Measurement of neutron-capture cross sections of ${}^{70,72}\mathrm{Ge}$ using the DANCE facility

Background: Approximately half of all atomic nuclei heavier than iron are synthesized by the slow neutron-capture process. The weak component of this process is not well understood and the reaction rates of each isotope in the s-process path affect nucleosynthesis abundances downstream.

Purpose: To measure the neutron-capture cross sections of two weak s-process nuclei, ${}^{70,72}\mathrm{Ge}$, using the neutron time-of-flight technique. Measuring the capture cross sections for isotopes in this region of the chart of nuclides has proven challenging due to dominant scattering cross sections.

Method: Samples consisted of pellets made of pressed enriched metallic powders. The ${}^{70,72}\mathrm{Ge}$ neutron-capture cross sections were measured as a function of neutron energy using the Detector for Advanced Neutron Capture Experiments at Los Alamos National Laboratory.

Results: Neutron-capture cross sections were measured from 10 eV to 1 MeV. These are the first measurements for ${}^{70,72}\mathrm{Ge}$ between 300 keV and 1 MeV neutron energy. Maxwellian-averaged cross sections were calculated in the astrophysically relevant neutron energy range (5 keV $\le kT\le$ 100 keV). Their value at $kT=30$ keV was found to be $89\pm 11$ mb for ${}^{70}\mathrm{Ge}$ and $58\pm 5$ mb for ${}^{72}\mathrm{Ge}$. Both values are in agreement with recent time-of-flight measurements at n_TOF (neutron Time-Of-Flight facility at the European Organization for Nuclear Research).

Conclusions: The average cross section results from this work for ${}^{70}\mathrm{Ge}$ show minor ($<1\sigma$) disagreement with a recent measurement by the n_TOF collaboration at higher neutron energies. This corresponds to the neutron energy region that had previously never been measured ($>300$ keV). Two reaction library databases underestimate the ${}^{72}\mathrm{Ge}$ average cross section below 30 keV according to n_TOF and DANCE. This is likely due to capture resonances that are missing from the theoretical cross sections in the databases that were identified in both time-of-flight measurements. Additionally, a rudimentary analysis of the impact of both cross section measurements on stellar nucleosynthesis abundances using the NETZ nucleosynthesis tool is presented.

Figure 1

The $E_{\mathrm{\Sigma }}$ vs $E_n$ spectrum for cluster multiplicities $M_{\text{cl}}=2–5$ from ${}^{72}\mathrm{Ge}$. Note the different line lengths in $E_{\mathrm{\Sigma }}$ indicating different reaction $Q$ values from different isotopes in the target. Horizontal lines at 6.78 and 10.2 MeV have been placed to denote the $S_n$ of ${}^{72}\mathrm{Ge}$ and ${}^{73}\mathrm{Ge}$, respectively.

Figure 2

An example of a $E_{\mathrm{\Sigma }}$ spectrum from the ${}^{72}\mathrm{Ge}$ target data at $E_n=94–95$ eV and $M_{\text{cl}}=2–5$. This shows the raw data (black), the scaled $E_{\mathrm{\Sigma }}$ spectrum from capture on ${}^{73}\mathrm{Ge}$ (red), the scaled scattering spectrum (magenta), and the results of the ${}^{73}\mathrm{Ge}$ and scattering subtraction (blue). The scattering subtraction is unrealistic below about 4.5 MeV so the shaded region is excluded from the yield calculation (see text for details).

Figure 3

A comparison of DANCE's simulated response (gray) with data from four different neutron resonances, specified in legend, for ${}^{72}\mathrm{Ge}$. Simulations were performed using MGLO model of $E1$ PSF, $\mathrm{SF}+\mathrm{SP}$ combination in $M1$ PSF in conjunction with CT NLD model.

Figure 4

Efficiency for detecting a $\gamma$ cascade from neutron capture with $2\le M_{\text{cl}}\le 5$ as a function of $E_{\mathrm{\Sigma }}^{\min }$ for (a) ${}^{70}\mathrm{Ge}$ and (b) ${}^{72}\mathrm{Ge}$. The $1\sigma$ bounds from the simulation of each line are given by shaded bands.

Figure 5

Comparisons of the neutron capture cross sections of (a) ${}^{70}\mathrm{Ge}$ and (b) ${}^{72}\mathrm{Ge}$ with evaluated cross sections from the ENDF/B-VIII.0 database.

Figure 6

Comparisons of the MACS from this work with previous measurements and evaluated database values for (a) ${}^{70}\mathrm{Ge}$ and (b) ${}^{72}\mathrm{Ge}$.

Figure 7

A ratio of the NETZ weak s-process simulation results at (a) $kT=30$ keV and (b) $kT=90$ keV when including this work's measurements. Points are color coded according to elements and appear in order from lightest to heaviest.