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

A high-power Liquid-Lithium Target (LiLiT) was used for the first time for neutron production via the thick-target 7Li(p,n)7Be 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 3-5e10 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+-0.6 mb and 12.4+-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)8Be reaction with yields of ~3e8 gammas/s/mA and ~4e8 gammas/s/mA, respectively, evidenced by the 90Zr(gamma,n)89Zr photonuclear reaction.

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, N (Zr) N (N b) , 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 94,96 Zr isotopes. In our experiments, the liquid-lithium target bombarded by a high-intensity proton beam yields also intense (∼ 7×10 8 γ/s/mA) high-energy prompt gamma rays (17.6 and 14.6 MeV) from the 7 Li(p, γ) 8 [3] for details of the target design). The (windowless) lithium film, bombarded by a ∼1-2 mA proton beam (E p ∼ 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 (∼ 2-3 kW) by fast transport of the liquid lithium to a reservoir and heat exchanger. With the proton beam focused transversally to an approximate radial Gaussian distribution (σ r ∼ 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 (∼ 170 µm) in the liquid lithium is of the order of 1 MW/cm 3 [3] while maintaining stable temperature and vacuum conditions with a lithium flow velocity of ∼2.5 m/s. In the experiments described here, we activated a nat Zr 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 ± 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 γ counting of the 198 Au activity. A γ 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 (∼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 Figure 1: Detail diagram of the Liquid-Lithium Target (LiLiT) and activation target assembly. The (1-2 mA, ∼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. 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 13 C(p, γ) resonance (E p (lab) = 1.746 MeV) and the 7 Li(p, n) threshold region. A beam energy spread of ∼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 95,97 Zr and 198 Au products (Supp. mat.). In the experiments, two different HPGe detectors (respectively shielded and unshielded) were used.
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 7 Li(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 [24,26]. We also measured the neutron time  Table 1) with a shielded HPGe. The photo-peaks from the decay of the activated Zr isotopes and daughters are labeled in keV.
directly determined in the experiment (Table 1), averaged over the neutron spectrum, are obtained from the expression where N actexp (A + 1) (N actexp (Au)) is the number of (A+1) Zr ( 198 Au) activated nuclei determined experimentally, n t (A) (n t (Au)) is the A Zr (Au) target thickness (atom/cm 2 ) and f (A) (f (Au)) accounts for the decay of activated nuclei during In (2), σ EN DF (E n ; Au) is taken from the ENDF/B-VII.1 (USA,2011) [27] library for 197 Au. The latter library (denoted henceforth ENDF) was extensively validated for 197 Au [28,29] and especially in the neutron energy range relevant to our measurements [26,30] and serves here for neutron fluence normalization.
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 where σ(E n ) is the true energy-dependent reaction cross section. We determine here an experimental value MACS exp lib of the radiative neutron capture (n, γ) for the target nucleus A Zr (A = 94,96) using the expression: In (4), σ A lib (E n ) is the A Zr(n, γ) cross section given by a neutron library lib and C lib (A) a correction factor for the library Table 1: Experimental parameters (E p : proton mean energy and ∆E p : energy spread (1σ), ∆z: distance lithium surfaceactivation target and accumulated proton charge during the activations), experimental cross sections (multiplied by 2 √ π ) and MACS (30 keV) values determined in this work for 94,96 Zr (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 In (5) 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). The values 2 √ π · σ 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 7 Li(p, n) neutron time-of-flight spectra measured in [26] in the range 0 • − 80 • and those simulated by SimLiT-GEANT4 in the conditions of this experiment were converted to energy spectra using the same algorithm (see [24,26] for details of algorithm) and the two resulting spectra were then convoluted with the same energy-dependent 197 Au(n, γ) 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 ∆E p was estimated from the change of MACS values when distributing E p and ∆E p in their respective range; we note the insensitivity of the final value to E p and ∆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 94,96 Zr [31]. Fig. 4 illustrates a comparison of our results with existing sets of experimental data for 94,96 Zr MACS  [17,18], values in fig. 4 were corrected for sake of consistency to the ENDF 197 Au(n, γ) 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. We observe in general a slightly larger uncertainty for 96 Zr (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 96 Zr(n, γ) 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]. 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 γ rays from the radiative capture 7 Li(p, γ) 8 Be reaction. We observe these γ rays in our experiments via the photonuclear reaction 90 Zr(γ, n) 89 Zr ( fig. 2). No other (γ, n) reaction on the nat Zr target is readily observable by γ spectrometry of the activated target; we note also that the 96 Zr(γ, n) 95 Zr reaction (which could potentially interfere with the 94 Zr(n, γ) 95 Zr activation) has negligible yield compared to that of the (n, γ) reaction due to the low 96 Zr abundance. The 7 Li(p, γ) 8 Be reaction produces principally 17.6 MeV and 14.6 MeV γ rays and their yield was measured in [32] with a thin Li target. The high-energy γ spectrum was measured (Supp. mat.) with the LiLiT setup in a separate experiment (under neutron threshold) with a 6 ×4 NaI(Tl) detector positioned behind a 1.5 m thick concrete wall (shielding the overwhelming 478-keV γ-rays from 7 Li(p, p γ)). Using 90 Zr(γ, n) 89 Zr cross section values of 173 mb (85 mb) for E γ0 = 17.6 (E γ1 = 14.6) MeV (in the Giant Dipole Resonance region) measured in [33] and an averaged branching ratio γ1 γ0 ∼ 1.3 obtained by integrating the data of Zahnow et al. [32] into a thick-target yield between 0.1 ≤ E p ≤ 1.9 MeV, the respective measured gamma yields are 3×10 8 γ 0 /s/mA (4×10 8 γ 1 /s/mA). These yields can be compared with the values 1.2×10 8 γ 0 /s/mA (1.5×10 8 γ 1 /s/mA) calculated from the data of [32] and show a considerable additional yield, possibly due in part to additional resonances in 8 Be 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 94 Zr and 96 Zr as 28.0 ± 0.6 mb and 12.4 ± 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 ∼ 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 ∼ 3 × 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 60 Fe(n, γ) 61 Fe cross section, as performed in [34], would be possible with a ∼100 ng 60 Fe 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     [17,18] obtained by activation using the 197 Au(n, γ) cross section as reference were corrected to the value established in [28,29] as done in this work. For 96 Zr, 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.

Activation results
The number of activated nuclei at the end of the irradiation, N actexp , is obtained from equation (6) N actexp = C where C is the number of counts in the photo-peak, γ is the detector photoelectric efficiency, I γ is the γ-intensity per decay, K γ is the correction due to γ-ray self absorption in the sample. In the case of a disk sample of thickness x, where µ is the γ-ray absorption coefficient [37]. λ = ln(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 γ-ray absorption coefficients, µ, used in this analysis were taken from [38]. The number of activated nuclei at the end of the irradiation, N actexp , obtained from equation (6) are summarized in Table 5.

Extrapolation to MB distribution
In order to separate the contributions to the MACS uncertainty resulting from the experimentally measured value σ exp and from the extrapolation to a MB distribution, we express the MACS (30 keV) as: where φ M B (30) and φ exp are the normalized MB and experimental neutron energy distribution respectively and σ is the true energy dependent cross section. The first term in Eq. (7) is (Eq. (1) and (5)) and includes the experimental uncertainties listed in Table 6. The second term in Eq. (7) can be re-written as and contributes to the uncertainty to the extent that C EN DF determined in the experimental energy range (φ exp ) is not valid in the whole MB energy range due to uncertainties ∆σ EN DF . We obtain thus the overall uncertainty as where ∆σ EN DF are taken from the reported uncertainties for the ENDF cross section library [31]. Note that we conservatively use here the quoted ∆σ EN DF although an overall correction (C EN DF ) was already applied and that ∆σ EN DF Similarly to Eq. (7), The MACS at any energy kT can be denoted as The first term is the MACS at 30 keV, so equation (11) can be written as The uncertainty is therefore given by 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 MACS(kT ) using other neutron libraries [27,[41][42][43][44] with Eq. (12), see Tables 11 and 12 (Table 12).  (7) and (10).  6 Gamma spectrum from 7 Li(p, γ) 8 Be prompt capture Figure 5: Gamma ray spectrum from the thick-target 7 Li(p, γ) 8 Be capture reaction measured with a ∼ 1.5 mA proton beam at 1.79 MeV (below neutron threshold) incident on the LiLiT target. The spectrum was measured with a 6 × 4 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.