2021

[1,2]Vincent Lelasseux

[1]Julien Fuchs

[1]LULI-CNRS, CEA, UPMC Univ Paris 06: Sorbonne Université, École
Polytechnique, Institut Polytechnique de Paris, Palaiseau, 91128, France
2]IFIN-HH, Str Reactorului, Magurele, 077125, Romania

3]IAP, Russian Academy of sciences, Nizhny Novgorod, 603950, Russia

4]Jozef Stefan Institute, Jamova cesta, Ljubljana, 1000, Slovenia

5]Marvel Fusion GmbH, Munich, 80339, Germany

6]DAM, DIF, CEA, Arpajon, 91297, France

7]Joint Institute for High Temperature RAS, Russian Academy of sciences,
Izhorskaya St, Moscow, 125412, Russia

# Experimental investigation of the effect of ionization on the 51V(p,n)51Cr
reaction

<EMAIL_ADDRESS>Pär-Anders Söderström  Soiciro Aogaki  Konstantin
Burdonov  Sophia Chen  Aleksandra Cvetinović  Emmanuel Dechefdebien  Sandra
Dorard  Alice Fazzini  Laurent Gremillet  Marius Gugiu  Vojtech Horny  Matej
Lipoglavsek  Sergey Pikuz  Florin Rotaru  Yao Weipeng  Florin Negoita
<EMAIL_ADDRESS>*  [  [  [  [  [  [

###### Abstract

The investigation of the effects of average atomic ionization on nuclear
reactions is of prime importance for nuclear astrophysics. No direct
experimental measurement using a plasma target has been done yet. In this
regard, we measured for the first time the neutron production of a (p,n)
reaction in different states of ionization. The studied nuclear reaction was
51V(p,n)51Cr. We measured a significantly lower neutron production than
expected when the target was ionized, even when taking into account existing
electron screening theory or the effect of the stopping power in the target on
the injected proton beam. This experiment is a first step in the process to
characterize the influence of ionization at astrophysically relevant energies.

###### keywords:

neutron, nuclear reaction, ionization

##  1 Introduction

The effect of the plasma-electron screening on nucleosynthesis is a long-
standing problem. Experimental data obtained with solid targets at
astrophysically relevant energies, i.e. energies in the Gamow peak, is far
from the theoritical predictionssalpeter1954electron ; strieder2001electron ;
spitaleri2016electron ; lipoglavsek2020electron . The latest experiments
report screening measurements in solid targets an order of magnitude above the
theoritical predictionscvetinovic2020electron .

When it comes to plasma targets, there is simply no experimental data
available to constrain the modelscasey2023towards . Reliable theoritical
predictions are difficult to produce since plasma behaviour is often very
subtle and depends on a lot of parameters cereceda2000dielectric ;
hayes2020plasma . However, such predictions are of prime importance since, for
example, this screening effect should imply a change of a few percents in the
nucleosynthesis reaction rates in the Sun but could reach six orders of
magnitude for others astrophysical sitesnational2003frontiers .

With the development of multi-PW lasers, such as Apollonpapadopoulos2019first
; burdonov2021characterization  or ELI-NPradier202210 ; tanaka2020current ,
the particle beams which can be produced by condensing light on a target reach
new milestones. In particular, the proton and neutron beams those facilities
will be able to allow experimental nuclear physics to study problems which
cannot be addressed by conventional facilitieszamfir2014nuclear .

In the work presented here, we took advantage of the possibility that high-
power lasers can both produce a bright proton beam, and ionize targets at the
same time. The protons being produced in bunches of picosecond timescale
duration, the state of plasma target can be considered as a steady state. In
this way, we could test the effects of ionization on a nuclear reaction, which
we chose here to be a (p,n) reaction in vanadium.

To reach this goal, we developed a high efficiency neutron counter adapted to
the high intensity laser environment lelasseux2021design . As almost no
neutrons are produced during the production of a laser-driven proton beam,
(p,n) reactions are good candidates to measure cross sections in such harsh
environments. As shown by Lelasseux et al. lelasseux2021design , neutron
measurement was partly delayed to avoid the electromagnetic background
produced by the prompt laser-matter interaction.

The paper is organized as follows. In Section 2 , we detail the experimental
setup and the parameters of the shots that were performed. In Section 3, we
detail the analysis of the proton and neutron signals that were recorded in
order to retrieve the actual number of neutrons emitted each shot. Section 4
presents the result of this analysis, mainly the unexpectedly low number of
neutrons measured when the vanadium target was in a plasma state. Section 5
discusses possible reasons behind our observation and Section 6 concludes this
study.

##  2 Experimental setup

###  2.1 Setup of the lasers and targets used in the experiment

The experiment was performed at the LULI2000 facility located at École
Polytechnique in Palaiseau, France. It took place in the experimental area #1
using the MILKA experimental chamber. During this experiment, we used two
laser beams. The first one, called the North beam, could deliver an energy up
to 1 kJ at 1.053 $\mu$m wavelength in the ns duration regime. The second one,
called the South beam, could deliver up to 60 J in 1 ps duration also at 1.053
$\mu$m wavelength.

We used a two targets setup shown in Fig.1. The primary target was a 23 $\mu$m
thick PolyEthylene Teraphtalate (PET) sheet with a 300 nm aluminum layer on
the front face to enhance the laser absorption. It was used to produce a
proton beam driven by the South laser beam through the Target Normal Sheath
Acceleration (TNSA) macchi2013ion  mechanism. By changing the size of the
focal spot on the target, thus changing the laser intensity, it was possible
to modulate the maximum energy of the spectrum obtained from the TNSA, without
modifying the spectrum otherwisefoccutoff .

The proton beam impinged onto a secondary target in which the (p,n) reactions
occurred. In order to try to investigate the reactions at proton energies
astrophysically relevant, we decided to use vanadium, due to the 50V stable
isotope having a 255.78 keV positive Q-value and vanadium having the highest
(p,n) cross-section endf  among this kind of materials. We decided to use a
thin vanadium target. Indeed, a thin target ensures that the proton beam can
be analyzed by a spectrometer placed downstream due to the scattering and
stopping power being negligible in such a case. A thin target will also ensure
that the heating, following the ns-duration laser irradiation, is as
homogeneous as possible. Neutron production calculations and MULTI, a 1D
radiation-hydrodynamic code ramis1988multi , simulations were used to
determine that a 1 $\mu$m thickness was a good compromise between having the
maximal mean ionization in the target, which required a thin target, and
generate enough neutrons for us to be able to measure them, which would favor
using thick targets.

The distance between the two targets is also the result of a compromise
between having the targets close enough to limit the angular dispersion of the
diverging proton beam bolton2014instrumentation , and far enough for the x-ray
emission of the vanadium target during its heating by the North beam, not to
blow the primary target and prevent the proton beam generation
mackinnon2001effect ; fuchs2007laser . We decided to set the minimum distance
to fulfill the second condition at 600 $\mu$m. Hence, considering a maximum
proton beam full divergence of 50°bolton2014instrumentation , this gives us a
disk of the projected proton beam with a 560 + X $\mu$m diameter on the
secondary target, X being the diameter of the focal spot on the primary
target. In practice, for the shots discussed below, we set X = 150 $\mu$m. To
make sure that the ionized section of the target encompasses the proton beam,
the North beam focal spot diameter was set to 900 $\mu$m.

Figure 1: Sketch of the targets setup with angles and distances between them.
The cone between the two targets represents the generated proton beam that
also extends behind the vanadium target.

###  2.2 Diagnostics setup

In order to maximize the angular coverage of the neutron detector, we limited
the overall number of diagnostics to three. First, to monitor the ionization
degree of the target, we used a FSSRFSSR  x-ray emission spectrometer. Second,
to monitor the proton energy spectrum, we used a magnetic
spectrometercowan1999high .

Third, to measure the neutron emission, we used a scintillator-based neutron
counter lelasseux2021design  whose dimensions have been determined taking into
account constraints due to the experimental chamber size, the laser paths and
other elements in the chamber, and using Geant4 simulationsGeant4 . A top-view
and a side-view of the placement of those diagnostics are respectively
presented Figs.2 and 3. The biggest hole in angular coverage in the right side
of the top view is due to the path of the picosecond laser beam, and
especially to accomodate a lead shield which has the purpose to protect the
experimental and technical teams from the proton beam which comes out from the
front face of the PET targetmckenna2004characterization . To prevent those
protons to reach the lead shield and produce a massive amount of unwanted
neutrons, a plastic shield has been installed between the target setup and the
lead shield. Another angular opening on the top left side of the top view (see
Fig.2) has been created for the nanosecond laser beam path. For alignment
purposes, it was also necessary to leave two spaces on the opposite side of
the laser paths, here on the left side and on the bottom right side of the top
view. Finally, a hole was machined in one of the neutron detector modules, to
allow a part of the proton beam to go through it and reach the magnetic
spectrometer placed further away. All the neutron detector modules had a 60 cm
height except for units 7 and 8 for which the height is 45 cm. The target
chamber center at which the targets were shot was at a height of 40 cm from
the chamber breadboard.

Figure 2: Top-view of the setup in the experimental chamber. The numbers of
the detector modules are written in black and some parts of the setup are in
red. Figure 3: Side-view of the setup in the experimental chamber. Some parts
of the setup are labelled in red. FSSR stands for Focusing Spectrometer with
Spatial Resolution and IP for Imaging Plate.

###  2.3 Shot sequences

Four types, or series, of shots were performed during the experiment. First,
in order to characterize the proton beam that could be generated and observe
the neutron detector response, we performed shots without the secondary
vanadium target. These are called ”background” shots in the following. Second,
we added a solid vanadium target on the path of the protons, as shown in
Fig.1. These are called ”cold” shots in the following. Third, the vanadium
target was ionized by the North beam. These are called ”hot” shots in the
following. Fourth and last, to check the influence on the detector of the
North beam used to heat the secondary target, we also performed a number of
shots only with the North beam.

##  3 Analysis

Typical traces recorded by the neutron counter are shown in Figs.4. In these
traces, we can observe that the unresponsive time in the PhotoMultiplier Tubes
(PMTs) that are part of the neutron counter was much higher than what we could
expect from the tests we run during other high intensity
experimentslelasseux2021design . This unresponsive time depending strongly on
the PMT and its position, the dead time ranged from 100 $\mu$s (see detector
15_D in Fig.4d) to more than 1 ms in the worst cases (see detector 7_U in
Fig.4c), 1 ms being the recording duration of the signal. To cope with this
unexpectedly long unresponsiveness and the strong background, we established
the analysis procedure detailed below, in order to ensure the nature and
validity of our measurements.

###  3.1 Proton analysis

First of all, to be able to compare equivalent shots, we quantitatively
analyzed the emitted proton spectrum for each shot with a procedure presented
in Ref.lelasseux2022detection . An example of the spectra are shown in Fig.6a.
All the proton spectra present an exponentially decreasing behaviour,
characteristic of TNSA, with a maximum energy cutoff around 16 MeV.

###  3.2 Neutron analysis

####  3.2.1 PMT response to gamma flash/EMP

We are then able to compare the neutron signals for shots having equivalent
proton beams. To do so, we have to analyze properly the traces recorded by the
pair of PMTs, working in coincidence, from each detector module. However, as
mentioned above, the unresponsive time from most of the PMTs was longer than
expected, as can be seen in Figs.4. The PMTs which are the closest to the
picosecond laser direction, i.e. of detector units 6, 7 and 9 are more
affected and cannot be used for quantitative analysis. The detector unit 8 had
an issue during its construction and was not functioning. Only the PMTs of
detector units 1, 14 and 15 have traces that we were able to analyze for all
shots of interest. Taking the position of the lead shield into account, we
suspect that the energy deposited in the scintillators by the gamma flash,
induced by the prompt South beam/PET target interaction, is mainly responsible
for the saturation observed after the first main peak around t = 0.12 ms.

Figure 4: Examples of traces obtained from different detector units and PMTs
during shot 28. During this shot, the proton energy cutoff was 16.31 MeV, a 1
$\mu$m solid vanadium target was in place and the North beam was not shot. ”U”
corresponds to PMTs on the up side of the modules and ”D” to the ones on the
down side.

From a closer look at the behaviour of those traces (see D13_U in Fig.4a), we
see that, after the unresponsive time, the maximum peak height increases to
values between 250 mV and 300 mV. We note that this behaviour is abnormal
since the mean peak height for a neutron detection is around 50 mV in normal
conditionslelasseux2021design . Following this, the maximum peak height
decreases on the scale of a few hundred $\mu$s, as shown with the trace of the
down PMT from detector unit 13 in Fig.4b. For some PMTs, as shown in Fig.4c
for D7_U, the saturation is so important that the 1 ms long recording time is
shorter than the recovery time. For other PMTs, as D15_D, the peak height
remains at the higher than expected value for the whole recording time, as
shown in Fig.4d.

As it can be deduced from Figs.4 and the complete set of traces, the duration
of the time window during which the maximum peak height is first at the noise
level, and then increases to reach a maximum value, seems to mainly depend on
the position of the PMT. The light distribution between the two coupled PMTs
depends strongly on which scintillator cylinder the energy deposition takes
place in, as detailed in Ref.lelasseux2021design . Hence, PMTs on the upper
side should indeed receive more light than the ones on the down side.

However, the time it takes for this maximum peak height to decrease seems to
be PMT dependent. We can draw two conclusions from this. First, since for some
PMTs, the maximum peak height eventually comes back to what we can expect from
a regular neutron capture event, most of those peaks probably correspond to
neutron capture events, even though their height is higher than expected.
Second, the characteristics of the neutron peak in the energy histograms will
probably be different than what is expected, on the base of the calibration
using a source lelasseux2021design . Indeed, the peaks which have a higher
height than expected will most probably also have higher integrals and, hence,
higher associated energies. Then, the best case scenario is that the mean peak
height stays constant and high for both coupled PMTs. This way, the events
corresponding to a neutron in the energy deposition histogram, i.e. the
neutron peak, should be located at a higher energy than during the
calibration. For all other cases, the maximum peak height varies in time for
at least one of the two PMTs and hence the definition itself of the neutron
peak is more complicated. In conclusion, only the units for which the mean
peak height stays high for both PMTs, will produce energy deposition
histograms with a clear neutron peak. These are the units that we will use for
the following analysis.

For the shots we conducted using only the North beam to ionize the vanadium
target, we observe that the North beam generates only electronic background.
No angular or U/D dependence can be seen when we examine all the different
traces. We do not observe any 200 mV-high peak during the shots without the
South beam. Hence, the addition of the North beam should not have a
significant effect, apart from a possible higher electronic noise depending on
the PMT.

####  3.2.2 Trace analysis

First, we need to perform a temporal selection since the PMTs are unresponsive
or not responsive in a satisfying way for some time after the shot. According
to Geant4 simulations done using the actual experimental setup and detailed
later, we know that the neutron detection rate should decrease according to
the sum of two exponentials. In the range of neutron energy we are interested
in, shown in Fig.7a, the two moderation components have exponential time
constants of around 12 and 110 $\mu$s. Taking the dead time duration into
account, which lasts at least 100 $\mu$s, the detection rate should then be
satisfyingly fitted by a decreasing exponential with a time constant of 110
$\mu$s.

Figure 5: Histogram of the light collected by the detector unit 15 according
to the time during shot 28. The red curve represents a decreasing exponential
with a half-life of 110 $\mu$s.

As shown in Fig.5, we see that, after the prompt gamma flash peak and some
dead time, the peak detection rate increases until reaching a maximum and
later decreases. If we represent a decreasing exponential with a 110 $\mu$s
time constant and the right amplitude, we indeed see a satisfactory agreement
between this exponential and the detection rate after some time. Using this
information, we defined a time cutoff value after which we considered that the
detector unit functions satisfyingly.

Since the background level is different for each PMT and each shot, we also
had to set new more adapted thresholds. To do so, we first directly looked at
the traces and choose as threshold the half of the mean height of the noise.
After that, we tried to improve those thresholds by looking at the histogram
where the number of peaks was represented according to its energy, and have
the neutron peak as clear as possible above the background. The result of this
exercise can be seen in Fig.6b for the different laser configurations.

Figure 6: a) Proton spectra for three shots with equivalent laser parameters
(the South beam focal spot is $\sim$150 $\mu$m), one with a solid vanadium
secondary target, one without and one with a vanadium secondary target heated
by the 100 J ns-duration laser beam. b) Histograms of the light collected by
the detector unit 15 according to the energy during those three shots. All
peaks detected before 340 $\mu$s are excluded from those histograms.

####  3.2.3 Input of Geant4 simulations

We used Geant4 Geant4  simulations to calculate the information needed in
order to retrieve an actual number of emitted neutrons from the number of
detected neutrons, namely (i) the total efficiency of the neutron detector for
a given neutron spectrum, and (ii) the temporal evolution of the detection
rate. The neutron energy spectra during the shots were calculated using the
measured proton spectra and TALYS package tendl , and are shown in Fig.7a. The
detector setup has been reproduced in the simulations. A 10 million events
simulation was done to retrieve a simulated efficiency for each neutron
spectrum. These efficiencies were compared to the efficiency of the detector
calculated with Geant4 using the spectrum of the PuBe neutron source used for
the calibration (shown in Fig.7b) lelasseux2021design , and to the actual
measured efficiency with the source. The PET shield and lead shield that can
be seen in the middle of the detector array were removed for the simulations
using the PuBe neutron source since that calibration stage was done without
the presence of those shields.

Figure 7: a) Neutron spectrum calculated from the measured proton spectrum
using the TENDL datatendl , for the two hot shots 52 and 55 and the two cold
shots 28 and 44. b) Neutron spectrum of the PuBe neutron source used for the
calibration according to Söderström et al. soderstrom2021characterization .

In order to use accurate cross-sections for scattering and nuclear reactions
for neutrons below 20 MeV, we used the NeutronHP physics list. To handle more
generic interactions, we also used the physics lists G4DecayPhysics,
G4RadioactiveDecayPhysics and G4EmStandardPhysics. Material descriptions are
presented in Ref.lelasseux2021design . We only considered the deposited energy
in the scintillator and not the production of light since attempts to do so
using Geant4 have been shown to lead to underestimations CompositionEJ254 ;
amare2019boronated . Hence, we considered the Q-value peak, i.e. the energy
depositions between 2310 and 2320 keV, as representative of the efficiency. We
also considered the neutron sources to be isotropic since the difference
between the maximum and minimum calculated angular neutron fluence was only
around 3%.

During the calibration (which was performed after the experiment), we noticed
that, contrary to what happened during the experiment, the detector units 1
and 15 presented a significant noise level which prevented most of the neutron
detections. Hence, we used simulations with a neutron source corresponding to
the PuBe neutron spectrum to retrieve a credible efficiency during the
experiment for those two units. The detector unit efficiencies are calculated
using the following equations :

$\displaystyle Eff_{unit}=$ $\displaystyle Eff_{sum}\frac{h_{unit}}{h_{sum}}$
(1) $\displaystyle Err_{unit}=$ $\displaystyle
Err_{sum}*\frac{h_{unit}}{h_{sum}}+Eff_{sum}*\frac{\sqrt{h_{unit}}}{h_{sum}}$
(2) $\displaystyle+Eff_{sum}*\frac{h_{unit}}{h_{sum}^{2}}*\sqrt{h_{sum}}$

Where Effunit is the calculated efficiency for a given unit for the PuBe
neutron source, Effsum is the sum of measured efficiencies for all detector
units except 1, 8 and 15, hunit and hsum the 2310-2320 keV peak height
obtained during simulations with a given number of events respectively for one
detector unit and for all detector units except 1, 8 and 15, and Errunit and
Errsum are the errors associated respectively to Effunit and Effsum. The
calculated and measured efficiencies for all detector units for the PuBe
neutron source are presented in Fig.8. From now on, the measured efficiencies
for detector units 1 and 15 are replaced by the calculated ones.

Figure 8: Efficiencies of each detector unit for the PuBe neutron source. The
measured efficiencies obtained during calibration are presented in red. The
efficiencies calculated thanks to the Geant4 simulations are presented in
black for detector units 2 to 14 and in blue for detector units 1 and 15.

Using the efficiency related to the PuBe neutron source and the Geant4
simulations presented earlier, we can then calculate efficiencies for each
detector unit according to the expected neutron spectrum (showed in Fig.7a).
The efficiency values and associated errors have been calculated using the
following equations:

$\displaystyle Eff_{shot}=$ $\displaystyle
Eff_{calib}*\frac{h_{shot}}{h_{calib}}$ (3) $\displaystyle Err_{shot}=$
$\displaystyle
Err_{calib}*\frac{h_{shot}}{h_{calib}}+Eff_{calib}*\frac{\sqrt{h_{shot}}}{h_{calib}}$
(4)
$\displaystyle+Eff_{calib}*\frac{h_{shot}}{h_{calib}^{2}}*\sqrt{h_{calib}}$

Where Effshot is the calculated efficiency for a given shot, Effcalib the
efficiency related to the PuBe neutron source, hshot and hcalib the 2310-2320
keV peak height obtained during simulations with a given number of events and
with a neutron emission spectrum corresponding to respectively a shot or the
PuBe neutron source, and Errshot and Errcalib are the errors associated
respectively to Effshot and Effcalib. Those efficiencies are presented in
Table.1.

Detector unit | PuBe source | Shot 28 | Shot 44 | Shot 52 | Shot 55
---|---|---|---|---|---
1 | 0.192(27) | 0.297(48) | 0.295(48) | 0.303(49) | 0.292(48)
14 | 0.390(44) | 0.372(49) | 0.368(48) | 0.369(48) | 0.358(47)
15 | 0.289(41) | 0.311(50) | 0.315(51) | 0.322(52) | 0.317(51)
All | 4.78(62) | 8.49(125) | 8.53(126) | 8.65(128) | 8.36(124)
Table 1: Calculated efficiencies for every detector unit and shot of interest.
Shots 28 and 44 are cold vanadium target shots, while for shots 52 and 55, the
vanadium target is ionized.

In order to accurately determine the temporal evolution of the detection rate
after hundreds of $\mu$s, we needed to simulate more events. Using the shot 28
spectrum, we simulated the emission of 180 million neutrons. We decided to use
the same temporal evolution for all shots. This temporal evolution and its
equation are shown in Fig.9 for the first 300 $\mu$s.

Figure 9: Histogram of energy deposition between 2310 and 2320 keV according
to the time of the last interaction depositing energy, from 0 to 300 $\mu$s,
according to a Geant4 simulation Geant4 . The red curve represents the fit and
the equation written above corresponds to this fit. The zoom-in view shows the
first 100 ns and especially the peak representing mainly events where the
neutron capture took place without any rebound in the HDPE.

Using this temporal evolution and the calculated efficiencies, it is possible
to retrieve from the count of events in the neutron peaks, like the ones shown
in Fig.6b, the number of neutrons produced in the vanadium foil during a shot,
using Eqs.5 and 6.

$\displaystyle n_{unit/shot}=$
$\displaystyle\frac{N_{unit/shot}-N_{unit/background}}{Eff_{unit/shot}}*\frac{f(1)}{f(1)-f(t_{cutoff})}$
(5) $\displaystyle errn_{unit/shot}=$
$\displaystyle\frac{\sqrt{N_{unit/shot}}+errN_{unit/background}}{Eff_{unit/shot}}*\frac{f(1)}{f(1)-f(t_{cutoff})}$
$\displaystyle+\frac{N_{unit/shot}-N_{unit/background}}{(Eff_{unit/shot})^{2}}*\frac{f(1)}{f(1)-f(t_{cutoff})}*\sqrt{Eff_{unit/shot}}$
(6)

Where nunit/shot is the number of neutrons produced during the shot as
detected by the detector unit, Nunit/shot the count of events in the neutron
peak for the detector unit during the shot, Nunit/background the mean count of
events in the neutron peak for the detector unit during background shots and
errNunit/background the associated error, Effunit/shot the efficiency of the
detector unit according to the neutron spectrum calculated for the shot, f(t)
is the integral from 0 to t of the histogram represented in Fig.9 with t in
ms, tcutoff is the cutoff time used in ms and errnunit/shot is the error
associated to nunit/shot. As shown in Eq.6, we did not take into account the
error induced by the simulated time evolution of the detection rate. Due to
the high statistic in the simulations, this error is negligible compared to
the other sources of error.

##  4 Results

Retaining only the six shots for which the proton spectra were similar (see
examples in Fig.6a) and the detectors for which every corresponding trace was
usable, we find the results presented in Tables 2 and 3. During the hot shots
52 and 55, the North beam delivered 100 J on the target.

Detector | Peak | Time | Background shots | Cold shots | Hot shots
---|---|---|---|---|---
unit | Emin | Emax | cutoff ($\mu$s) | s27 | s37 | s28 | s44 | s52 | s55
1 | 80 | 180 | 370 | 17 | 19 | 53 | 72 | 62 | 74
14 | 60 | 160 | 380 | 13 | 69 | 225 | 229 | 73 | 102
15 | 80 | 210 | 230 | 54 | 129 | 403 | 427 | 132 | 275
Table 2: Neutron detection counts for a given set of analysis parameters for the shots of interest. For the analysis parameters, delimitation of the neutron peak and time cutoffs are presented in this table. Detector | Cold shots | Hot shots
---|---|---
unit | s28 | s44 | s52 | s55
1 | 6.2(30)x105 | 9.6(31)x105 | 7.6(46)x105 | 1.00(53)x106
14 | 2.81(72)x106 | 2.90(79)x106 | 4.9(38)x105 | 9.7(48)x105
15 | 1.57(42)x106 | 1.67(45)x106 | 2.0(16)x105 | 9.1(30)x105
Estimation | 2.56x106 | 1.96x106 | 1.62x106 | 4.19x106
Table 3: Total number of emitted neutrons according to the measurement of each
detector unit for each shot when using conservative parameters. The last row
presents estimations based on the measured proton spectra and experimental
cross-sections extrapolations from experimental measurementsamare2019boronated
.

It is important to compare the measured number of neutrons with the
estimations we can calculate from the measured proton spectrum. Cross-sections
from TENDL tendl  tend to be overestimated for low energies, hence, we decided
to use cross sections extrapolated from experimental measurements
amare2019boronated  to get a precise number of produced neutrons.

Using such cross-sections, we calculate the number of neutrons that should
have been produced in the secondary vanadium target. Those estimations are
shown in the last row of Table.3 and the ratio of the measurements over the
neutron production expectations is plotted in Fig.10. Note that the fact that
we used calculated efficiencies for detector unit 1 and 15 does not affect the
final result, which is the ratio of neutrons emitted from solid versus plasma
targets. As can be seen in Table.3 and Fig.10, there is a good match between
the measurements and expectations for the cold shots. This would tend to
validate our methodology. We observed however a significant drop of produced
neutrons from the ionized vanadium target, that is compared to what could be
expected using the same (p,n) reaction cross-section.

Figure 10: Ratio of the total number of emitted neutrons inferred from the
measurements, over the estimated neutron production according to the measured
proton spectrum, vs the angle of the detector unit from the picosecond South
laser direction.

##  5 Discussion

We will now discuss various potential reasons that could lead to the observed
low number of neutrons in the case where the vanadium target is ionized. A
first explanation could be a geometrical effect: as the vanadium target
expands in vacuum, and as the proton beam is also expanding conically from its
source targetbolton2014instrumentation  (as illustrated in Fig.1), there will
be a reduced amount of vanadium ions that will be intercepted by the protons,
compared to the cold case. We estimated quantitatively this effect by doing
hydrodynamic simulations of the target expansion using MULTI, conducted in the
conditions of the experiment. Using these, we could calculate how many
vanadium ions are seen by the proton beam. This led to a $\sim$9.1% decrease
in ions seen by the proton beam in the hot case compared to the cold case.
Hence, this cannot explain our observation.

Secondly, we evaluated how much the ionization of the vanadium target could
influence the screening of the (p,n) reaction. For this, we estimated the
ionization state of the target. As the signal was too low on our X-ray
spectrometer for our shot conditions, we raised the North beam energy to 600 J
on specific shots, in order to measure the heated vanadium target emission.
For these, we measured, at the laser-solid interface, that the heated plasma
had a 1021 cm-3 electron density and a temperature between 1130 and 1200 eV.
According to the NIST Atomic Spectra Databasenist , 1.2 keV corresponds to an
ionization rate of 16 for vanadium, the corresponding ionization energy being
1165.2 eV. These values allowed us to anchor our MULTI simulations.

Then, we used MULTI simulations scaled down to our irradiation conditions (100
J) to determine the actual density and ionization level for the shots we
analyzed.

Using this density and ionization level, we were able to calculate the
evolution of the mean ionization of the target in time. Notably, approximately
2 ns after the start of irradiation by the North beam, this mean target
ionization reaches a maximum in time of 12.54. We will consider this maximum
value as our ionization in the following in order to look for the maximum
possible effect.

Now, accounting for this target ionization of 12.54, we evaluated how this
would impact our neutron production, according to the standard theory
salpeter1954electron ; cvetinovic2014electron . Following it, it would lead to
a change of 0.01% of the neutron yield, clearly insufficient to account for
the observed reduction in the hot plasma. However, several publications
rolfs1995status ; cvetinovic2020electron ; bystritsky2014experimental  present
experimental results which suggest that the screening potential value is
strongly underestimated by the standard theory. In this frame, Lipoglavsek and
Cvetinovic lipoglavsek2020electron  proposed an empirical formula to calculate
the screening potential value following Eq.7.

$U_{e}=Z^{2}*U_{0}$ (7)

Where Ue is the screening potential, U0=0.8 keV is the maximum electron
screening potential measured for the 2H(d,p)3H reaction and Z is the
electronic cloud charge of the target nucleus. Using this equation, we found
new values for the screening potential, of 423.2 keV for the solid vanadium
and 87.5 keV for for an ionization of 12.54. This implies a much greater
change in the neutron production. The corresponding new estimations for
neutron production are given in the second row of Table.4.

Taking into account a strong screening effect reduces the difference observed
between the hot and cold shots, as can be seen by comparing the first two rows
of Table.4, but it is not enough to fully explain it.

Finally, we also considered the difference in stopping power in a plasma or a
solid. Since the foil is only 1 $\mu$m thick, we neglected this effect on the
measurement of the proton spectrum until now. Since the proton stopping power
in a plasma depends on many parameters, we can consider an extreme case to see
if this can explain the difference between the hot and the cold shots. We take
into account on one side the stopping power in the solid vanadium according to
SRIM SRIM  to rebuild a more accurate emitted proton spectrum. Indeed, since
the proton spectrum measurement is performed after passing through the target,
the measured proton spectrum is not exactly the same as the emitted one. On
the other hand, we consider, as an extreme case, the stopping power in the
vanadium in a plasma state as null. Taking into account the important
screening potential, the stopping power difference in this extreme case and
the plasma expansion, we found the new estimations in the neutron production
shown in the fourth row of Table.4.

As it could be expected, this does not change the resulting ratios
significantly and, again, this cannot explain the measured difference between
the hot and the cold shots (compare the third and fourth rows of Table.4).

Assumptions | Cold shots | Hot shots
---|---|---
| s28 | s44 | s52 | s55
Experimental Cross Section (ECS) amare2019boronated  | 2.56x106 | 1.96x106 | 1.62x106 | 4.19x106
ECS + Electron Screening (ES) lipoglavsek2020electron  | 3.16x106 | 2.47x106 | 2.22x106 | 4.87x106
ECS + ES + Stopping Power (SP) | 3.12x106 | 2.43x106 | 2.22x106 | 4.87x106
ECS + ES + SP + Plasma Expansion | 3.12x106 | 2.43x106 | 2.02x106 | 4.43x106
Experimental data | 0.62-2.81 | 0.96-2.90 | 2.0-7.6 | 9.1-10.0
(range over detectors 1, 14, 15) | x106 | x106 | x105 | x105
Table 4: Estimations of neutron production for the four shots of interest
depending on different sets of assumptions, each set containing the
assumptions on the line above and a new one, and summary of the experimental
measurements (bottom row).

##  6 Conclusion

Using the unique capabilities of laser facilities such as LULI2000, we aimed
to investigate the influence of the ionization level in plasmas on a nuclear
reaction. To do so, we used a (p,n) reaction and a high efficiency neutron
detector. The measurements done for the shots with non-ionized solid target
gave satisfactory results in the expected range, based on current experimental
knowledge. However, we observed an unexpectedly large drop in the neutron
production when the target was ionized. We have shown that classical electron
screening, plasma effect on the stopping power or plasma expansion are not
enough to explain this decrease, which is yet to be explained.

##  7 Acknowledgments

We acknowledge discussions with I. Pomerantz (Tel-Aviv University) and B. Qiao
(Peking University). The authors acknowledge the expertise of the LULI2000
laser facility staff. This work was supported by funding from the European
Research Council (ERC) under the European Unions Horizon 2020 research and
innovation program (Grant Agreement No. 787539, Project GENESIS) and by Grant
No. ANR-17-CE30-0026-Pinnacle from the Agence Nationale de la Recherche. We
acknowledge, in the framework of Project GENESIS, the support provided by
Extreme Light Infrastructure Nuclear Physics (ELI-NP) Phase II, a project co-
financed by the Romanian Government and the European Union through the
European Regional Development Fund, and by the Project No. ELI-RO-2020-23,
funded by IFA (Romania), and by the Romanian Ministry of Research and
Innovation under research contract PN 23 21 01 06, to design, build, and test
the neutron detectors used in this project.

##  8 Data Availability

All data needed to evaluate the conclusions in the paper are present in the
paper. Experimental data are archived on servers at LULI and are available
from the corresponding author upon reasonable request.

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