# Stellar 30-keV neutron capture in 94,96Zr and the 90Zr$(\gamma,n)^{89}$Zr
photonuclear reaction with a high-power liquid-lithium target

M. Tessler  Racah Institute of Physics, Hebrew University, Jerusalem, Israel
91904 M. Paul  Racah Institute of Physics, Hebrew University, Jerusalem,
Israel 91904 A. Arenshtam  Racah Institute of Physics, Hebrew University,
Jerusalem, Israel 91904 Soreq NRC, Yavne, Israel 81800 G. Feinberg  Racah
Institute of Physics, Hebrew University, Jerusalem, Israel 91904 Soreq NRC,
Yavne, Israel 81800 M. Friedman  Racah Institute of Physics, Hebrew
University, Jerusalem, Israel 91904 S. Halfon  Racah Institute of Physics,
Hebrew University, Jerusalem, Israel 91904 Soreq NRC, Yavne, Israel 81800 D.
Kijel  Soreq NRC, Yavne, Israel 81800 L. Weissman  Soreq NRC, Yavne, Israel
81800 O. Aviv  Soreq NRC, Yavne, Israel 81800 D. Berkovits  Soreq NRC, Yavne,
Israel 81800 Y. Eisen  Soreq NRC, Yavne, Israel 81800 I. Eliyahu  Soreq NRC,
Yavne, Israel 81800 G. Haquin  Soreq NRC, Yavne, Israel 81800 A. Kreisel
Soreq NRC, Yavne, Israel 81800 I. Mardor  Soreq NRC, Yavne, Israel 81800 G.
Shimel  Soreq NRC, Yavne, Israel 81800 A. Shor  Soreq NRC, Yavne, Israel 81800
I. Silverman  Soreq NRC, Yavne, Israel 81800 Z. Yungrais  Soreq NRC, Yavne,
Israel 81800

## Abstract

A high-power Liquid-Lithium Target (LiLiT) was used for the first time for
neutron production via the thick-target 7Li$(p,n)^{7}$Be reaction and
quantitative determination of neutron capture cross sections. Bombarded with a
1-2 mA proton beam at 1.92 MeV from the Soreq Applied Research Accelerator
Facility (SARAF), the setup yields a 30-keV quasi-Maxwellian neutron spectrum
with an intensity of 3-5 $\times 10^{10}$ n/s, more than one order of
magnitude larger than present near-threshold 7Li$(p,n)$ neutron sources. The
setup was used here to determine the 30-keV Maxwellian averaged cross section
(MACS) of 94Zr and 96Zr as $28.0\pm 0.6$ mb and $12.4\pm 0.5$ mb respectively,
based on activation measurements. The precision of the cross section
determinations results both from the high neutron yield and from detailed
simulations of the entire experimental setup. We plan to extend our
experimental studies to low-abundance and radioactive targets. In addition, we
show here that the setup yields intense high-energy (17.6 and 14.6 MeV) prompt
capture $\gamma$ rays from the 7Li$(p,\gamma)^{8}$Be reaction with yields of
$\sim 3\times 10^{8}$ $\gamma$/s/mA and $\sim 4\times 10^{8}$ $\gamma$/s/mA,
respectively, evidenced by the 90Zr$(\gamma,n)^{89}$Zr photonuclear reaction.

Keywords: 7Li$(p,n)$, high-intensity neutron source, Maxwellian Averaged Cross
Section (MACS), 94,96Zr$(n,\gamma)$, 90Zr$(\gamma,n)$

The availability of high-intensity (mA range) linear accelerators [1, 2] and
the recent commissioning of the high-power (kW range) Liquid-Lithium Target
(LiLiT [3, 4]) pave the way to a new generation of experimental investigations
in nuclear physics and astrophysics. The 7Li$(p,n)^{7}$Be reaction just above
the 7Li$(p,n)$ threshold (Ep = 1.880 MeV) has been traditionally used to
produce neutrons in the epithermal energy regime; the thick-target angle-
integrated neutron yield is known to have an energy distribution similar to
that of a flux of Maxwellian neutrons $v\cdot dn_{MB}/dE_{n}\propto
E_{n}exp(-E_{n}/kT)$ at $kT\sim 25$ keV [5]. It has been used in particular
for the study of $s$-process nucleosynthesis (see [6] for a review) but the
neutron yield ($\lesssim 10^{9}$ n/s) was so far limited by the beam power
dissipation in a solid Li (or Li-compound) target. An increase in available
neutron intensity and flux is considered an important goal [7] in order to
extend experimental investigations to low-abundance and radioactive targets.
We report here on first activation measurements of neutron capture cross
sections by activation and their extrapolation to Maxwellian-Averaged Cross
Sections (MACS) in stable Zr isotopes using the high-intensity (1-2 mA)
continuous-wave proton beam from the superconducting linear accelerator SARAF
[2] and the Liquid-Lithium Target (LiLiT [3, 4]). The neutron yield of
$\sim$3-5$\times 10^{10}$ n/s is 30-50 times larger than in existing
facilities based on the near-threshold 7Li$(p,n)$ reaction for neutron
production. Preliminary results of these experiments were reported recently
[8, 9]. The choice of a natZr target for these first experiments was motivated
by the importance of the Zr isotopes along the path of $s$-process
nucleosynthesis [6]. Notably, Zr isotopic anomalies (relative to Solar
abundances) detected in presolar grains are attributed to materials
synthesized by the $s$-process at various stages of He core and inter-shell
burning in Asymptotic Giant Branch stars, contributing a complex patchwork of
nucleosynthesis information [10, 11]. A detailed analysis of these data in
terms of astrophysical models [12, 13] emphasizes the importance of the
$s$-process neutron capture cross sections in this region of nuclides; several
sets of experimental values of the neutron capture cross sections are
available in the literature [14, 15, 16, 17, 18, 19, 20, 21, 22]. It was also
shown recently [23] that the ratio of Zr to Nb abundances,
$\frac{N(Zr)}{N(Nb)}$, in $s$-process enriched stars (S-stars) can be used to
estimate the relevant stellar temperatures. We report here on new MACS ($kT$ =
30 keV) determinations for the 94,96Zr isotopes. In our experiments, the
liquid-lithium target bombarded by a high-intensity proton beam yields also
intense ($\sim$ 7$\times 10^{8}$ $\gamma$/s/mA) high-energy prompt gamma rays
(17.6 and 14.6 MeV) from the 7Li$(p,\gamma)^{8}$Be capture reaction, evidenced
by activation through the 90Zr$(\gamma,n)^{89}$Zr photonuclear reaction.

The Liquid-Lithium Target (LiLiT) consists of a film of liquid lithium ($\sim
200\degree$C), 1.5 mm thick and 18 mm wide, forced-flown at high velocity
($\sim$ 2-5 m/s) onto a concave thin (0.3 mm) stainless steel wall by an
electromagnetic induction pump (fig. 1; see [3] for details of the target
design). The (windowless) lithium film, bombarded by a $\sim$1-2 mA proton
beam (E${}_{p}\sim$ 1.92 MeV) from the SARAF accelerator [2] acts as both the
neutron-producing target and the power beam dump for the mA-proton beam
($\sim$ 2-3 kW) by fast transport of the liquid lithium to a reservoir and
heat exchanger.

Figure 1:  Detail diagram of the Liquid-Lithium Target (LiLiT) and activation
target assembly. The (1-2 mA, $\sim$10 mm diameter) proton beam (dashed red
arrow) impinges on the free-surface lithium film (yellow ellipse). The solid
blue arrows show the inlet and outlet of the external circulating loop (see
[3] for details). The activation target sandwich (Au-Zr-Au) is mounted on a
circular holder and positioned in the outgoing neutron cone (green dotted
lines) at a distance of 6-8 mm from the lithium surface in a vacuum chamber
separated from the LiLiT chamber by a 0.5 mm stainless steel wall convex to
the beam. The retractable shaft (at left) is used to load and unload rapidly
the target assembly.

With the proton beam focused transversally to an approximate radial Gaussian
distribution ($\sigma_{r}\sim$ 2.8 mm) in order to increase the neutron output
flux, the power volume density continuously deposited by the beam at the Bragg
peak depth ($\sim$ 170 $\mu$m) in the liquid lithium is of the order of 1
MW/cm3 [3] while maintaining stable temperature and vacuum conditions with a
lithium flow velocity of $\sim$2.5 m/s. In the experiments described here, we
activated a natZr target positioned in a separate vacuum chamber behind a thin
stainless wall (0.5 mm) of opposite curvature to that of the liquid-lithium
duct (fig. 1), reducing thus the distance from the neutron source; the
distance of the 25-mm diameter Zr target can be as small as $6\pm 1$ mm,
intercepting a large fraction ($>90\%$) of the outgoing neutrons. Table 1
lists the activation conditions in three independent runs and their results.
In each activation run, the Zr target was tightly sandwiched by two Au foils
of the same diameter serving as neutron fluence monitors by off-line $\gamma$
counting of the 198Au activity. A $\gamma$ autoradiograph of the activated Au
foils [8] allowed us to determine the centering of the neutron beam relative
to the target assembly; correction for a slight misalignment ($\sim$2-3.5 mm),
observed in the different experiments and due to the difficulty in precise
steering of the high-intensity proton beam, was taken into account in the
analysis. The proton beam energies, measured with concordant results by
Rutherford back scattering off a Au target after the acceleration module and
by a time-of-flight pick-up system, were found to be slightly different in the
three experiments (see Table 1) due to different tuning of the linear
accelerator. In some of the experiments, the energy calibration was confirmed
by a scan of the narrow 13C$(p,\gamma)$ resonance ($E_{p}(lab)=1.746$ MeV) and
the 7Li$(p,n)$ threshold region. A beam energy spread of $\sim$15 keV,
estimated from beam dynamics calculations, was verified experimentally [9].
The activities of the Zr targets were measured (fig. 2) in the same geometry
as the Au monitors with a High-Purity Ge (HPGe) detector and corrected for
decay, line intensity, self-shielding and photopeak efficiency to extract the
number of 95,97Zr and 198Au products (Supp. mat.). In the experiments, two
different HPGe detectors (respectively shielded and unshielded) were used.

Figure 2:  $\gamma$-ray spectrum obtained by measuring the Zr sample for
226348 s, starting 83700 s after end of Exp i@ (see Table 1) with a shielded
HPGe. The photo-peaks from the decay of the activated Zr isotopes and
daughters are labeled in keV.

Characterization of the activation data in terms of a cross section requires
knowledge of the neutron spectrum seen by the targets. The integral neutron
spectrum seen by a target under the conditions of the current experiment is
however not measurable and we rely for its shape on detailed simulations using
the codes SimLiT [24] for the thick-target 7Li$(p,n)$ neutron yield and GEANT4
[25] for neutron transport (fig. 3a). The SimLiT-GEANT4 simulations have been
carefully benchmarked in a separate experiment [26] and excellent agreement
with experimental time-of-flight and (differential and integral) energy
spectra was obtained [26, 24]. We also measured the neutron time-of-flight
spectrum (fig. 3b) with the present LiLiT setup using a 1-inch thick 6Li-glass
detector positioned at 0$\degree$ at a distance of 180 cm downstream of the
lithium target and a chopped proton beam (200 ns width). Despite extensive
scattering of neutrons between source and detector, the SimLiT-GEANT4
simulation is in good agreement with the measured spectrum and confirms its
reliability. The simulated spectrum $\frac{dn_{sim}}{dE_{n}}$ is well fitted
in the range $E_{n}\sim 0-80$ keV by a Maxwell-Boltzmann (MB) flux
$v\frac{dn_{MB}}{dE_{n}}\propto E_{n}e^{-\frac{E_{n}}{kT}}$ with $kT\sim 30$
keV (fig. 3a), except for small glitches due to resonances of neutron
reactions in structural materials (Fe, Al, Ni and Cr) having a negligible
contribution to the integral yield. The AZr$(n,\gamma)$ cross sections
directly determined in the experiment (Table 1), averaged over the neutron
spectrum, are obtained from the expression

$\sigma_{exp}(A)=\sigma_{ENDF}(\textrm{Au})\frac{N_{act_{exp}}(A+1)}{N_{act_{exp}}(\textrm{Au})}\frac{n_{t}(\textrm{Au})}{n_{t}(A)}\frac{f(\textrm{Au})}{f(A)}$
(1)

where $N_{act_{exp}}(A+1)$ ($N_{act_{exp}}(\textrm{Au})$) is the number of
(A+1)Zr (198Au) activated nuclei determined experimentally, $n_{t}(A)$
($n_{t}(\textrm{Au})$) is the AZr (Au) target thickness (atom/cm2) and $f(A)$
($f(\textrm{Au})$) accounts for the decay of activated nuclei during the
activation time and variations in the neutron rate (see Supp. mat.). In (1),
we use as reference a 197Au$(n,\gamma)$ cross section

$\sigma_{ENDF}(\textrm{Au})=\frac{\int\sigma_{ENDF}(E_{n};\textrm{Au})\frac{dn_{sim}}{dE_{n}}dE_{n}}{\int\frac{dn_{sim}}{dE_{n}}dE_{n}}.$
(2)

In (2), $\sigma_{ENDF}(E_{n};\textrm{Au})$ is taken from the ENDF/B-VII.1
(USA,2011) [27] library for 197Au. The latter library (denoted henceforth
ENDF) was extensively validated for 197Au [28, 29] and especially in the
neutron energy range relevant to our measurements [26, 30] and serves here for
neutron fluence normalization.

Figure 3: (a) Simulated neutron spectrum
$\left(\frac{dn_{sim}}{dE_{n}}\right)$ impinging on the Zr target (Exp. ii@)
(dots) and fit (solid line) of a Maxwell-Boltzmann flux (see text). (b)
neutron time-of-flight spectrum (black) measured with a 200 ns-wide chopped
proton beam and a $1^{\prime\prime}$-thick 6Li-glass detector at a distance of
180 cm from the liquid-lithium target. The separated group at the right-end of
the experimental spectrum results from prompt 478-keV $\gamma$ rays from
7Li$(p,p^{\prime})$. The spectrum obtained from a simulation of the entire
experimental system using the SimLiT-GEANT4 codes is shown in red and
reproduces closely the main neutron group. The neutron group around channel
550, observed in both the experimental and simulated spectrum is due to the
n+56Fe resonance at $E_{n}$ = 26 keV (see (a)) and extensive neutron
interactions in the stainless steel flanges between target and detector. The
simulated spectrum, calculated in absolute time-of-flight units (ns), is
converted into channels relative to the gamma peak starting at t=6 ns; its
ordinate (counts/channel/mC) is calculated based on the proton charge
accumulated in the measurement with no further normalization. Neutrons
observed at large time-of-flight values are attributed to scattering off
materials outside the scope of the simulation.

In order to extrapolate the activation results and extract experimental MACS
values we use available neutron cross section libraries, corrected by our
activation data in the measured energy range, and detailed SimLiT-GEANT4
simulations of the setup. The MACS of a reaction at the temperature $T$ of an
astrophysical site is defined as

$MACS(kT)=\frac{\Braket{\sigma
v}}{v_{T}}=\frac{2}{\sqrt{\pi}}\frac{\intop_{0}^{\infty}\sigma(E_{n})E_{n}e^{-\frac{E_{n}}{kT}}dE_{n}}{\intop_{0}^{\infty}E_{n}e^{-\frac{E_{n}}{kT}}dE_{n}}$
(3)

where $\sigma(E_{n})$ is the true energy-dependent reaction cross section. We
determine here an experimental value MACS${}_{lib}^{exp}$ of the radiative
neutron capture $(n,\gamma)$ for the target nucleus AZr (A = 94,96) using the
expression:

$\textrm{MACS}_{lib}^{exp}(A;kT)=\frac{2}{\sqrt{\pi}}\frac{\intop_{0}^{\infty}C_{lib}(A)\sigma_{lib}^{A}(E_{n})E_{n}e^{-\frac{E_{n}}{kT}}dE_{n}}{\intop_{0}^{\infty}E_{n}e^{-\frac{E_{n}}{kT}}dE_{n}}.$
(4)

In (4), $\sigma_{lib}^{A}(E_{n})$ is the AZr$(n,\gamma)$ cross section given
by a neutron library $lib$ and $C_{lib}(A)$ a correction factor for the
library $lib$ extracted from our activity measurements by the expression

$C_{lib}\left(A\right)=\frac{\left(\frac{N_{act_{exp}}\left(A+1\right)}{N_{act_{exp}}\left(\textrm{Au}\right)}\right)}{\left(\frac{N_{act_{lib}}\left(A+1\right)}{N_{act_{ENDF}}\left(\textrm{Au}\right)}\right)}.$
(5)

In (5), $N_{act_{lib}}(A+1)$ and $N_{act_{ENDF}}$(Au) are the number of
activated A+1Zr and 198Au nuclei obtained in a single overall SimLiT-GEANT4
simulation of the experimental system (including the Au-Zr target sandwich),
using the neutron library $lib$ for AZr. The final results for the MACS (30
keV) of 94,96Zr, listed in Table 1, are extracted using the ENDF library (see
Supp. mat. Table 11 for a comparison of MACS values using extrapolation with
different neutron libraries).

Table 1: Experimental parameters ($E_{p}$: proton mean energy and $\Delta E_{p}$: energy spread (1$\sigma$), $\Delta z$: distance lithium surface-activation target and accumulated proton charge during the activations), experimental cross sections (multiplied by $\frac{2}{\sqrt{\pi}}$) and MACS (30 keV) values determined in this work for 94,96Zr (see text and Supp. mat.). The final value of the MACS is obtained by an unweighted average of the three experiments and the uncertainty is determined based on the individual uncertainties taking into consideration their systematic component. Exp | $E_{p}\pm\Delta E_{p}$ | $\Delta z$ | charge | Isotope | $\frac{2}{\sqrt{\pi}}\sigma_{exp}$ | $C_{ENDF}$ | MACS${}_{ENDF}^{exp}$
---|---|---|---|---|---|---|---
| (keV) | (mm) | (mA$\cdot$h) |  | (mb) |  | (mb)
i@ | $1908\pm 15$ | 8 | 1.1 |  94Zr | $29.9\pm 0.8$ | $0.98\pm 0.03$ | $28.7\pm 0.8$
96Zr | $13.6\pm 0.7$ | $1.22\pm 0.08$ | $12.6\pm 0.8$
ii@ | $1917\pm 15$ | 6 | 1.1 |  94Zr | $28.2\pm 0.8$ | $0.96\pm 0.03$ | $27.9\pm 0.8$
96Zr | $13.4\pm 0.5$ | $1.18\pm 0.04$ | $12.1\pm 0.5$
iii@ | $1942\pm 15$ | 6 | 1.5 |  94Zr | $24.5\pm 0.7$ | $0.93\pm 0.03$ | $27.3\pm 0.7$
96Zr | $12.3\pm 0.3$ | $1.20\pm 0.06$ | $12.4\pm 0.6$
unweighted |  |  |  |  94Zr |  |  | $28.0\pm 0.6$
average |  |  |  |  96Zr |  |  | $12.4\pm 0.5$

The values $\frac{2}{\sqrt{\pi}}\cdot\sigma_{exp}$ (which depends on the
proton incident energy via the resulting neutron spectrum) and the MACS (a
property of the nuclide) differ by 4% to 13 %, giving a measure of the
moderate correction involved in the extrapolation to the MACS. Table 2 (and
Supp. mat.) lists the uncertainties in the MACS values determined in one of
our experiments. In order to have a quantitative estimate of the uncertainty
associated with the use of a simulated neutron energy spectrum, we use the
data of [26] as follows. The 7Li$(p,n)$ neutron time-of-flight spectra
measured in [26] in the range $0\degree-80\degree$ and those simulated by
SimLiT-GEANT4 in the conditions of this experiment were converted to energy
spectra using the same algorithm (see [26, 24] for details of algorithm) and
the two resulting spectra were then convoluted with the same energy-dependent
197Au$(n,\gamma)$ ENDF cross section. The resulting averaged cross sections
are 608 mb and 599 mb, respectively and an uncertainty of 1.5% is
correspondingly ascribed to the use of the simulated spectrum for cross
section calculation. An uncertainty component resulting from the proton energy
$E_{p}$ and energy spread $\Delta E_{p}$ was estimated from the change of MACS
values when distributing $E_{p}$ and $\Delta E_{p}$ in their respective range;
we note the insensitivity of the final value to $E_{p}$ and $\Delta E_{p}$.
The uncertainty associated with the use of the ENDF library for the
extrapolation to the MB spectrum was calculated (see Supp. mat. for details)
based on the quoted ENDF (energy-dependent) uncertainties for Au and 94,96Zr
[31].

Table 2: Random (rand) and systematic (sys) relative uncertainties in the MACS
(30 keV) of 94,96Zr for Exp. ii@ (see text and Supp. mat.).

Uncertainty (%) 94Zr 96Zr Source of uncertainty rand sys rand sys target
thickness 0.4 0.4 activated nuclei 1.6 0.6 photopeak eff. rel. to Au 0.5 0.5
simulation 1.5 1.5 Ep, $\Delta$Ep and $\Delta$z 0.4 2.3 $\sigma_{ENDF}$(Au)
1.0 1.0 $\sigma_{ENDF}$(Zr) 1.6 2.2 Total random uncertainty 1.6 0.7 Total
systematic uncertainty 2.5 3.7 Total uncertainty 3.0 3.8

Fig. 4 illustrates a comparison of our results with existing sets of
experimental data for 94,96Zr MACS (30 keV) values. For measurements obtained
by activation [17, 18], values in fig. 4 were corrected for sake of
consistency to the ENDF 197Au$(n,\gamma)$ cross section used in the present
analysis and established since as reference value [28, 29] and for updated
photo-peak intensities used in this work [35, 36] (see Table 4 in Supp. mat.).
We stress the lower uncertainties compared to most experiments, owed to both
the higher neutron intensity and corresponding better counting statistics and
the detailed simulations of the experimental setup.

Figure 4: Comparison of MACS (30 keV) from the literature (black dots) [14,
15, 16, 17, 18, 19, 20, 21, 22] and the present work (red squares) for 94Zr
(top) and 96Zr (bottom). Wyrick et al. and Toukan et al. values [17, 18]
obtained by activation using the 197Au$(n,\gamma)$ cross section as reference
were corrected to the value established in [28, 29] as done in this work. For
96Zr, The open circle value is the value obtained by by Tagliente et al. [21]
from a time-of-flight measurement and the full circle is the value obtained by
adding a direct radiative capture (DRC) component.

We observe in general a slightly larger uncertainty for 96Zr (and also larger
correction factors $C_{lib}$(96)). We expect the present results to be
significant in $s$-process calculations in the Zr region and we note
especially that the lower 96Zr$(n,\gamma)^{97}$Zr MACS value (open circle in
Fig. 4) used recently in the detailed astrophysical model calculations by
Lugaro et al. [13] is inconsistent with our result. This lower value was in
fact corrected in [21] by adding a direct-capture component; the corrected
value (full circle in Fig. 4) is consistent with the present work. Although
the thermal energy of 30 keV considered so far is widely adopted as a
reference point for $s$-process nucleosynthesis, the relevant values for its
“weak” (“main”) regimes are considered to be 90 keV (8 and 23 keV) [6]. Since
Zr lies at the border line between these regimes, we extrapolate our
experimental values for 94,96Zr to these temperatures (see Supp. mat. for
details of these extrapolations). From our analysis, the MACS at 8, 23 and 90
keV for 94Zr (96Zr) are $63.9\pm 3.7$ ($45.3\pm 5.5$), $32.5\pm 1.1$ ($15.6\pm
1.1$) and $18.5\pm 2.1$ ($8.6\pm 1.7$) respectively. The larger uncertainties
are due mainly to the smaller overlap between the experimental neutron
spectrum and the respective MB spectra at temperatures far from 30 keV; they
are based here also on the quoted ENDF energy-dependent uncertainties
$\Delta\sigma_{ENDF}$ (Supp. mat.). Any future update in these uncertainties
could be applied using the same formalism.

An additional feature of the use of a thick liquid-lithium target with a high-
intensity proton beam is the copious production of high-energy $\gamma$ rays
from the radiative capture 7Li$(p,\gamma)^{8}$Be reaction. We observe these
$\gamma$ rays in our experiments via the photonuclear reaction
90Zr$(\gamma,n)^{89}$Zr (fig. 2). No other $(\gamma,n)$ reaction on the natZr
target is readily observable by $\gamma$ spectrometry of the activated target;
we note also that the 96Zr$(\gamma,n)^{95}$Zr reaction (which could
potentially interfere with the 94Zr$(n,\gamma)^{95}$Zr activation) has
negligible yield compared to that of the $(n,\gamma)$ reaction due to the low
96Zr abundance. The 7Li$(p,\gamma)^{8}$Be reaction produces principally 17.6
MeV and 14.6 MeV $\gamma$ rays and their yield was measured in [32] with a
thin Li target. The high-energy $\gamma$ spectrum was measured (Supp. mat.)
with the LiLiT setup in a separate experiment (under neutron threshold) with a
$6^{\prime\prime}\times 4^{\prime\prime}$ NaI(Tl) detector positioned behind a
1.5 m thick concrete wall (shielding the overwhelming 478-keV $\gamma$-rays
from 7Li$(p,p^{\prime}\gamma)$). Using 90Zr$(\gamma,n)^{89}$Zr cross section
values of 173 mb (85 mb) for $E_{\gamma_{0}}=17.6$ ($E_{\gamma_{1}}=14.6$) MeV
(in the Giant Dipole Resonance region) measured in [33] and an averaged
branching ratio $\frac{\gamma_{1}}{\gamma_{0}}\sim 1.3$ obtained by
integrating the data of Zahnow et al. [32] into a thick-target yield between
0.1 $\leq$ $E_{p}$ $\leq$ 1.9 MeV, the respective measured gamma yields are
3$\times 10^{8}$ $\gamma_{0}$/s/mA (4$\times 10^{8}$ $\gamma_{1}$/s/mA). These
yields can be compared with the values 1.2$\times 10^{8}$ $\gamma_{0}$/s/mA
(1.5$\times 10^{8}$ $\gamma_{1}$/s/mA) calculated from the data of [32] and
show a considerable additional yield, possibly due in part to additional
resonances in 8Be for $E_{p}>1.5$ MeV, above the range measured in [32].

In conclusion, we have shown that the high-power Liquid-Lithium Target
bombarded by a mA proton beam, in conjunction with detailed simulations of the
experimental system, allows us precise determination of 30-keV MACS values. In
this first experiment, we determined the 30-keV MACS of 94Zr and 96Zr as
$28.0\pm 0.6$ mb and $12.4\pm 0.5$ mb, respectively. The SARAF-LiLiT facility
is being upgraded in several aspects. Since the LiLiT device is capable of
sustaining higher power levels than those used so far, the primary proton
intensity, presently on average of $\sim$ 1 mA, is being upgraded to 2 mA. The
neutron intensity, intersecting a small target (6 mm diameter) at a typical
distance of 5.5 mm from the liquid Li surface, is estimated as $\sim 3\times
10^{10}$ n/s for a 2-mA proton beam at 1.93 MeV, considered suitable in view
of the energy spread. It is expected that, with gained experience on operation
and control of the accelerator, the beam limitation will be improved towards a
final goal of 4 mA. A pneumatic rabbit is in construction for the transport
(in vacuo) of activation targets with short half-life products (down to a few
seconds). Finally a dedicated target room, designed for the housing of an
upgraded LiLiT-II neutron source, will give more flexibility in the use of the
facility. The system will be particularly useful for neutron activation
measurements of low-abundance isotopes or radioactive targets. As an example,
a measurement of the important 60Fe$(n,\gamma)^{61}$Fe cross section, as
performed in [34], would be possible with a $\sim$100 ng 60Fe radioactive
target or correspondingly, improve the statistical uncertainty with a target
of larger mass. We stress also the possibility to use the present setup (above
or below neutron threshold) for the study of photonuclear reactions in the
Giant Dipole Resonance region with intense yields of $\sim 7\times 10^{8}$
$\gamma/$s/mA from prompt 7Li$(p,\gamma)$ capture $\gamma$ rays, as
demonstrated here with the 90Zr$(\gamma,n)^{89}$Zr photonuclear reaction. The
setup is planned to be used towards investigations of photodissociation and
photofission reactions.

We acknowledge gratefully the support of the Pazi Foundation (Israel) and of
the German-Israeli Foundation (GIF Research Grant No. G-1051-103.7/2009).

## References

  * [1] J. Wei, in Proceedings of IPAC2014, Dresden, Germany, MOYBA01 (2014) 17; available online: http://accelconf.web.cern.ch/AccelConf/IPAC2014/papers/moyba01.pdf.
  * [2] A. Kreisel, et al., in Proceedings of Linac 2014, Geneva (Switzerland), WEIOB02 (2014) 770; and references therein; available online: http://accelconf.web.cern.ch/AccelConf/LINAC2014/papers/weiob02.pdf.
  * [3] S. Halfon, et al., Rev. Sci. Instr. 84 (2013) 12350.
  * [4] S. Halfon, et al., Rev. Sci. Instr. 85 (2014) 056105.
  * [5] W. Ratynski and F. Käppeler, Phys. Rev. C 37 (1988) 595.
  * [6] F. Käppeler, et al., Rev. Mod. Phys. 83 (2011) 157.
  * [7] U. Ratzinger, et al., in Proceedings of of IPAC’10, Kyoto, Japan, MOPEC059 (2010) 597; available online: http://accelconf.web.cern.ch/AccelConf/IPAC10/papers/mopec059.pdf.
  * [8] M. Paul, et al., in Proceedings of the 13th International Symposium on Nuclei in the Cosmos (2014), PoS(NIC XIII)059; available online: http://pos.sissa.it/archive/conferences/204/059/NIC\%20XIII_059.pdf.
  * [9] G. Feinberg, PhD thesis submitted to Hebrew University (2014), unpublished.
  * [10] G. K. Nicolussi, et al., Science 277 (1997) 1281.
  * [11] E. Zinner, Ann. Rev. Earth Planet. Sci. 26 (1998) 147.
  * [12] M. Lugaro, et al., Ap. J. 593 (2003) 486.
  * [13] M. Lugaro, et al., Ap. J. 780 (2014) 95.
  * [14] R. L. Macklin and J. H. Gibbons, Phys. Rev. 159 (1967) 1007.
  * [15] J. W. Boldeman, et al., Nucl. Phys. A 269 (1976) 31.
  * [16] A. de L. Musgrove, et al., in Neutron Physics and Nuclear Data for Reactors and Other Applied Purposes (OECD, Paris, 1978), p. 449.
  * [17] J. Wyrick and W. Poenitz, Technical Report No. ANL-83-4, Argonne National Laboratory, 1983, p. 196.
  * [18] K. A. Toukan and F. Käppeler, Ap. J. 348 (1990) 357.
  * [19] G. Tagliente, et al., Phys. Rev. C 84 (2011) 015801.
  * [20] B. Allen, J. Gibbons, and R. Macklin, Adv. Nucl. Phys. 4 (1971) 205.
  * [21] G. Tagliente, et al., Phys. Rev. C 84 (2011) 055802.
  * [22] I. Dillmann, et al., in Capture Gamma-Ray Spectroscopy and Related Topics, AIP Conference Series 819, edited by A. Woehr and A. Aprahamian (American Institute of Physics, New York, 2005), p. 123; available online: http://www.kadonis.org.
  * [23] P. Neyskens, et al., Nature 517 (2015) 174.
  * [24] M. Friedman, et al., Nucl. Instr. Meth. Phys. Res. A 698 (2013) 117.
  * [25] S. Agostinelli, et al., Nucl. Inst. Meth. A 506 (3) (2003) 250.
  * [26] G. Feinberg, et al., Phys. Rev. C 85 (2012) 055810.
  * [27] M. B. Chadwick, et al., Nucl. Data Sheets 112 (2011) 2887.
  * [28] C. Lederer, et al., Phys. Rev. C 83 (2011) 034608.
  * [29] C. Massimi, et al., Eur. Phys. J. A 50 (2014) 124.
  * [30] C. Lederer, et al., Phys. Rev. C 85 (2012) 055809.
  * [31] R. E. MacFarlane, (2011); available online: http://t2.lanl.gov/nis/data/endf/covVII.1/.
  * [32] D. Zahnow, et al., Z. f. Physik A Hadrons and Nuclei 351 (1995) 229.
  * [33] S. S. Dietrich and B. L. Berman, At. Data Nucl. Data Tables 38 (1988) 199.
  * [34] E. Uberseder, et al., Phys. Rev. Lett. 102 (2009) 151101.
  * [35] H. Xiaolong, Nucl. Data Sheets 110 (2009) 2533.
  * [36] N. Nica, Nucl. Data Sheets 111 (2010) 525.

Supplementary material

##  1 Activation target properties

Table 3: Properties of natZr and 197Au targets used in the LiLiT experiments. The order of the samples listed for each experiment is the order in which the samples were placed downstream the Li target. Exp | Sample | Diameter (mm) | Mass (mg) |  $n_{t}$ ($cm^{-2}$)
---|---|---|---|---
i@ | Au-1 | 24 | 184.0(1) | $1.244(4)\times 10^{20}$
natZr-1 | 24 | 60.80(1) | $8.87(3)\times 10^{19}$
Au-2 | 24 | 185.7(1) | $1.255(5)\times 10^{20}$
ii@ | Au-6 | 25 | 115.85(7) | $7.22(2)\times 10^{19}$
natZr-X | 25 | 312.5(1) | $4.20(1)\times 10^{20}$
Au-7p | 25 | 116.73(6) | $7.27(2)\times 10^{19}$
iii@ | Au-16 | 25 | 116.93(6) | $7.28(2)\times 10^{19}$
natZr-3 | 25 | 312.10(6) | $4.20(1)\times 10^{20}$
Au-17 | 25 | 112.30(6) | $6.84(2)\times 10^{19}$

##  2 Activation results

The number of activated nuclei at the end of the irradiation, $N_{act_{exp}}$,
is obtained from equation (6)

$N_{act_{exp}}=\frac{C}{\epsilon_{\gamma}I_{\gamma}K_{\gamma}}\frac{e^{\lambda
t_{cool}}}{1-e^{-\lambda t_{real}}}\frac{t_{real}}{t_{live}},$ (6)

where $C$ is the number of counts in the photo-peak, $\epsilon_{\gamma}$ is
the detector photoelectric efficiency, $I_{\gamma}$ is the $\gamma$-intensity
per decay, $K_{\gamma}$ is the correction due to $\gamma$-ray self absorption
in the sample. In the case of a disk sample of thickness $x$,
$K_{\gamma}=\frac{1-e^{-\mu x}}{\mu x}$ where $\mu$ is the $\gamma$-ray
absorption coefficient [37]. $\lambda=\frac{ln(2)}{t_{\frac{1}{2}}}$ is the
decay constant of the activated nucleus, $t_{cool}$ is the time between the
end of the irradiation and the activity measurement, $t_{real}$ is the real
measuring time, and $t_{live}$ is the live measuring time. The decay
parameters used in this analysis are listed in Table 4. The $\gamma$-ray
absorption coefficients, $\mu$, used in this analysis were taken from [38].

Table 4: Properties of the relevant target and product nuclei used in this work. Target | natural | Product | Half-life, |  $\gamma$-ray energy, | Intensity per | Ref.
---|---|---|---|---|---|---
nucleus | abundance | nucleus | $t_{\frac{1}{2}}$ |  $E_{\gamma}$ (keV) | decay, $I_{\gamma}$ (%) |
197Au | 1 |  198Au |  $2.6947(3)$ d | $411.80205(17)$ | $95.62(6)$ | [35]
90Zr | 0.5145 |  89Zr |  $78.41(12)$ h | $909.15(15)$ | $99.04(3)$ | [39]
94Zr | 0.1738 |  95Zr |  $64.032(6)$ d | $756.725(12)$ | $54.38(22)$ | [40]
96Zr | 0.028 |  97Zr |  $16.749(8)$ h | $743.36(3)$ | $93.09(16)$ | [36]

The number of activated nuclei at the end of the irradiation, $N_{act_{exp}}$,
obtained from equation (6) are summarized in Table 5.

Table 5: Summary of the number of activated nuclei at the end of the three experiments, $N_{act_{exp}}$. $E_{p}$ is the laboratory proton beam mean energy, $\Delta E_{p}$ the energy spread (1$\sigma$), and $\Delta$z is the Li to target distance. $f(A)$, $f(Au)$ is a correction applied to $N_{act_{exp}}$ to account for the decay of activated nuclei during the activation time ($t_{a}$) and the variations in the neutron rate: $f(A)=\frac{\intop_{0}^{t_{a}}\Phi(t)e^{-\lambda_{A}(t_{a}-t)}dt}{\intop_{0}^{t_{a}}\Phi(t)dt}$ (for a constant neutron flux, $f(A)$ reduces to $f(A)=\frac{1-e^{-\lambda_{A}t_{a}}}{\lambda_{A}t_{a}})$. Exp |  $E_{p}\pm\Delta E_{p}$ (keV) |  $\Delta z$ (mm) | Sample | Nuclei | $N_{act_{exp}}$ |  $f(A)$, $f(Au)$
---|---|---|---|---|---|---
i@ | $1908\pm 15$ | 8 | Au-1 |  198Au | $6.78\pm 0.08\times 10^{9}$ | 0.99
natZr-1 |  95Zr | $3.83\pm 0.05\times 10^{7}$ | 1.0
97Zr | $2.72\pm 0.03\times 10^{6}$ | 0.96
Au-2 |  198Au | $6.73\pm 0.08\times 10^{9}$ | 0.99
ii@ | $1917\pm 15$ | 6 | Au-6 |  198Au | $5.4\pm 0.1\times 10^{9}$ | 0.99
natZr-X |  95Zr | $2.34\pm 0.06\times 10^{8}$ | 1.0
97Zr | $1.75\pm 0.03\times 10^{7}$ | 0.98
Au-7p |  198Au | $5.3\pm 0.1\times 10^{9}$ | 0.99
iii@ | $1942\pm 15$ | 6 | Au-16 |  198Au | $1.26\pm 0.03\times 10^{10}$ | 0.99
natZr-3 |  95Zr | $5.3\pm 0.1\times 10^{8}$ | 1.0
97Zr | $4.18\pm 0.08\times 10^{7}$ | 0.98
Au-17 |  198Au | $1.18\pm 0.03\times 10^{10}$ | 0.99

##  3 Experimental cross section

Table 6: Summary of experimental and ENDF library averaged cross section results. $\sigma_{exp}$ is calculated from Eq. (1), $\sigma_{ENDF}$ is averaged over the simulated neutron spectrum $\frac{dn_{sim}}{dE_{n}}$. $E_{p}$ is the proton beam mean energy and $\Delta E_{p}$ the energy spread (1$\sigma$), $\Delta z$ the distance lithium surface - activation target. Exp |  $E_{p}\pm\Delta E_{p}$ (keV) |  $\Delta z$ (mm) | Isotope |  $\sigma_{exp}$ (mb) |  $\sigma_{ENDF}$ (mb)
---|---|---|---|---|---
i@ | $1908\pm 15$ | 8 |  197Au |  | $583\pm 12$
94Zr | $26.5\pm 0.7$ | $26.8\pm 0.5$
96Zr | $12.1\pm 0.6$ | $9.5\pm 0.2$
ii@ | $1917\pm 15$ | 6 |  197Au |  | $580\pm 12$
94Zr | $25.0\pm 0.7$ | $26.4\pm 0.5$
96Zr | $11.9\pm 0.4$ | $9.9\pm 0.2$
iii@ | $1942\pm 15$ | 6 |  197Au |  | $521\pm 10$
94Zr | $21.7\pm 0.6$ | $23.9\pm 0.5$
96Zr | $10.9\pm 0.3$ | $9.1\pm 0.2$

##  4 Uncertainties

###  4.1 Beam and target parameters

Table 7: Sensitivity of extracted MACS in Exp. ii@ to changes in proton beam energy within its uncertainty range for an energy spread of 15 keV. $E_{p}$ (keV) | MACS (mb)
---|---
|  94Zr |  96Zr
1914 | 27.9 | 12.1
1915 | 27.9 | 12.1
1916 | 27.9 | 12.2
1917 | 27.9 | 12.1
1918 | 27.9 | 12.1
1919 | 28.0 | 12.0
1920 | 28.0 | 11.9
standard deviation | 0.05 | 0.1
Table 8: Sensitivity of extracted MACS in Exp. ii@ to changes in proton beam energy spread within its uncertainty range for Ep=1915 keV. $\Delta$Ep (keV) | MACS (mb)
---|---
|  94Zr |  96Zr
5 | 28.0 | 11.8
10 | 28.0 | 11.9
15 | 27.9 | 12.1
20 | 27.8 | 12.2
25 | 27.9 | 12.2
standard deviation | 0.1 | 0.2
Table 9: Sensitivity of extracted MACS in Exp. ii@ to changes in target distance from lithium surface within its uncertainty range for Ep=1915 keV and an energy spread of 15 keV. $\Delta$z (mm) | MACS (mb)
---|---
|  94Zr |  96Zr
5 | 27.9 | 11.9
6 | 27.9 | 12.1
7 | 28.0 | 12.3
standard deviation | 0.1 | 0.2

###  4.2 Extrapolation to MB distribution

In order to separate the contributions to the MACS uncertainty resulting from
the experimentally measured value $\sigma_{exp}$ and from the extrapolation to
a MB distribution, we express the MACS (30 keV) as:

$\textrm{MACS(30{\
}keV)}=\frac{2}{\sqrt{\pi}}\intop_{0}^{\infty}\phi_{MB}(30)\sigma
dE=\frac{2}{\sqrt{\pi}}\left(\intop_{0}^{\infty}\phi_{exp}\sigma
dE+\intop_{0}^{\infty}\left(\phi_{MB}(30)-\phi_{exp}\right)\sigma dE\right)$
(7)

where $\phi_{MB}(30)$ and $\phi_{exp}$ are the normalized MB and experimental
neutron energy distribution respectively and $\sigma$ is the true energy
dependent cross section. The first term in Eq. (7) is

$\sigma_{exp}=\intop_{0}^{\infty}\phi_{exp}\sigma
dE=C_{ENDF}\intop_{0}^{\infty}\phi_{exp}\sigma_{ENDF}dE$ (8)

(Eq. (1) and (5)) and includes the experimental uncertainties listed in Table
6. The second term in Eq. (7) can be re-written as

$\intop_{0}^{\infty}\left(\phi_{MB}(30)-\phi_{exp}\right)\sigma
dE=C_{ENDF}\intop_{0}^{\infty}\left(\phi_{MB}(30)-\phi_{exp}\right)\sigma_{ENDF}dE$
(9)

and contributes to the uncertainty to the extent that $C_{ENDF}$ determined in
the experimental energy range ($\phi_{exp}$) is not valid in the whole MB
energy range due to uncertainties $\Delta\sigma_{ENDF}$. We obtain thus the
overall uncertainty as

$\Delta\textrm{MACS (30{\ }
keV)}=\frac{2}{\sqrt{\pi}}\sqrt{\Delta\sigma_{exp}^{2}+\left(C_{ENDF}\intop_{0}^{\infty}\left(\phi_{MB}(30)-\phi_{exp}\right)\Delta\sigma_{ENDF}dE\right)^{2}}$
(10)

where $\Delta\sigma_{ENDF}$ are taken from the reported uncertainties for the
ENDF cross section library [31]. Note that we conservatively use here the
quoted $\Delta\sigma_{ENDF}$ although an overall correction ($C_{ENDF}$) was
already applied and that $\Delta\sigma_{ENDF}$ in different energy bins are
added linearly and not in quadrature. The values of $\Delta\textrm{MACS (30{\
} keV)}$ are listed in Tables 2 and 10.

###  4.3 Extrapolation from 30 keV to $kT$ = 8, 23 and 90 keV

Similarly to Eq. (7), The MACS at any energy $kT$ can be denoted as

$\textrm{MACS}(kT)=\frac{2}{\sqrt{\pi}}\intop_{0}^{\infty}\phi_{MB}(kT)\sigma
dE=\frac{2}{\sqrt{\pi}}\left(\intop_{0}^{\infty}\phi_{MB}(30)\sigma
dE+\intop_{0}^{\infty}\left(\phi_{MB}(kT)-\phi_{MB}(30)\right)\sigma
dE\right).$ (11)

The first term is the MACS at 30 keV, so equation (11) can be written as

$\textrm{MACS}(kT)=\textrm{MACS(30{\
}keV)}+\frac{2}{\sqrt{\pi}}\intop_{0}^{\infty}\left(\phi_{MB}(kT)-\phi_{MB}(30)\right)C_{ENDF}\sigma_{ENDF}dE.$
(12)

The uncertainty is therefore given by

$\Delta\textrm{MACS}(kT)=\sqrt{\left(\Delta\textrm{MACS (30{\ }
keV)}\right)^{2}+\left(\frac{2}{\sqrt{\pi}}\intop_{0}^{\infty}\left(\phi_{MB}(kT)-\phi_{MB}(30)\right)C_{ENDF}\Delta\sigma_{ENDF}dE\right)^{2}}.$
(13)

Here again as in Eq. (10), the second term under the square root is an
estimate of the uncertainty due to the fact that the correction $C_{lib}$,
valid in the experimental range (quasi-MB at 30 keV), may not be valid in a
different energy range. This uncertainty estimate is based on the ENDF library
uncertainties [31] in the corresponding energy range. It is also useful to
calculate the $\textrm{MACS}(kT)$ using other neutron libraries [27, 42, 41,
44, 43] with Eq. (12), see Tables 11 and 12. Except for ENDF, the absence of
quoted library uncertainties prevents calculating an associated MACS
uncertainty. We note the close agreement between MACS values from the
different (corrected) libraries at 30 and 23 keV and the expected larger
spread of values for 8 and 90 keV. We adopt as our final values for MACS at 8,
23 and 90 keV the average values of the different libraries and as the
uncertainties the larger between Eq. (13) and the standard deviation between
the libraries (Table 12).

Table 10: Experimental random (rand) and systematic (sys) relative
uncertainties in this work.

| Uncertainty (%)
---|---
| Exp i@ |  | Exp ii@ |  | Exp iii@
|  94Zr |  |  96Zr |  |  94Zr |  |  96Zr |  |  94Zr |  |  96Zr
Source of uncertainty | rand | sys |  | rand | sys |  | rand | sys |  | rand | sys |  | rand | sys |  | rand | sys
target thickness, $n_{t}$ | 0.5 |  |  | 0.5 |  |  | 0.4 |  |  | 0.4 |  |  | 0.4 |  |  | 0.4 |
activated nuclei, $N_{act_{exp}}$ | 0.9 |  |  | 0.8 |  |  | 1.6 |  |  | 0.6 |  |  | 1.8 |  |  | 0.8 |
photopeak eff., $\epsilon_{\gamma}$a |  | 0.5 |  |  | 0.5 |  |  | 0.5 |  |  | 0.5 |  |  | 0.5 |  |  | 0.5
simulation |  | 1.5 |  |  | 1.5 |  |  | 1.5 |  |  | 1.5 |  |  | 1.5 |  |  | 1.5
Ep, $\Delta$Ep and $\Delta$zb |  | 0.9 |  |  | 4.5 |  |  | 0.4 |  |  | 2.3 |  |  | 0.6 |  |  | 1.6
$\sigma_{ENDF}$(Au)c |  | 1.0 |  |  | 1.0 |  |  | 1.0 |  |  | 1.0 |  |  | 1.0 |  |  | 1.0
$\sigma_{ENDF}$(Zr)d |  | 1.4 |  |  | 3.7 |  |  | 1.6 |  |  | 2.2 |  |  | 0.2 |  |  | 4.4
Total random uncertainty | 1.0 |  |  | 0.9 |  |  | 1.6 |  |  | 0.7 |  |  | 1.8 |  |  | 0.9 |
Total systematic uncertainty |  | 2.5 |  |  | 6.1 |  |  | 2.5 |  |  | 3.7 |  |  | 2.0 |  |  | 5.0
Total uncertainty | 2.7 |  | 6.2 |  | 3.0 |  | 3.8 |  | 2.7 |  | 5.1

  * a

Uncertainty in gamma photopeak efficiency relative to the 198Au 412-keV line.

  * b

See separate tables 7, 8 and 9.

  * c

Ref. [31].

  * d

See equations (7) and (10).

##  5 MACS with other neutron cross section libraries

Table 11: MACS (30 keV) and correction factor, $C_{lib}$, for 94Zr and 96Zr with different cross-section libraries [27, 41, 42, 43, 44]. | Exp i@ |  | Exp ii@ |  | Exp iii@ |
---|---|---|---|---|---|---
| MACS (mb) |  | $C_{lib}$ |  | MACS (mb) |  | $C_{lib}$ |  | MACS (mb) |  | $C_{lib}$ |
Library |  94Zr |  96Zr |  |  94Zr |  96Zr |  |  94Zr |  96Zr |  |  94Zr |  96Zr |  |  94Zr |  96Zr |  |  94Zr |  96Zr |
ENDF/B-VII.1 | 28.7 | 12.6 |  | 0.98 | 1.22 |  | 27.9 | 12.1 |  | 0.96 | 1.18 |  | 27.3 | 12.4 |  | 0.93 | 1.20 |
JENDL-4.0 | 27.8 | 12.5 |  | 1.08 | 1.04 |  | 27.1 | 12.1 |  | 1.05 | 1.00 |  | 27.3 | 12.8 |  | 1.05 | 1.06 |
CENDL-3.1 | 28.9 | 12.4 |  | 1.00 | 1.00 |  | 27.8 | 11.8 |  | 0.96 | 0.96 |  | 27.3 | 12.1 |  | 0.94 | 0.98 |
ROSFOND 2010 | 28.4 | 13.2 |  | 1.00 | 1.20 |  | 27.6 | 12.6 |  | 0.97 | 1.15 |  | 27.3 | 12.5 |  | 0.96 | 1.14 |
JEFF-3.2 | 29.1 | 12.4 |  | 0.99 | 1.00 |  | 28.0 | 11.9 |  | 0.96 | 0.96 |  | 26.7 | 12.4 |  | 0.91 | 1.00 |
Table 12: MACS (30 keV) of the 94,96Zr$(n,\gamma)$ reactions averaged over the
three experiments and the extrapolated values at $kT$ = 8, 23 and 90 keV,
using different libraries [27, 41, 42, 43, 44].

| MACS (mb) |
---|---|---
$kT$ | 8 keV |  | 23 keV |  | 30 keV |  | 90 keV
|  94Zr |  96Zr |  |  94Zr |  96Zr |  |  94Zr |  96Zr |  |  94Zr |  96Zr
ENDF/B-VII.1a | $64.1\pm 3.7$ | $49.8\pm 5.5$ |  | $32.6\pm 1.1$ | $15.7\pm 1.1$ |  | $28.0\pm 0.6$ | $12.4\pm 0.5$ |  | $20.0\pm 1.1$ | $9.0\pm 0.7$
JENDL-4.0 | 67.6 | 42.5 |  | 33.1 | 15.8 |  | 27.5 | 12.5 |  | 15.4 | 8.0
CENDL-3.1 | 61.5 | 42.8 |  | 32.2 | 15.3 |  | 28.1 | 12.1 |  | 18.9 | 7.1
ROSFOND 2010 | 65.4 | 48.3 |  | 32.9 | 15.6 |  | 27.8 | 12.7 |  | 17.5 | 11.3
JEFF-3.2 | 60.7 | 43.1 |  | 31.9 | 15.4 |  | 27.9 | 12.2 |  | 20.5 | 7.7
average | 63.9 | 45.3 |  | 32.5 | 15.6 |  | 27.9 | 12.4 |  | 18.5 | 8.6
st. dev. | 2.8 | 3.5 |  | 0.5 | 0.2 |  | 0.2 | 0.3 |  | 2.1 | 1.7
this workb | $63.9\pm 3.7$ | $45.3\pm 5.5$ |  | $32.5\pm 1.1$ | $15.6\pm 1.1$ |  | $28.0\pm 0.6$ | $12.4\pm 0.5$ |  | $18.5\pm 2.1$ | $8.6\pm 1.7$

  * a

Uncertainties calculated using Eq. (10) and (13).

  * b

Final uncertainties are adopted as the larger values between Eq. (13) and the
standard deviation between the various libraries.

##  6 Gamma spectrum from 7Li$(p,\gamma)^{8}$Be prompt capture

Figure 5:  Gamma ray spectrum from the thick-target 7Li$(p,\gamma)^{8}$Be
capture reaction measured with a $\sim 1.5$ mA proton beam at 1.79 MeV (below
neutron threshold) incident on the LiLiT target. The spectrum was measured
with a $6^{\prime\prime}\times 4^{\prime\prime}$ NaI(Tl) detector placed at a
distance of 2.7 m from LiLiT behind a 1.5 m thick concrete wall. The black
spectrum is the spectrum obtained while the proton beam impinged on the LiLiT,
the red spectrum was obtained while there was no protons on LiLiT and the blue
spectrum is the net counts.

## References

  * [37] W. R. Dixon, Nucl. Instr. Meth. 103 (1972) 415.
  * [38] J. Hubbell and S. Seltzer, Technical Report, National Institute of Standards and Technology (2004); available online: http://physics.nist.gov/PhysRefData/XrayMassCoef/.
  * [39] B. Singh, Nucl. Data Sheets 114 (2013) 1.
  * [40] S. K. Basu, et al., Nucl. Data Sheets 111 (2010) 2555.
  * [41] K. Shibata, et al., Journal of Nuclear Science and Technology 48 (2011) 1.
  * [42] Z. G. Ge, et al., J. Korean Phys. Soc. 59 (2011) 1052.
  * [43] ROSFOND-2010 Library, Institute of Physics and Power Engineering (2010); available online: http://www.ippe.ru/podr/abbn/libr/rosfond.php.
  * [44] JEFF-3.2 Library, Joint Evaluated Fission and Fusion (2014); available online: https://www.oecd-nea.org/dbforms/data/eva/evatapes/jeff_32/.