a natural carbon target; charged particles were detected
through $\Delta$E-E position sensitive silicon detectors. The THM results for
$\alpha$ and p channels are in good agreement with direct data except for the
$2.14\,\mathrm{MeV}{}$ region, where the claim of a strong resonance by
previous works Spillane et al. (2007) is not confirmed. Instead the indirect
data show a resonance at $2.095\,\mathrm{MeV}{}$, one order of magnitude less
intense with respect to the $2.14\,\mathrm{MeV}{}$ resonance found by Spillane
in the ${}^{20}\mathrm{Ne}+\alpha$ channel and of similar intensity in the
${}^{23}\mathrm{Na}+\mathrm{p}{}$ one. In addition, several low-energy
resonances are evident below $1.5\,\mathrm{MeV}{}$, never detected before in a
direct measurement. The results of the THM raised some criticism
Mukhamedzhanov et al. (2019) mainly because of the neglected Coulomb
interaction between ${}^{2}\mathrm{H}$, the spectator nucleus in the THM, and
${}^{24}\mathrm{Mg}$.

The ${}^{12}\mathrm{C}({}^{12}\mathrm{C},\mathrm{p}{}){}^{23}\mathrm{Na}$ has
also been measured by Zickefoose et al. (2018) in the $2-4\,\mathrm{MeV}{}$
energy range by particle spectroscopy. The beam, provided by the tandem
accelerator of the Center for Isotopic Research on the Cultural and
Environmental (CIRCE) heritage, was sent onto highly ordered pyrolytic
graphite targets; protons were detected through $\Delta$E-E silicon detectors.
The total S-factor, including also the contribution of the $\alpha$ channel,
has been obtained using the ratio between the p-channel and total S-factor
provided by Becker et al. (1981). Due to the poor statistics and beam induced
background problems, this work needs a further experimental effort to improve
the knowledge of the total S-factor in the relevant energy range. For this
reason the experimental campaign continued with a new study devoted to the
reduction of light species contaminant, especially ${}^{1}\mathrm{H}$ and
${}^{2}\mathrm{H}$ in the carbon targets Morales-Gallegos et al. (2018).
Measurements were done with natural graphite and highly ordered pyrolytic
graphite targets. ${}^{1}\mathrm{H}$ and ${}^{2}\mathrm{H}$ content were
reduced up to 70-85% by means of diffusion at high temperatures (higher than
$1000{}^{\circ}\mathrm{C}{}$). A further reduction of a factor of 2.5 was
obtained enclosing the scattering chamber in dry nitrogen to minimize leaks
into the rest gas within the chamber. The bulk contamination finally achieved
by the authors is 0.3 ppm. Further measurements are planned with the new
experimental setup.

An upper limit on the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ S-factor has been
recently suggested from the measurement of the
${}^{12}\mathrm{C}+{}^{13}\mathrm{C}$ reaction by Zhang et al. (2020); in fact
it has been observed that the ${}^{12}\mathrm{C}+{}^{13}\mathrm{C}$ and
${}^{13}\mathrm{C}+{}^{13}\mathrm{C}$ cross sections at energies below and
above the Coulomb barrier are upper bounds of the non-resonant contribution of
the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ cross section. The measurement of
the ${}^{13}\mathrm{C}+{}^{13}\mathrm{C}$ reaction was performed by studying
the ${}^{12}\mathrm{C}({}^{13}\mathrm{C},\mathrm{p}{}){}^{24}\mathrm{Na}$
channel; ${}^{24}\mathrm{Na}$ has an half life of 15.0 hours, allowing an
activation measurement. The resulting upper limit on the
${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ S-factor agrees nicely with available
direct experimental data down to $\approx 2.5\,\mathrm{MeV}{}$, while for
lower energies the THM results are significantly higher compared to the Zhang
upper limit. However, this result should be taken with caution considering
that the obtained upper limit is only valid for the non-resonant component of
the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ cross section. Recent theoretical
calculations of the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ sub-barrier fusion
cross section highlighting the role of resonances can be found in Bonasera and
Natowitz (2020).

Another step forward in the knowledge of the
${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ rate has been recently moved by Fruet et
al. (2020). They performed a direct measurement down to $\approx
2.2\,\mathrm{MeV}{}$ using the particle-gamma coincidence technique. The
experiment was performed at the Andromede accelerator facility at IPN Orsay,
France with a ${}^{12}\mathrm{C}$ beam, maximum beam current of 2 p$\mu$A for
astrophysically relevant energies, impinging on a natural carbon target.
Charged particles were detected through three annular silicon strip detectors
covering 30% of the total solid angle. For gamma-ray detection, an array of
LaBr3(Ce) scintillator detectors has been employed. The results are in good
agreement with the data reported by Jiang et al. (2018) and with Tumino et al.
(2018). However, a more prominent resonance has been observed around
$3.8\,\mathrm{MeV}{}$ compared to other measurements ( Spillane et al. (2007);
Zickefoose et al. (2018)).

The most recent measurement of the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ cross
section has been performed by Tan et al. (2020) at the University of Notre
Dame. The simultaneous detection of protons and alphas, through a silicon
detector array, and $\gamma$-rays with a 109% HPGe detector, allowed for
particle-$\gamma$ coincidence technique. The S-factor upper limit at
$2.2\,\mathrm{MeV}{}$ for proton (p1) and alpha ($\alpha_{1}$) channels are
lower than THM data. We note that the upper limit for the proton channel
disagrees significantly with the recent measurement of Fruet et al. (2020).
The discrepancy is less evident, but still present, for the alpha channel. In
the energy region between $2.5$ and $3\,\mathrm{MeV}{}$, there is some tension
between the results of Tan et al. (2020) and previous measurements Jiang et
al. (2018) both for proton and alpha channel. The S-factor results at center
of mass energies above $4\,\mathrm{MeV}{}$ agree nicely with other data.

A comparison between the total S-factor values obtained by Spillane et al.
(2007), Jiang et al. (2018), Tumino et al. (2018), Fruet et al. (2020) and Tan
et al. (2020) is shown in Figure 9. It should be underlined that Tumino et al.
(2018) data are normalized to direct measurements, so a difference in the
absolute value of the S factor can also be attributed to systematic errors
affecting direct data. Significant discrepancies between the results of the
reported experiments are evident in whole energy range and, for this reason, a
further experimental effort is needed.

Figure 9: S-factor values obtained by Spillane et al. (2007), Jiang et al.
(2018), Tumino et al. (2018), Fruet et al. (2020) and Tan et al. (2020)

###  6.2 The measurement in an underground laboratory

An underground location such as the one of the LUNA experiment is the perfect
environment to perform the measurement of the
${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ cross section detecting $\gamma$-rays
emitted in the decay of the ${}^{23}\mathrm{Na}$ and ${}^{20}\mathrm{Ne}$
excited states. A high-efficiency and ultra-low intrinsic background germanium
detector (HPGe) is suitable for the measurement in combination with a massive
lead shielding to avoid the contribution of the low-energy gamma-rays coming
from the decay of the ${}^{238}\mathrm{U}$ and ${}^{232}\mathrm{Th}$ chains.
In figure 10 the counting rate, expressed in counts per day, is reported as a
function of the interaction energy. To calculate the rate, the S-factor
provided by Spillane et al. (2007) has been adopted, considering that the
decay of the first excited state to the ground state accounts for $\approx$
50% of the total cross section and produces photons of 440$\,\mathrm{keV}$ and
1634$\,\mathrm{keV}$ in the case of proton or alpha emission, respectively. It
is evident that if the trend of the S-factor observed by Tumino et al. (2018)
is confirmed the reaction rates can be higher by 1-3 order of magnitude. The
two horizontal lines represent a typical rate of $\gamma$ background measured
at LNGS with a shielded setup Caciolli et al. (2009) (blue and red line for
440$\,\mathrm{keV}$ and 1636$\,\mathrm{keV}$ $\gamma$ energies, respectively).
In particular for the proton channel, crucial issues are the choice of the
materials to limit the intrinsic contaminants and a proper detectors
shielding. In addition, constant nitrogen fluxing around the setup could help
to further reduce the background, avoiding radon contaminants. The
$\gamma$-detection efficiency adopted in the calculation is just a standard
value, new high efficiency setups will be developed for the future
measurements. From a rough estimation considering the data provided by
Spillane et al. (2007) and the setup described in Figure 10, we can say that
the dominant contribution to the background for the proton channel will come
from the environmental radioactivity if a 0.3 ppm H contamination level is
achieved in the targets (Morales-Gallegos et al. (2018)) making the induced
background not an issue at least down to $\sim$ 2 MeV. The limitation in the
alpha channel, is conversely related to the low rate.  To provide the total
cross section, the measurement of the charged particle channels is also
needed. In this case the advantage of the underground location is less evident
but still present; in fact secondary particles produced by the passage of
cosmic rays through the detectors could contribute to the background and they
are effectively reduced at LNGS (Bruno et al. (2015)).

Figure 10: Counting rate, in counts per day, obtained considering data
provided by Spillane et al. (2007), a $\gamma$ detection efficiency of 6% and
2% for 440$\,\mathrm{keV}$ and 1636$\,\mathrm{keV}$ $\gamma$ energies,
respectively and a beam current of 50-150 $\mu$A. The two horizontal lines
represent a typical rate of $\gamma$ background measured at LNGS with a
shielded setup Caciolli et al. (2009) (blue and red lines for
440$\,\mathrm{keV}$ and 1636$\,\mathrm{keV}$ $\gamma$ energies, respectively)

##  7 Conclusions

The enhancement in the sensitivity provided by the strong background reduction
in a underground laboratory, together with the best experimental techniques,
have made possible, during twenty-five years of LUNA activity, to take clear
steps forward in the knowledge of nuclear processes relevant to astrophysical
scenarios. The installation of a new MV accelerator in the Gran Sasso
laboratory will allow over a broad time window of at least twenty years, to
extend these studies to key processes of helium, carbon and neon burning
phases. Even if more extensively studied, also other important processes of
H-burning will be better constrained thanks to the new facility. An example is
the ${}^{14}\mathrm{N}(\mathrm{p},\gamma){}^{15}\mathrm{O}$ reaction,
presently known only at energies well above the Gamow peak. By combining the
existing LUNA 400 kV machine with new LUNA-MV facility it will be possible to
cover the necessary energy range with a sufficient overlap and without any
hole between 200$\,\mathrm{keV}$ and 1.5$\,\mathrm{MeV}$, allowing to reduce
the systematics in the extrapolations down to the 5% level. The
${}^{14}\mathrm{N}(\mathrm{p},\gamma){}^{15}\mathrm{O}$ reaction will also be
suitable to perform the commissioning and the tuning of LUNA MV accelerator.

As already said, the success of the LUNA approach has motivated similar
facilities already in operation in the United States or under construction in
the Republic of China. This worldwide effort will allow in the next decades to
take important steps forward in the field of nuclear astrophysics.

## References

  * Eddington (1920) Eddington AS.  The Internal Constitution of the Stars.  The Scientific Monthly 11 (1920) 297–303.
  * von Weizsäcker (1938) von Weizsäcker CF.  Über Elementumwandlungen im Innern der Sterne, ii.  Phys. Z. 39 (1938) 633–646.
  * Bethe and Critchfield (1938) Bethe A, Critchfield C.  The Formation of Deuterons by Proton Combination.  Phys. Rev. 54 (1938) 248.  10.1103/PhysRev.54.248.
  * Rolfs and Rodney (1988) Rolfs C, Rodney W.  Cauldrons in the Cosmos (Chicago: The University of Chicago Press) (1988).
  * Iliadis (2015) Iliadis C.  Nuclear physics of stars.  Physics textbook (Weinheim: Wiley-VCH), 2., rev. and enlarged ed edn. (2015).  OCLC: 910238416.
  * Käppeler et al. (2011a) Käppeler F, Gallino R, Bisterzo S, Aoki W.  The $s$ process: Nuclear physics, stellar models, and observations.  Rev. Mod. Phys. 83 (2011a) 157–193.  10.1103/RevModPhys.83.157.
  * Greife et al. (1994) Greife U, Arpesella C, Barnes C, Bartolucci F, Bellotti E, Broggini C, et al.  Laboratory for Underground Nuclear Astrophysics (LUNA).  Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 350 (1994) 327–337.  10.1016/0168-9002(94)91182-7.
  * Formicola et al. (2003) Formicola A, Imbriani G, Junker M, Bemmerer D, Bonetti R, Broggini C, et al.  The LUNA II 400 kV accelerator.  Nucl. Inst. Meth. A 507 (2003) 609–616.  10.1016/S0168-9002(03)01435-9.
  * Bonetti et al. (1999) Bonetti R, Broggini C, Campajola L, Corvisiero P, D’Alessandro A, Dessalvi M, et al.  First measurement of the ${}^{3}\mathrm{He}$(${}^{3}\mathrm{He}$,2 p)${}^{4}\mathrm{He}$ cross-section down to the lower edge of the solar Gamow peak.  Phys. Rev. Lett. 82 (1999) 5205–5208.  10.1103/PhysRevLett.82.5205.
  * Casella et al. (2002) Casella C, Costantini H, Lemut A, Limata B, Bonetti R, Broggini C, et al.  First measurement of the d(p,$\gamma$)3He cross section down to the solar Gamow peak.  Nucl. Phys. A 706 (2002) 203–216.  10.1016/S0375-9474(02)00749-2.
  * Mossa et al. (2020) Mossa V, Stöckel K, Cavanna F, Ferraro F, Aliotta M, Barile F, et al.  Setup commissioning for an improved measurement of the D(p,$\gamma$)3He cross section at Big Bang Nucleosynthesis energies.  Eur. Phys. J. A 56 (2020) 144.  10.1140/epja/s10050-020-00149-1.
  * Broggini et al. (2018) Broggini C, Bemmerer D, Caciolli A, Trezzi D.  Luna: Status and prospects.  Prog. Part. Nucl. Phys. 98 (2018) 55–84.  10.1016/j.ppnp.2017.09.002.
  * Cavanna and Prati (2018) Cavanna F, Prati P.  Direct measurement of nuclear cross-section of astrophysical interest: Results and perspectives.  Int. J. Mod. Phys. A 33 (2018) 1843010-346.  10.1142/S0217751X18430108.
  * Broggini et al. (2019) Broggini C, Straniero O, Taiuti M, De Angelis G, Benzoni G, Bruno G, et al.  Experimental nuclear astrophysics in Italy.  Rivista del Nuovo Cimento 42 (2019) 103–152.  10.1393/ncr/i2019-10157-1.
  * Liu et al. (2016) Liu W, Li Z, He J, Tang X, Lian G, An Z, et al.  Progress of Jinping Underground laboratory for Nuclear Astrophysics (JUNA).  Science China Physics, Mechanics & Astronomy 59 (2016) 642001\.  10.1007/s11433-016-5785-9.
  * Robertson, Daniel et al. (2016) Robertson, Daniel, Couder, Manoel, Greife, Uwe, Strieder, Frank, Wiescher, Michael.  Underground nuclear astrophysics studies with CASPAR.  EPJ Web of Conferences 109 (2016) 09002.  10.1051/epjconf/201610909002.
  * Sen et al. (2019) Sen A, Domínguez-Cañizares G, Podaru N, Mous D, Junker M, Imbriani G.  A high intensity, high stability 3.5 MV SingletronTM accelerator.  Nuclear Inst. and Methods in Physics Research B 460 (2019) 390–395.  10.1016/j.nimb.2018.09.016.
  * Wolfgang Hammer et al. (1986) Wolfgang Hammer J, Bulski G, Grum W, Kratschmer W, Postner H, Schleussner G.  Scorpion, the Stuttgart scattering facility for fast polarized neutrons.  Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 244 (1986) 455–476.  10.1016/0168-9002(86)91069-7.
  * Chen et al. (2020) Chen C, Li YJ, Zhang H, Li ZH.  Preparation of large-area isotopic magnesium targets for the 25mg(p,$\gamma$)26al experiment at JUNA.  Nuclear Science and Techniques 31 (2020) 91.  10.1007/s41365-020-00800-y.
  * Caciolli et al. (2009) Caciolli A, Agostino L, Bemmerer D, Bonetti R, Broggini C, Confortola F, et al.  Ultra-sensitive in-beam $\gamma$-ray spectroscopy for nuclear astrophysics at LUNA.  The European Physical Journal A 39 (2009) 179–186.  10.1140/epja/i2008-10706-3.
  * Boeltzig et al. (2018) Boeltzig A, Best A, Imbriani G, Junker M, Aliotta M, Bemmerer D, et al.  Improved background suppression for radiative capture reactions at LUNA with HPGe and BGO detectors.  Journal of Physics G: Nuclear and Particle Physics 45 (2018) 025203.  10.1088/1361-6471/aaa163.
  * Ferraro et al. (2018) Ferraro F, Takács MP, Piatti D, Mossa V, Aliotta M, Bemmerer D, et al.  A high-efficiency gas target setup for underground experiments, and redetermination of the branching ratio of the 189.5 kev ${}^{22}\mathrm{Ne}(p,\gamma)^{23}\mathrm{Na}$ resonance.  Eur. Phys. J. A 54 (2018) 44.  10.1140/epja/i2018-12476-7.
  * Burbidge et al. (1957) Burbidge EM, Burbidge GR, Fowler WA, Hoyle F.  Synthesis of the elements in stars.  Rev. Mod. Phys. 29 (1957) 547–650.  10.1103/RevModPhys.29.547.
  * Käppeler (1999) Käppeler F.  The origin of the heavy elements: the s process.  Prog. Part. Nucl. Phys. (UK), Vol. 43, p. 419 - 483 43 (1999) 419–483.
  * Cristallo et al. (2018) Cristallo S, Cognata ML, Massimi C, Best A, Palmerini S, Straniero O, et al.  The importance of the 13c($\alpha$,n)16o reaction in asymptotic giant branch stars.  The Astrophysical Journal 859 (2018) 105.  10.3847/1538-4357/aac177.
  * Kimura and Bonasera (2013) Kimura S, Bonasera A.  Gamow peak approximation near strong resonances.  Phys. Rev. C 87 (2013) 058801.  10.1103/PhysRevC.87.058801.
  * Ajzenberg-Selove (1986) Ajzenberg-Selove F.  Energy levels of light nuclei A = 16-17.  Nucl. Phys. A460 (1986) 1–110.  10.1016/0375-9474(86)90038-2.
  * Faestermann et al. (2015) Faestermann T, Mohr P, Hertenberger R, Wirth HF.  Broad levels in ${}^{17}\text{O}$ and their relevance for the astrophysical $s$ process.  Phys. Rev. C 92 (2015) 052802.  10.1103/PhysRevC.92.052802.
  * Drotleff et al. (1993) Drotleff HW, Denker A, Knee H, Soine M, Wolf G, Hammer JW, et al.  Reaction rates of the s-process neutron sources ${N}e22(\alpha,n){M}g25$ and ${C}13(\alpha,n){O}16$.  Astrophysical Journal 414 (1993) 735–739.  10.1086/173119.
  * Brune et al. (1993) Brune CR, Licot I, Kavanagh RW.  Low-energy resonances in ${}^{13}\mathrm{C}$($\alpha$,n).  Phys. Rev. C 48 (1993) 3119–3121.  10.1103/PhysRevC.48.3119.
  * Harissopulos et al. (2005) Harissopulos S, Becker HW, Hammer JW, Lagoyannis A, Rolfs C, Strieder F.  Cross section of the ${}^{13}\mathrm{C}$($\alpha,n$)${}^{16}\mathrm{O}$ reaction: A background for the measurement of geo-neutrinos.  Phys. Rev. C 72 (2005) 062801.  10.1103/PhysRevC.72.062801.
  * Araki et al. (2005) Araki T, Enomoto S, Furuno K, Gando Y, Ichimura K, Ikeda H, et al.  Experimental investigation of geologically produced antineutrinos with KamLAND.  Nature 436 (2005) 499–503.  10.1038/nature03980.
  * Heil et al. (2008) Heil M, Detwiler R, Azuma RE, Couture A, Daly J, Görres J, et al.  The ${}^{13}{C}(\alpha,n)$ reaction and its role as a neutron source for the $s$ process.  Phys. Rev. C 78 (2008) 025803.  10.1103/PhysRevC.78.025803.
  * Febbraro et al. (2020) Febbraro M, deBoer RJ, Pain SD, Toomey R, Becchetti FD, Boeltzig A, et al.  New ${}^{13}\mathrm{C}(\alpha,n)^{16}\mathrm{O}$ cross section with implications for neutrino mixing and geoneutrino measurements.  Phys. Rev. Lett. 125 (2020) 062501.  10.1103/PhysRevLett.125.062501.
  * Kubono et al. (2003) Kubono S, Abe K, Kato S, Teranishi T, Kurokawa M, Liu X, et al.  Determination of the Subthreshold State Contribution in 13C($\alpha$,n)16O, the Main Neutron-Source Reaction for the s Process.  Physical Review Letters 90 (2003) 062501.  10.1103/PhysRevLett.90.062501.
  * Keeley et al. (2003) Keeley N, Kemper K, Khoa DT.  DWBA analysis of the 13C(6Li,d)17O reaction at 10Â MeV/nucleon and its astrophysical implications.  Nuclear Physics A 726 (2003) 159 – 172.  10.1016/S0375-9474(03)01622-1.
  * Johnson et al. (2006) Johnson ED, Rogachev GV, Mukhamedzhanov AM, Baby LT, Brown S, Cluff WT, et al.  Astrophysical reaction rate for the neutron-generator reaction ${}^{13}\mathrm{C}(\alpha,n)^{16}\mathrm{O}$ in asymptotic giant branch stars.  Phys. Rev. Lett. 97 (2006) 192701.  10.1103/PhysRevLett.97.192701.
  * Avila et al. (2015) Avila ML, Rogachev GV, Koshchiy E, Baby LT, Belarge J, Kemper KW, et al.  New measurement of the $\alpha$ asymptotic normalization coefficient of the ${1/2}^{+}$ state in ${}^{17}\mathrm{O}$ at 6.356 mev that dominates the ${}^{13}\mathrm{C}(\alpha,n)^{16}\mathrm{O}$ reaction rate at temperatures relevant for the $s$ process.  Phys. Rev. C 91 (2015) 048801.  10.1103/PhysRevC.91.048801.
  * Tumino, A. et al. (2018) Tumino, A, Spitaleri, Claudio, Cherubini, Silvio, D´Agata, Giuseppe, Giovanni Luca, Guardo, Gulino, Marisa, et al.  The trojan horse method in nuclear astrophysics.  EPJ Web Conf. 184 (2018) 01016.  10.1051/epjconf/201818401016.
  * La Cognata M. et al. (2013) La Cognata M, Spitaleri C, Trippella O, Kiss GG, Rogachev GV, Mukhamedzhanov AM, et al.  On the measurement of the $13{C}(\alpha,n)^{16}{O}$ ${S}$-factor at negative energies and its influence on the s-process.  The Astrophysical Journal 777 (2013) 143.  10.1088/0004-637X/777/2/143.
  * O. Trippella and M. La Cognata (2017) O Trippella, M La Cognata.  Concurrent Application of ANC and THM to assess the ${}^{13}\mathrm{C}(\alpha,n)^{16}\mathrm{O}$ Absolute Cross Section at Astrophysical Energies and Possible Consequences for Neutron Production in Low-mass AGB Stars.  The Astrophysical Journal 837 (2017) 41.  10.3847/1538-4357/aa5eb5.
  * Balibrea-Correa et al. (2018) Balibrea-Correa J, Ciani GF, Buompane R, Cavanna F, Csedreki L, Depalo R, et al.  Improved pulse shape discrimination for high pressure 3He counters.  Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 906 (2018) 103 – 109.  10.1016/j.nima.2018.07.086.
  * Csedreki et al. (2019) Csedreki L, Ciani GF, Best A, Balibrea-Correa J, Gyürky G.  The LUNA Neutron Detector Array for the Direct Measurement of the ${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$ Nuclear Reaction.  Formicola A, Junker M, Gialanella L, Imbriani G, editors, Nuclei in the Cosmos XV (Cham: Springer International Publishing) (2019), 331–334.
  * Ciani, G. F. et al. (2020) Ciani, G F, Csedreki, L, Balibrea-Correa, J, Best, A, Aliotta, M, Barile, F, et al.  A new approach to monitor 13C-targets degradation in situ for 13C($\alpha$ ,n)16O cross-section measurements at LUNA.  Eur. Phys. J. A 56 (2020) 75.  10.1140/epja/s10050-020-00077-0.
  * Käppeler et al. (2011b) Käppeler F, Gallino R, Bisterzo S, Aoki W.  The $s$ process: Nuclear physics, stellar models, and observations.  Rev. Mod. Phys. 83 (2011b) 157–193.  10.1103/RevModPhys.83.157.
  * Peters (1968) Peters JG.  Nucleosynthesis by the s-PROCESS in Stars of 9 and 15 Solar Masses.  ApJ 154 (1968) 225.  10.1086/149753.
  * Couch et al. (1974) Couch RG, Schmiedekamp AB, Arnett WD.  S-PROCESS Nucleosynthesis in Massive Stars: Core Helium Burning.  ApJ 190 (1974) 95–100.  10.1086/152851.
  * Lamb et al. (1977) Lamb SA, Howard WM, Truran JW, Iben J I.  Neutron-capture nucleosynthesis in the helium-burning cores of massive stars.  ApJ 217 (1977) 213–221.  10.1086/155571.
  * Prantzos et al. (1990) Prantzos N, Hashimoto M, Nomoto K.  The s-process in massive stars : yields as a function of stellar mass and metallicity.  Astronomy and Astrophysics 234 (1990) 211.
  * Raiteri et al. (1991a) Raiteri CM, Busso M, Gallino R, Picchio G, Pulone L.  S-Process Nucleosynthesis in Massive Stars and the Weak Component. I. Evolution and Neutron Captures in a 25 Msun Star.  ApJ 367 (1991a) 228.  10.1086/169622.
  * Pignatari et al. (2010) Pignatari M, Gallino R, Heil M, Wiescher M, Käppeler F, Herwig F, et al.  THE WEAK $s$-PROCESS IN MASSIVE STARS AND ITS DEPENDENCE ON THE NEUTRON CAPTURE CROSS SECTIONS.  The Astrophysical Journal 710 (2010) 1557–1577.  10.1088/0004-637x/710/2/1557.
  * Raiteri et al. (1991b) Raiteri CM, Busso M, Gallino R, Picchio G.  S-Process Nucleosynthesis in Massive Stars and the Weak Component. II. Carbon Burning and Galactic Enrichment.  ApJ 371 (1991b) 665.  10.1086/169932.
  * Arnett and Truran (1969) Arnett WD, Truran JW.  Carbon-Burning Nucleosynthesis at Constant Temperature.  ApJ 157 (1969) 339.  10.1086/150072.
  * Gallino et al. (1988) Gallino R, Busso M, Picchio G, Raiteri CM, Renzini A.  On the Role of Low-Mass Asymptotic Giant Branch Stars in Producing a Solar System Distribution of s-Process Isotopes.  ApJl 334 (1988) L45.  10.1086/185309.
  * Hollowell and Iben (1988) Hollowell D, Iben J Icko.  Nucleosynthesis of Solar System Material in a Low-Mass, Low-Metallicity Asymptotic Giant Branch Star.  ApJl 333 (1988) L25.  10.1086/185279.
  * Bisterzo et al. (2014) Bisterzo S, Travaglio C, Gallino R, Wiescher M, Käppeler F.  Galactic Chemical Evolution and Solar s-process Abundances: Dependence on the 13C-pocket Structure.  ApJ 787 (2014) 10.  10.1088/0004-637X/787/1/10.
  * Bisterzo et al. (2015) Bisterzo S, Gallino R, Käppeler F, Wiescher M, Imbriani G, Straniero O, et al.  The branchings of the main s-process: their sensitivity to $\alpha$-induced reactions on 13C and 22Ne and to the uncertainties of the nuclear network.  Monthly Notices of the Royal Astronomical Society 449 (2015) 506–527.  10.1093/mnras/stv271.
  * Lugaro et al. (2003) Lugaro M, Herwig F, Lattanzio JC, Gallino R, Straniero O.  s-process nucleosynthesis in asymptotic giant branch stars: A test for stellar evolution.  The Astrophysical Journal 586 (2003) 1305–1319.  10.1086/367887.
  * Garcia-Hernandez et al. (2006) Garcia-Hernandez DA, Garcia-Lario P, Plez B, D’Antona F, Manchado A, Trigo-Rodriguez JM.  Rubidium-rich asymptotic giant branch stars.  Science 314 (2006) 1751–1754.  10.1126/science.1133706.
  * Garcia-Hernandez, D. A. et al. (2007) Garcia-Hernandez, D A, Garcia-Lario, P, Plez, B, Manchado, A, D’Antona, F, Lub, J, et al.  Lithium and zirconium abundances in massive galactic o-rich agb stars ***.  A&A 462 (2007) 711–730.  10.1051/0004-6361:20065785.
  * Garcia-Hernandez et al. (2009) Garcia-Hernandez DA, Manchado A, Lambert DL, Plez B, Garcia-Lario P, D’Antona F, et al.  Rb-RICH ASYMPTOTIC GIANT BRANCH STARS IN THE MAGELLANIC CLOUDS.  The Astrophysical Journal 705 (2009) L31–L35.  10.1088/0004-637x/705/1/l31.
  * van Raai, M. A. et al. (2012) van Raai, M A, Lugaro, M, Karakas, A I, García-Hernández, D A, Yong, D.  Rubidium, zirconium, and lithium production in intermediate-mass asymptotic giant branch stars.  A&A 540 (2012) A44.  10.1051/0004-6361/201117896.
  * Ashery (1969) Ashery D.  Study of the $\mathrm{{}^{22}Ne(\alpha,n)^{25}Mg}$ reaction: a possible source of stellar neutrons.  Nuclear Physics A 136 (1969) 481 – 495.  10.1016/0375-9474(69)90122-5.
  * Haas and Bair (1973) Haas FX, Bair JK.  Total neutron yield from the ($\alpha$, $n$) reaction on ${}^{21,22}\mathrm{Ne}$.  Phys. Rev. C 7 (1973) 2432–2436.  10.1103/PhysRevC.7.2432.
  * Mak et al. (1974) Mak HB, Ashery D, Barnes C.  Cross sections of the $\mathrm{{}^{21}Ne(\alpha,n)^{24}Mg}$ and $\mathrm{{}^{22}Ne(\alpha,n)^{25}Mg}$ reactions at low energies of astrophysical interest.  Nuclear Physics A 226 (1974) 493 – 505.  10.1016/0375-9474(74)90496-5.
  * Wolke et al. (1989) Wolke K, Becker HW, Rolfs C, Schröder U, Trautvetter HP, Harms V, et al.  Helium burning of 22Ne.  Zeitschrift fur Physik A Hadrons and Nuclei 334 (1989) 491–510.  10.1007/BF01294757.
  * Harms et al. (1991) Harms V, Kratz KL, Wiescher M.  Properties of ${}^{22}\mathrm{Ne}$($\alpha$,n${)}^{25}$mg resonances.  Phys. Rev. C 43 (1991) 2849–2861.  10.1103/PhysRevC.43.2849.
  * Drotleff et al. (1993) Drotleff HW, Denker A, Knee H, Soine M, Wolf G, Hammer JW, et al.  Reaction rates of the s-process neutron sources ${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$ and ${}^{13}\mathrm{C}(\alpha,\mathrm{n}){}^{16}\mathrm{O}$.  The Astrophysical Journal 414 (1993) 735.  10.1086/173119.
  * Giesen et al. (1993) Giesen U, Browne C, J Görres, Graff S, Iliadis C, Trautvetter HP, et al.  The astrophysical implications of low-energy resonances in ${}^{22}\mathrm{Ne}+\alpha$.  Nuclear Physics A 561 (1993) 95 – 111.  10.1016/0375-9474(93)90167-V.
  * Jaeger et al. (2001) Jaeger M, Kunz R, Mayer A, Hammer JW, Staudt G, Kratz KL, et al.  ${}^{22}ne(\alpha,\mathit{n})^{25}mg$: The key neutron source in massive stars.  Phys. Rev. Lett. 87 (2001) 202501.  10.1103/PhysRevLett.87.202501.
  * Longland et al. (2009) Longland R, Iliadis C, Rusev G, Tonchev AP, deBoer RJ, Görres J, et al.  Photoexcitation of astrophysically important states in ${}^{26}\mathrm{Mg}$.  Phys. Rev. C 80 (2009) 055803.  10.1103/PhysRevC.80.055803.
  * Longland et al. (2012) Longland R, Iliadis C, Karakas AI.  Reaction rates for the s -process neutron source ${}^{22}\mathrm{Ne}+\alpha$.  Physical Review C 85 (2012) 065809.  10.1103/PhysRevC.85.065809.
  * Talwar et al. (2016) Talwar R, Adachi T, Berg GPA, Bin L, Bisterzo S, Couder M, et al.  Probing astrophysically important states in the ${}^{26}\mathrm{Mg}$ nucleus to study neutron sources for the $s$ process.  Phys. Rev. C 93 (2016) 055803.  10.1103/PhysRevC.93.055803.
  * Massimi et al. (2017) Massimi C, Altstadt S, Andrzejewski J, Audouin L, Barbagallo M, Bécares V, et al.  Neutron spectroscopy of 26mg states: Constraining the stellar neutron source ${}^{22}\mathrm{Ne}(\alpha,\mathrm{n}){}^{25}\mathrm{Mg}$.  Physics Letters B 768 (2017) 1 – 6.  10.1016/j.physletb.2017.02.025.
  * Ota et al. (2020) Ota S, Christian G, Lotay G, Catford W, Bennett E, Dede S, et al.  Decay properties of ${}^{22}\mathrm{Ne}+\alpha$ resonances and their impact on s-process nucleosynthesis.  Physics Letters B 802 (2020) 135256.  10.1016/j.physletb.2020.135256.
  * Jayatissa et al. (2020) Jayatissa H, Rogachev G, Goldberg V, Koshchiy E, Christian G, Hooker J, et al.  Constraining the ${}^{22}\mathrm{Ne}$($\alpha$,$\gamma$)${}^{26}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}$($\alpha$,n)${}^{25}\mathrm{Mg}$ reaction rates using sub-Coulomb $\alpha$-transfer reactions.  Physics Letters B 802 (2020) 135267.  10.1016/j.physletb.2020.135267.
  * Cyburt et al. (2010) Cyburt RH, Amthor AM, Ferguson R, Meisel Z, Smith K, Warren S, et al.  THE JINA REACLIB DATABASE: ITS RECENT UPDATES AND IMPACT ON TYPE-i x-RAY BURSTS.  The Astrophysical Journal Supplement Series 189 (2010) 240–252.  10.1088/0067-0049/189/1/240.
  * Caughlan and Fowler (1988) Caughlan GR, Fowler WA.  Thermonuclear reaction rates v.  Atomic Data and Nuclear Data Tables 40 (1988) 283 – 334\.  10.1016/0092-640X(88)90009-5.
  * Angulo et al. (1999) Angulo C, Arnould M, Rayet M, Descouvemont P, Baye D, Leclercq-Willain C, et al.  A compilation of charged-particle induced thermonuclear reaction rates.  Nuclear Physics A 656 (1999) 3 – 183.  10.1016/S0375-9474(99)00030-5.
  * Rauscher and Thielemann (2000) Rauscher T, Thielemann FK.  Astrophysical reaction rates from statistical model calculations.  Atomic Data and Nuclear Data Tables 75 (2000) 1 – 351.  10.1006/adnd.2000.0834.
  * Iliadis et al. (2010) Iliadis C, Longland R, Champagne A, Coc A, Fitzgerald R.  Charged-particle thermonuclear reaction rates: Ii. tables and graphs of reaction rates and probability density functions.  Nuclear Physics A 841 (2010) 31 – 250.  10.1016/j.nuclphysa.2010.04.009.  The 2010 Evaluation of Monte Carlo based Thermonuclear Reaction Rates.
  * Guglielmetti (2014) Guglielmetti A.  The LUNA experiment at Gran Sasso Laboratory.  EPJ Web of Conferences 78 (2014) 07001.  10.1051/epjconf/20147807001.
  * Prati (2019) Prati P.  Nuclear reaction of astrophysical interest with luna projects.  Formicola A, Junker M, Gialanella L, Imbriani G, editors, Nuclei in the Cosmos XV (Cham: Springer International Publishing) (2019), 247–252.
  * Fowler (1984) Fowler WA.  The Quest for the Origin of the Elements.  Science 226 (1984) 922–935.  10.1126/science.226.4677.922.
  * deBoer et al. (2017) deBoer R, Görres J, Wiescher M, Azuma R, Best A, Brune C, et al.  The ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction and its implications for stellar helium burning.  Reviews of Modern Physics 89 (2017) 035007.  10.1103/RevModPhys.89.035007.
  * Kremer et al. (1988) Kremer RM, Barnes CA, Chang KH, Evans HC, Filippone BW, Hahn KH, et al.  Coincidence measurement of the 12C($\alpha,\gamma$)16O cross section at low energies.  Physical Review Letters 60 (1988) 1475–1478.  10.1103/PhysRevLett.60.1475.
  * Schürmann et al. (2005) Schürmann D, Di Leva A, Gialanella L, Rogalla D, Strieder F, De Cesare N, et al.  First direct measurement of the total cross-section of ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$.  The European Physical Journal A 26 (2005) 301–305.  10.1140/epja/i2005-10175-2.
  * Matei et al. (2006) Matei C, Buchmann L, Hannes WR, Hutcheon DA, Ruiz C, Brune CR, et al.  Measurement of the Cascade Transition via the First Excited State of ${}^{16}\mathrm{O}$ in the ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ Reaction, and Its S Factor in Stellar Helium Burning.  Physical Review Letters 97 (2006) 242503.  10.1103/PhysRevLett.97.242503.
  * Schürmann et al. (2011) Schürmann D, Di Leva A, Gialanella L, Kunz R, Strieder F, De Cesare N, et al.  Study of the 6.05 MeV cascade transition in ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$.  Physics Letters B 703 (2011) 557–561.  10.1016/j.physletb.2011.08.061.
  * Kunz et al. (2001) Kunz R, Jaeger M, Mayer A, Hammer JW, Staudt G, Harissopulos S, et al.  ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$: The Key Reaction in Stellar Nucleosynthesis.  Physical Review Letters 86 (2001) 3244–3247.  10.1103/PhysRevLett.86.3244.
  * Fey (2004) Fey M.  Im Brennpunkt der Nuklearen Astrophysik: Die Reaktion ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$.  PhD, Universität Stuttgart, Stuttgart (2004).
  * Assunção et al. (2006) Assunção M, Fey M, Lefebvre-Schuhl A, Kiener J, Tatischeff V, Hammer JW, et al.  E1 and E2 S factors of ${}^{12}\mathrm{C}(\alpha,\gamma_{0}){}^{16}\mathrm{O}$ from $\gamma$-ray angular distributions with a $4\pi$-detector array.  Physical Review C 73 (2006) 055801.  10.1103/PhysRevC.73.055801.
  * Makii et al. (2009) Makii H, Nagai Y, Shima T, Segawa M, Mishima K, Ueda H, et al.  E1 and E2 cross sections of the ${}^{12}\mathrm{C}(\alpha,\gamma_{0}){}^{16}\mathrm{O}$ reaction using pulsed $\alpha$ beams.  Physical Review C 80 (2009) 065802.  10.1103/PhysRevC.80.065802.
  * Plag et al. (2012) Plag R, Reifarth R, Heil M, Käppeler F, Rupp G, Voss F, et al.  ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ studied with the Karlsruhe $4\pi$ BaF2 detector.  Physical Review C 86 (2012) 015805.  10.1103/PhysRevC.86.015805.
  * Fujita et al. (2015) Fujita K, Yamaguchi H, Ban T, Hamamoto K, Narikiyo Y, Tao N, et al.  Direct Measurement of the ${}^{4}\mathrm{He}({}^{12}\mathrm{C},{}^{16}\mathrm{O})\gamma$ Total Cross Section Near Stellar Energies.  EPJ Web of Conferences 93 (2015) 03005.  10.1051/epjconf/20159303005.
  * Bemmerer et al. (2018) Bemmerer D, Cowan TE, Grieger M, Hammer S, Hensel T, Junghans AR, et al.  Felsenkeller 5 MV underground accelerator: Towards the Holy Grail of Nuclear Astrophysics ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$.  EPJ Web of Conferences 178 (2018) 01008.  10.1051/epjconf/201817801008.
  * Liu (2017) Liu WP.  Underground Nuclear Astrophysics Experiment JUNA in China.  JPS Conference Proceedings (Niigata: Journal of the Physical Society of Japan) (2017), 011101.  10.7566/JPSCP.14.011101.
  * Becker and Iben (1980) Becker SA, Iben J I.  The asympiotic giant branch evolution of intermediate-mass stars as a function of mass and composition. II. Through the first major thermal pulse and the consequences of convective dredge-up.  ApJ 237 (1980) 111–129.  10.1086/157850.
  * Bravo et al. (2011) Bravo E, Piersanti L, Domínguez I, Straniero O, Isern J, Escartin JA.  Type Ia supernovae and the 12C+12C reaction rate.  Astronomy and Astrophysics 535 (2011) A114.  10.1051/0004-6361/201117814.
  * Tutusaus et al. (2019) Tutusaus I, Lamine B, Blanchard A.  Model-independent cosmic acceleration and redshift-dependent intrinsic luminosity in type-Ia supernovae.  Astronomy and Astrophysics 625 (2019) A15.  10.1051/0004-6361/201833032.
  * Spillane et al. (2007) Spillane T, Raiola F, Rolfs C, Schürmann D, Strieder F, Zeng S, et al.  ${}^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion reactions near the gamow energy.  Phys. Rev. Lett. 98 (2007) 122501.  10.1103/PhysRevLett.98.122501.
  * Jiang et al. (2018) Jiang CL, Santiago-Gonzalez D, Almaraz-Calderon S, Rehm KE, Back BB, Auranen K, et al.  Reaction rate for carbon burning in massive stars.  Phys. Rev. C 97 (2018) 012801.  10.1103/PhysRevC.97.012801.
  * Zickefoose et al. (2018) Zickefoose J, Di Leva A, Strieder F, Gialanella L, Imbriani G, De Cesare N, et al.  Measurement of the ${}^{12}\mathrm{C}(^{12}\mathrm{C},p)^{23}\mathrm{Na}$ cross section near the gamow energy.  Phys. Rev. C 97 (2018) 065806.  10.1103/PhysRevC.97.065806.
  * Tumino et al. (2018) Tumino A, Spitaleri C, La Cognata M, Cherubini S, Guardo GL, Gulino M, et al.  An increase in the 12C + 12C fusion rate from resonances at astrophysical energies.  Nature 557 (2018) 687–690.  10.1038/s41586-018-0149-4.
  * Mukhamedzhanov et al. (2019) Mukhamedzhanov AM, Pang DY, Kadyrov AS.  Astrophysical factors of ${}^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion extracted using the trojan horse method.  Phys. Rev. C 99 (2019) 064618.  10.1103/PhysRevC.99.064618.
  * Becker et al. (1981) Becker HW, Kettner KU, Rolfs C, Trautvetter HP.  The ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reaction at subcoulomb energies (ii).  Zeitschrift für Physik A Atoms and Nuclei 303 (1981) 305–312.  10.1007/BF01421528.
  * Morales-Gallegos et al. (2018) Morales-Gallegos L, Aliotta M, Bruno CG, Buompane R, Davinson T, De Cesare M, et al.  Reduction of deuterium content in carbon targets for ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reaction studies of astrophysical interest.  The European Physical Journal A 54 (2018) 132.  10.1140/epja/i2018-12564-8.
  * Zhang et al. (2020) Zhang N, Wang X, Tudor D, Bucher B, Burducea I, Chen H, et al.  Constraining the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ astrophysical S-factors with the ${}^{12}\mathrm{C}+{}^{13}\mathrm{C}$ measurements at very low energies.  Physics Letters B 801 (2020) 135170.  10.1016/j.physletb.2019.135170.
  * Bonasera and Natowitz (2020) Bonasera A, Natowitz JB.  Calculation of the ${}^{12}\mathrm{C}+^{12}\mathrm{C}$ sub-barrier fusion cross section in an imaginary-time-dependent mean field theory.  Phys. Rev. C 102 (2020) 061602.  10.1103/PhysRevC.102.061602.
  * Fruet et al. (2020) Fruet G, Courtin S, Heine M, Jenkins DG, Adsley P, Brown A, et al.  Advances in the direct study of carbon burning in massive stars.  Phys. Rev. Lett. 124 (2020) 192701.  10.1103/PhysRevLett.124.192701.
  * Tan et al. (2020) Tan WP, Boeltzig A, Dulal C, deBoer RJ, Frentz B, Henderson S, et al.  New measurement of ${}^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion reaction at astrophysical energies.  Phys. Rev. Lett. 124 (2020) 192702.  10.1103/PhysRevLett.124.192702.
  * Bruno et al. (2015) Bruno CG, Scott DA, Formicola A, Aliotta M, Davinson T, Anders M, et al.  Resonance strengths in the ${}^{17,18}\mathrm{O}$(p, $\alpha$)${}^{14,15}\mathrm{N}$ reactions and background suppression underground.  The European Physical Journal A 51 (2015) 94.  10.1140/epja/i2015-15094-y.