Edinburgh Research Explorer Measurement of the 72Ge(n,) cross section over a wide neutron energy range at the CERN n_TOF facility

The 72 Ge(n , γ ) cross section was measured for neutron energies up to 300 keV at the neutron time-of-ﬂight facility n TOF (CERN), for the ﬁrst time covering energies relevant to heavy-element synthesis in stars. The measurement was performed at the high-resolution beamline EAR-1, using an isotopically enriched 72 GeO 2 sample. The prompt capture γ rays were detected with four liquid scintillation detectors, optimised for low neutron sensitivity. We determined resonance capture kernels up to a neutron energy of 43 keV, and averaged cross sections from 43 to 300 keV. Maxwellian-averaged cross section values were calculated from kT = 5 to 100 keV, with uncertainties between 3 . 2 and 7 . 1%. The new results signiﬁcantly reduce uncertainties of abundances produced in the slow neutron capture process in massive stars.

The 72 Ge(n, γ) cross section was measured for neutron energies up to 300 keV at the neutron time-of-flight facility n TOF (CERN), for the first time covering energies relevant to heavy-element synthesis in stars. The measurement was performed at the high-resolution beamline EAR-1, using an isotopically enriched 72 GeO2 sample. The prompt capture γ rays were detected with four liquid scintillation detectors, optimised for low neutron sensitivity. We determined resonance capture kernels up to a neutron energy of 43 keV, and averaged cross sections from 43 to 300 keV. Maxwellianaveraged cross section values were calculated from kT = 5 to 100 keV, with uncertainties between 3.2 and 7.1%. The new results significantly reduce uncertainties of abundances produced in the slow neutron capture process in massive stars.

I. INTRODUCTION
The chemical elements heavier than Fe are predominantly produced by neutron capture processes in stars and stellar explosions. About half of the abundances are formed in the slow neutron capture process (s-process) at low neutron densities of 10 7 to 10 12 cm −3 in quiescent burning phases of stars [1][2][3]. In these environments, neutron capture rates are typically smaller than β-decay rates, which means that the reaction path closely follows the valley of stability on the nuclear chart. The s-process consists of three components: the main component occurs during H and He shell burning phases in low-mass Asymptotic Giant Branch (AGB) stars, at temperatures of about 0.09 and 0.3 GK, respectively (1 GK = 10 9 K) [4]. This component is responsible for s abundances of elements between mass number 90 to 210. The high neutron exposures reached allow the establishment of a reaction flow equilibrium of the form N × MACS ≈ const., where N is the abundance produced in the s-process, and MACS is the Maxwellian-Averaged Cross Section, i.e., the neutron capture cross section averaged over the stellar neutron velocity distribution. The weak component of the s-process occurs in massive stars during He core burning at around 0.3 GK temperature, and during C shell burning at around 1 GK and produces elements between mass numbers 60 to 90 [5][6][7][8]. Neutron exposures are too small for a reaction flow equilibrium to be established, which means that neutron capture cross sections are key to determine abundances for all isotopes along the reaction path. Finally, the strong component is responsible for the production of Pb and takes place in low metallicity AGB stars [9]. The other half of heavy element abundances is produced by the rapid neutron capture process (r -process), a sequence of neutron capture reactions at high neutron den-sities of about 10 26 cm −3 [10]. Nuclear reactions involve mainly radioactive nuclides, thus experimental information on nuclear properties is scarce. The stellar sources of r -nuclei are still a matter of debate, however, recent observations suggest neutron star mergers as a production site [11,12]. As r -process abundances cannot be reliably predicted, they are usually calculated by subtracting calculated s-process abundances off the solar abundance pattern [13]. In the last 20 years, there has been significant progress in measuring high precision neutron capture cross sections of intermediate mass nuclei relevant for weak sprocess nucleosynthesis [1]. However, at present, there are no experimental data on 72 Ge(n, γ) covering the entire astrophysical energy range. Experimental data on 72 Ge+n reactions include transmission data obtained for natural germanium by Harvey and Hockaday [14], providing total cross sections over a wide energy range from 6 eV to 178 keV. Maletski et al. [15] performed transmission and capture measurements on 72 Ge and identified 14 resonances up to 30 keV neutron energy, but radiative widths Γ γ are only known for three resonances up to 4 keV. Consequently, MACS values used in stellar models are exclusively based on theoretical predictions or evaluations taking into account the experimental information available at lower neutron energies. The latest version of the Karlsruhe Astrophysical Database KADoNiS-v1.0 [16] estimates an uncertainty of 25% for their recommended MACS values which was determined by averaging recent evaluations (TENDL-2015 [17,18], ENDF/B-VII.1 [19] / JENDL-4.0 [20]). Individual predicted values for the MACS at kT = 30 keV range from 39 mb [21] to 118 mb [22,23]. To reliably calculate abundances of isotopes from germanium to zirconium produced in the weak s-process component, accurate stellar neutron capture cross sections on germanium isotopes are indispensable. In addition, recent studies identified the 72 Ge(n, γ) reaction as a key reaction determining the uncertainty of 72 Ge produced in the s-process, both in massive stars [24] and in AGB stars [25]. Accurate knowledge of the 72 Ge s-abundance is also critical to determine the 72 Ge abundance produced in the r -process, which has been found to play a decisive role in powering the lightcurve of the kilonova emission observed following the binary neutron star merger event GW170817 [26]. This paper presents new resonance and cross section data for the 72 Ge(n, γ) reaction obtained at the CERN n TOF facility, following on from recently published results on 73 Ge(n, γ) [27] and 70 Ge(n, γ) [28].

II. EXPERIMENT AT N TOF
The 72 Ge(n, γ) cross section was measured at the neutron time-of-flight facility n TOF, located at CERN [29]. At n TOF, neutrons are produced by spallation reactions of a highly energetic (20 GeV), pulsed proton beam from the CERN Proton Synchrotron (PS) impinging on a massive 1.3 ton Pb target. The target is surrounded by 1 cm water and 4 cm borated water layers which serve to cool the target and moderate the neutron flux to achieve a high intensity neutron energy spectrum from 25 meV to several GeV. The measurement was performed at Experimental Area 1 (EAR-1) at a nominal flight path of 185 m, taking advantage of the excellent neutron energy resolution in the energy range of interest (0.11% at 10 keV neutron energy [29]). The prompt γ rays following a neutron capture event were detected by a set of four liquid scintillation detectors filled with about 1 litre of deuterated benzene (C 6 D 6 ) each. The detectors have been specially optimized for neutron capture measurements to achieve a low sensitivity to background from neutrons scattered into the detector [30,31]. The detectors were installed 7.7 cm upstream from the sample resulting in a position corresponding to an effective angle of 125 • relative to the neutron beam. The capture sample, with a mass of 2.68 g, consisted of 96.59% isotopically enriched 72 GeO 2 powder, which was pressed into a cylindrical pellet of 2 cm diameter. In addition, data were taken with a metallic Ge sample of natural composition which was used to identify resonances due to other Ge isotopes present in the sample, and an Au sample which was used to normalise the capture yield (both cylindrical with 2 cm diameter). All samples were glued on to a sample holder with 6 µm Mylar backing. To determine the background induced by the sample holder, measurements with an empty sample holder were performed as well. The neutron flux was continuously monitored using 6 Li(n, t)α reactions in a thin 300 µg/cm 2 LiF foil in the beam in conjunction with a set of silicon detectors placed outside the beam. The neutron flux spectrum was measured in a dedicated campaign: in addition to the silicon detection system mentioned above, the flux was also measured with a Micromegas detector using the reference reactions 10 B(n, α) and 235 U(n, f) and an ionisation chamber by Physikalisch-Technische Bundesanstalt (PTB) Braunschweig measuring 235 U(n, f) reactions. The neutron flux spectrum determined by combin-ing all these results has a systematic uncertainty of 2% for neutron energies < 10 keV and > 100 keV, and of up to 5% between 10 keV and 100 keV [32]. The methodology of the neutron flux evaluation at n TOF is described in Ref. [32].

III. DATA ANALYSIS AND RESULTS
The time of flight spectra were converted to neutron energy (E n ) spectra, using the flight path L = 183.96 (4) m which was determined using well-known low energy resonances in the 197 Au(n, γ) reaction [33]. The energy dependent neutron capture yield, defined as the probability for a neutron to undergo radiative capture in the sample, was calculated using: Here, C is the 72 Ge sample count rate, B is the background, ε is the efficiency to detect a capture event, Φ n is the neutron flux, and f N (E n ) is a normalisation factor. The efficiency of the capture setup was taken into account using the Total Energy Detection principle [34,35]. For a detection system where: (i) the detection efficiency for a single γ ray is proportional to its energy; (ii) the detection efficiency is small; and (iii) at most one γ ray per capture cascade is detected, it can be shown that the efficiency to detect a capture event ε is proportional to the excitation energy of the compound system. While (ii) and (iii) apply to the C 6 D 6 system, condition (i) can be achieved by applying weighting factors to the detected signal amplitudes. This approach is called the Pulse Height Weighting Technique [35]. Weighting factors were determined by simulating the detector response in GEANT4 [36] for a range of initial γ-ray energies, taking into account the geometry of the experimental setup. Corrections need to be applied for γ-ray signals below the detection threshold (in this case 200 keV) and for transitions without γ-ray emission (electron conversion). Correction factors were determined by simulating capture cascades using the code dicebox [37].
The normalisation factor f N accounts for the fact that the neutron beam is larger than the capture sample, and is determined using the saturated resonance technique [38]. The 197 Au(n, γ) reaction has a strong resonance at 4.9 eV neutron energy, for which the radiative width Γ γ is much larger than the neutron width Γ n . The 197 Au(n, γ) capture yield is measured using a sample of sufficient thickness, so that all neutrons at the resonance energy react with the sample, providing an absolute measure of the number of neutrons traversing the sample. Since the neutron beam size slightly varies with neutron energy, the normalisation factor is energy dependent. These small corrections with respect to the 4.9 eV normalisation point (< 2% in energy region of interest) were determined in simulations and verified experimentally [29].
The background consists of several components. Background induced by ambient radioactivity and cosmic rays is determined in runs without neutron beam. Background related to the neutron beam is determined in runs with an empty sample holder. The 72 Ge count spectrum, compared to both these components, is shown in Fig. 1 (weighting factors have been applied to all spectra). Another background component comes from neutrons scattered off the 72 GeO 2 sample which are subsequently captured elsewhere in the experimental area and produce background γ rays. The capture detectors and their support have been optimised to have minimum sensitivity to neutron capture [30,31], however neutrons may be captured on other structural material such as the walls of the experimental area. At low neutron energy, where resonances can be resolved with high resolution (resolved resonance region), this background is taken into account by including a constant background to the resonance fit. In the unresolved resonance region where we determined averaged cross sections, the background is estimated using neutron filters. Neutron filters consist of material with strong neutron resonances. They are placed into the neutron beam upstream of the capture sample and are chosen to be thick enough to block out all neutrons at certain resonance energies. Any counts measured in the filter dips consequently come from background of scattered neutrons. The background was determined from the filter dips due to strong resonances in Al around 35, 90 and 160 keV neutron energy and is at the level of 5-15 % compared to the sample spectrum in the region from 43 to 300 keV. The yield in the resolved resonance region was analysed with the multilevel, multichannel R-Matrix software SAMMY [39]. SAMMY fits resonance shapes taking into account all experimental effects such as resolution broadening, self shielding, multiple interactions, and sample impurities (e.g., other Ge isotopes). Resonances due to impurities are identified by comparing the capture yield of the enriched 72 Ge sample with the spectrum recorded with germanium of natural isotopic composition (background due to oxygen is negligible due to small neutron cross sections). Resonances were fitted using the Reich-Moore approximation and assuming a constant background. Capture data do not usually allow to reliably determine all individual resonance parameters (gamma and neutron widths, energy, spin and parity / neutron orbital momentum). Thus we report in Tables I  and II only well determined observables for each resonance -resonance energy and capture kernel k, defined as: with J, I and s being the resonance, target and neutron spin, respectively. In total, 93 resonance kernels were determined, with 77 resonances not listed in any database. Figure 2 shows examples of SAMMY fits in the keV neutron energy region. Systematic uncertainties of capture kernels (not included in uncertainties in Tables I and II) are due to the neutron flux (2% below 10 keV and 5% between 10 and 43 keV), the sample enrichment (1%), the normalisation (1%), and the Pulse Height Weighting Technique (2%) [35], resulting in total systematic uncertainties of 3.2% below, and 5.6% above 10 keV neutron energy.
Average resonance parameters were determined using the resonances below 20 keV assuming there are no unresolved doublets. As no spin assignment for resonances is available, during determination of the average radiative width Γ γ we relied on the assumption that the strongest resonances (in terms of Γ n ) are of s-wave character and on the predictions of statistical model simulations performed using the code dicebox [37]. These simulations indicated that Γ J π γ are very similar for resonances with all J π and they come from a normal distribution with standard deviation σ Γγ which is at most 20% of Γ γ . The strongest resonances were selected using the criterion Γ n ≥ 10 × Γ γ , to ensure that the capture kernel k is also a good measure of the radiative width, because for such criterion k ≈ gΓ γ . The resulting set of radiative widths was fitted using the maximum-likelihood approach (see [40] for details), yielding Γ γ = 177(10) meV and σ Γγ = 52(8) meV. Our value of Γ γ is ∼ 18% higher than the literature value 150(25) meV [41]. The sum of reduced neutron widths of the above mentioned strongest resonances gives an s-wave neutron strength function S 0 ∼ 1.3(5) × 10 −4 in agreement with S 0 ∼ 1.39(54) × 10 −4 available in [42]. The other average resonance parameters were determined similarly to Ref. [43], that is using the statistical model simulations of resonance sequences (assuming the above determined Γ γ , σ Γγ and S 0 values) and comparing the number of observed resonances above a certain threshold in k. Assuming that the kernel for resonances below 20 keV with J = 1/2 can not be higher than 300 meV, i.e. Examples of resonance fits of the neutron capture yield using the R-Matrix code SAMMY [39]. The data are compared to the yield calculated from resonance parameters listed in the ENDF/B-VIII.0 evaluation [33]. The bottom panel shows an example of resonances measured at n TOF for the first time.
Γ γ Γ γ +2.5σ Γγ , we observe four strong (with Γ n Γ γ ) p-wave resonances with J = 3/2. Their presence imposes a limit of S 1 0.7×10 −4 , the most probable S 1 value being about two times higher. Using these neutron strength functions we arrived at an s-wave resonance spacing of D 0 = 1800(300) eV. The available literature values of 1190(290) [41] and 2070(290) eV [42] are inconsistent due to the lack of experimental data.
In general, resonances were well separated up to neutron energies of 43 keV. At higher energies, individual resonances cannot be reliably identified, and instead we determined averaged cross sections. Background due to sample impurities (non-negligible contributions come from 73 Ge and 70 Ge with 2.86% and 0.35% abundance, respectively) was subtracted using recently-determined cross sections [27,28]. Multiple interaction and selfshielding corrections were determined in Monte-Carlo simulations, in the same way as described in [27,28]. Figure 3 shows the cross section with statistical uncertainties determined in this work compared to the recent evaluations ENDF/B-VIII.0 [33] and TENDL-2017 [17,44]. Total systematic uncertainties of our averaged cross sections are 6.6 − 10.4%. These are due to the neutron filter background (3.9 − 9.5%), multiple interaction and self shielding corrections (1.3%), and sample impurity TABLE I. Resonance energies Er and kernels k below 20 keV. The uncertainties listed are from the fitting procedure. In addition, systematic uncertainties of k (not included in the Table) are 3.2% (5.6%) below (above) 10 keV, as described in the text.

IV. MAXWELLIAN-AVERAGED CROSS SECTION AND ASTROPHYSICAL IMPLICATIONS
We calculated Maxwellian-averaged cross sections using for kT values up to 100 keV. The cross section contribution from outside the experimental range (> 300 keV) was taken from the ENDF/B-VIII.0 [33] evaluation, but scaled by 0.84 to match the experimentally-determined cross section at lower energies. The contribution of the scaled ENDF cross section to the MACS is negligible up to kT ≤ 50 keV and between 2.5 and 14.7% from 60 to 100 keV. MACS values, and total (systematic and statistical) uncertainties, are listed in Table III and shown in Fig. 4, with a 20% uncertainty assumed for the scaled ENDF cross section data. Our results are compared to MACS values recommended in KADoNiS-v1.0 [16], which exhibit a flatter energy dependence as a function of kT . The largest discrepancies of up to 60% are in the lower energy region (≤ 20 keV), while at higher kT values agreement is within 10 − 20%. The n TOF energy trend is more similar to the older evaluation of KADoNiS-v0.3 based on Ref. [46], but about 20% smaller overall. However, the new result of 57.4 ± 3.0 mb at kT = 30 keV is within 3% agreement with the KADoNiS-v1.0 estimation. The impact of our new cross section data on stellar abundances has been investigated using a 25 solar mass star with 2% metallicity, modelled with the code MESA [47]. The weak s-process nucleosynthesis was calculated with the post-processing code mppnp [48]. We have calculated abundances produced in the s-process using the 72 Ge(n, γ) MACS values recommended by KADoNiS-v1.0 and with the new MACSs determined in this work. We show the impact on both burning stages where the s-process takes place: s-process nucleosynthesis occurs first towards the end of He core burning (∼ 7 × 10 5 years duration) via 22 Ne(α, n) reactions with neutron densities of ∼ 10 7 cm −3 and temperatures of 0.3 GK (kT ∼ 26 keV). The material is later re-processed during C shell burning at around 1 GK (kT ∼ 90 keV), where the 22 Ne(α, n) neutron source is reactivated. During this shorter s-process phase (∼ 600 years) neutron densities reach 10 11 to 10 12 cm −3 [3,6,49]. Figure 5a shows abundances of s-process isotopes between mass 70 and 96 after He core burning, using 72 Ge(n, γ) MACSs of this work, relative to abundances obtained using KADoNiS-v1.0. Coincidentally, the new MACS value at 25 keV is in very good agreement with KADoNiS-v1.0, therefore we only observe abundance changes of 1 − 2% after He-core burning. The results include error bands indicating the abundance uncertainty due to uncertainties in the 72 Ge(n, γ) MACS, which are 25% for KADoNiS-v1.0 and 5% for results of this work. The figure clearly demonstrates that abundance uncertainties due to the cross section are now significantly reduced. Figure 5b shows abundance ratios after C shell burning, during which s-process material produced during He core burning is re-processed at higher temperatures of about kT = 90 keV. The smaller MACS of this work compared to KADoNiS-v1.0 leads to final 72 Ge abundances that are 14% higher, while heavier isotope abundances along the reaction path are affected by up to 7%. This panel does not include any uncertainty estimation as final abundances not only depend on MACS values at kT = 90 keV, but also on the seed abundances that have been produced during the earlier He core burning stage.
In conclusion, we have measured the 72 Ge(n, γ) cross section with high precision at the CERN n TOF facility, and for the first time covered the entire neutron energy range relevant for s-process nucleosynthesis. Our results significantly reduce uncertainties in calculations of abundances produced in the weak s-process component occurring in quiescent burning phases in massive stars.  Abundances are normalised to results using the 72 Ge(n, γ) MACSs recommended in KADoNiS-v1.0 [16]. Isotopes of the same elements are connected by thin solid lines. Panel (a) shows abundances after He core burning. The shaded areas represent abundance variations when taking into account uncertainties of KADoNiS (blue) or n TOF (red) cross sections. Panel (b) shows abundances after the later C shell burning phase.