The Stellar 72 Ge( n , γ ) Cross Section for weak s-process: A First Measurement at n_TOF

. The slow neutron capture process ( s -process) is responsible for producing about half of the elemental abundances heavier than iron in the universe. Neutron capture cross sections on stable isotopes are a key nuclear physics input for s -process studies. The 72 Ge(n ,γ ) Maxwellian-Averaged Cross Section (MACS) has an important inﬂuence on the production of isotopes between Ge and Zr in the weak s-process in massive stars and so far only theoretical estimations are available. An experiment was carried out at the neutron time-of-ﬂight facility n_TOF at CERN to measure the 72 Ge(n ,γ ) reaction for the ﬁrst time at stellar neutron energies. The capture measurement was performed using an enriched 72 GeO 2 sample at a ﬂight path length of 184 m, which provided high neutron energy resolution. The prompt gamma rays produced after neutron capture were detected with a set of liquid scintillation detectors (C 6 D 6 ). The neutron capture yield is derived from the counting spectra taking into account the neutron ﬂux and the gamma-ray detection e ﬃ ciency using the Pulse Height Weighting Technique. Over 70 new neutron resonances were identiﬁed, providing an improved resolved reaction cross section to calculate experimental MACS values for the ﬁrst time. The experiment, data analysis and the new MACS results will be presented including their impact on stellar nucleosynthesis, which was investigated using the post-processing nucleosynthesis code mppnp for a 25 solar mass model.


Introduction
The element production in the universe is a key question and drives the field of nuclear astrophysics since many decades. Neutron capture reactions are the main mechanism for the origin of heavier elements in the universe. Half of the elemental abundances heavier than iron are produced via the slow neutron capture process (s-process), which occurs in different burning stages of stars with low neutron densities of 10 7 to 10 12 cm −3 [1,2]. The resulting neutron capture rates are usually smaller than the betadecay rates of the unstable reaction products. This forces the reaction path on the nuclear chart along the so-called 'valley of stability'. Therefore, neutron capture cross sections on stable isotopes are a key nuclear physics input for s-process studies. More precisely, Maxwellian-averaged cross sections (MACS) are used, as the neutron capture cross section is averaged over the stellar neutron velocity distribution of a certain stellar temperature kT , where the reaction takes place.
Elements between mass number 60 and 90 are mainly produced by an s-process component which occurs in massive stars during He core burning ( 0.3 GK) and during Cshell burning ( 1 GK). Neutron exposures are too low to establish a reaction flow equilibrium [2]. Therefore, the neutron capture cross sections directly influence the abundances and are important to be measured precisely. Unfortunately, some intermediate mass nuclei like 72 Ge, still rely on theoretical cross sections based on scarce nuclear data, if one studies the database of KADoNiS-v0.3 [3]. Furthermore, the recommended theoretical MACS value for 72 Ge(n, γ) between 59 mb [4] and 73 mb [3] can have realistic uncertainties of up to 25%, taking the wide spread of predictions into account. This proceeding reports on the 72 Ge(n, γ) measurement performed at n_TOF. Lastly, there are more capture cross section results on other stable germanium isotopes from n_TOF recently [5][6][7]. * e-mail: mirco.dietz@ptb.de

Experiment
The experiment was performed at the neutron time-offlight facility n_TOF at CERN. At n_TOF, highly energetic protons (20 GeV/c) from the CERN Proton Synchroton (PS), 10 12 particles in a bunch, impinge on the 1.3 tonne lead target and spallation reactions occur. The surrounding water layers of few cm cool the target and act as a moderator for the high energy neutrons. This results in a wide neutron energy spectrum over up to 12 orders of magnitude from several GeV down to 25 meV. The measurement in the Experimental ARea 1 (EAR-1) with a flight path of 183.96(4) m exploited the excellent neutron energy resolution [8].
The detector setup consisted of four liquid C 6 D 6 scintillators (1 liter deuterated benzene each), optimized with Carbon fibre housing for low neutron sensitivity. The detectors were installed 7.7 cm upstream the sample under backwards angle of 125 • to register the prompt γ-rays from the capture reaction. The capture sample with a diameter of 2 cm and a mass of 2.68 g was made from 96.59% enriched 72 GeO 2 powder. Additional samples like Au and metallic natural germanium were used for comparison purposes and an empty sample for background estimation.
The neutron flux was measured extensively in a dedicated campaign during commissioning runs using different detectors system exploiting neutron standard cross sections on 6 Li and 235 U. More details on the neutron flux monitoring can be found in Ref. [9].

Data Analysis
At n_TOF, we study time and amplitude correlated signals of capture events to determine neutron energy dependent capture cross sections. Initial steps like stability checks, time-of-flight to neutron energy conversion (E n ) or the energy calibration of the C 6 D 6 amplitude signals are de-scribed in details in [10]. The capture yield Y was calculated via with weighted capture counting spectra (C w ), its background correction (B w ) and the neutron flux (Φ n (E n )). The factor f N reflects a normalization procedure with a thin gold sample exploiting the saturated resonance method [11] for the 4.9 eV resonance in 197 Au(n, γ). The efficiency of the detector setup is taken into account by the Pulse Height Weighting Technique [12], which includes detailed Geant4 simulations and certain assumptions on the detection technique chosen. A detailed description, the weighting factors and further small correction factors are given in [10].

Results
In total, 93 resonances from 72 Ge(n, γ) were identified and resolved in the neutron energy region up to 43 keV with 77 new resonances, which were not known in any database before. In general, capture data are not sensitive to individual decay widths such as the gamma width Γ γ or the neutron width Γ n , but to the kernel of a resonance K = g Γ γ Γ n Γ γ +Γ n with the spin factor g. The kernel data up to 43 keV, derived from the capture yield with R-Matrix code SAMMY, was presented in [13] and the data is available on EX-FOR [14]. Moreover, an averaged cross section between 43 keV and 300 keV was provided in EXFOR as well.
Here, we provide the neutron capture cross section on 72 Ge from 30 eV to 330 keV in Figure 1, which summarises our findings in the resolved and unresolved energy region. Furthermore, Figure 1 shows a comparison with data from ENDF/B-VIII.0 evaluation [15] and clearly states the improved range of resolved resonances from 12 keV up to 43 keV with the our data.   The Maxwellian-averaged cross sections of 72 Ge(n, γ) between 5 keV and 100 keV were derived via from the new capture cross section and scaled ENDF cross section above 300 keV, which only has minor contribution for kT ≥ 50 keV. The MACS results are shown in Figure 2 in comparison to values of KADoNiS-v0.3 [3]. The same energy dependence of the MACS is observed, but the n_TOF results are between 17% and 24% lower database values. Moreover, the new results exhibit only relative uncertainties between 3.2% and 7.1%, which marks a significant improvements to the 'theoretical' evaluation before. An detailed budget of the different sources of statistical and systematic uncertainties is described in [10]. Finally, the result at kT = 30 keV with 57.4 ± 3.0 mb has a total uncertainty under 5%, which is the general target for input data on stellar models.   [3] and a difference of about 20% is observed on average. Uncertainties are displayed in shaded area with 25% assumed for the KADoNiS values. Clearly, the n_TOF result brings a significant improvement with uncertainties below 5% for kT ≤ 30 keV.

Astrophysical Implication
The implication of the new cross section result was investigated using a 25 solar mass star with 2% metallicity, modelled with the code MESA [16]. The post-processing code mppnp [17] replicated the s-process nucleosynthesis. Abundances were calculated with different cross section inputs for 72 Ge(n, γ), comparing n_TOF and KADoNiS-v0.3 values. The resulting ratios for the two main stellar regions are shown in Figure 3 and more details on the stellar conditions can be found in [10]. The abundance ratio changes up to 20% or 25%, which is similar in He core (kT = 26 keV) and C shell (kT = 90 keV), as there is a consistent difference of about 20% between the MACS from KADoNiS-v0. 3   In conclusion, we have measured the 72 Ge(n, γ) cross section with high precision at the CERN n_TOF facility for the first time, and covered a wide neutron energy range relevant for s-process nucleosynthesis. The results drastically reduce uncertainties in the calculation of abundances produced via the s-process in He-core and C-shell burning phases in massive stars.
In line with the principles that apply to scientific publishing and the CERN policy in matters of scientific publications, the n_TOF Collaboration recognises the work of V. Furman and P. Sedyshev (JINR, Russia), who have contributed to the experiment used to obtain the results described in this paper. This work was supported by the European Research Council ERC-2015-STG Nr. 677497, the Austrian Science Fund FWF (J 3503), the Science and Technology Facilities Council UK (ST/M006085/1), the Adolf Messer Foundation, the Croatian Science Foundation under the project 8570, the MSMT of the Czech Re-public, the Charles University UNCE/SCI/013 project and by the funding agencies of the participating institutes.