Direct neutron capture cross section on ${}^{80}\mathrm{Ge}$ and probing shape coexistence in neutron-rich nuclei

Results are presented from the first neutron-transfer measurement on ${}^{80}\mathrm{Ge}$ using an exotic beam from the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory. Newly measured spins and spectroscopic factors of low-lying states of ${}^{81}\mathrm{Ge}$ are determined, and the neutron capture cross section on ${}^{80}\mathrm{Ge}$ was calculated in a direct-semidirect model to provide a more realistic ($n,\gamma$) reaction rate for $r$-process simulations. Furthermore, a region of shape coexistence around $N\approx 50$ is confirmed and implications for the magic nature of ${}^{78}\mathrm{Ni}$ are discussed.

Figure 1

A spectrum of detected particle energy vs. laboratory angle gated on a time coincidence with a forward-going recoil detected in the IC. Detected protons, deuterons, and carbon ions (surrounded by the red solid line) are from elastic scattering. Protons from the $(d,p)$ reaction are in the region marked by the black line. The horizontal band at 5.8 MeV (in the dashed red rectangle) arises from a ${}^{244}\mathrm{Cm}$ calibration source.

Figure 2

$Q$-value spectrum of protons in coincidence with a germanium recoil from the ${}^{80}\mathrm{Ge}(d,p){}^{81}\mathrm{Ge}$ reaction, detected in the SIDAR and Micron SX3 detectors. Considering 0.05-MeV FWHM energy resolution of one state from the energy calibration using ${}^{80}\mathrm{Se}(d,p){}^{81}\mathrm{Se}$ reactions and the precise level energies of ${}^{81}\mathrm{Ge}$ from Ref. [25], two states are expected to be populated in the peak at $E_x=0.69$ MeV with 0.25-MeV FWHM resolution. The ground-state $Q$ value of the reaction is $Q=2.63$ MeV.

Figure 3

Proton angular distributions in the center of mass from backward-angle detectors compared to differential cross sections calculated with fresco [41] for the unresolved doublet at $E_x=679$ and 711 keV. For the red curve, $3s_{\frac{1}{2}}$ transfer was assumed for the 679-keV state (dash blue) and $2d_{\frac{5}{2}}$ transfer to the 711-keV component (dash magenta). For the dark green curve, $2p_{\frac{1}{2}}$ transfer was assumed for the 679-keV state. The first five data points at the most forward angles are used to fit the curves. In parentheses after the shell-model configuration are the spectroscopic factors that result from the fit of the theoretical to experimental differential cross sections.

Figure 4

Intruder states ($J^{\pi }={\frac{1}{2}}^{+}, {\frac{5}{2}}^{+}$ and ${\frac{3}{2}}^{+}$) of the even $Z<40, N=49$ isotones. Spectroscopic factors extracted from transfer reactions (numbers on the left edge of the level) are also shown as well as spin and parity (right edge of the level). Data for ${}^{81}\mathrm{Ge}$ are from the present work (red numbers) and Ref. [25]. Data for the other odd-mass $N=49$ isotones: ${}^{87}\mathrm{Sr}$ from Ref. [51], ${}^{85}\mathrm{Kr}$ from Ref. [50], and ${}^{83}\mathrm{Se}$ from Ref. [26].

Figure 5

Calculated DSD cross sections (black curve) for the ${}^{80}\mathrm{Ge}(n,\gamma ){}^{81}\mathrm{Ge}$ reaction. Individual contributions are also plotted with the green curve for the $3s_{\frac{1}{2}}$ orbital and the brown curve for the $2d_{\frac{5}{2}}$ orbital. The lower limit of the red hashed band shows the calculation with $S_{3s\frac{1}{2}}=0.16$ and $S_{2d\frac{5}{2}}=0.56$, and the upper limit was calculated with $S_{3s\frac{1}{2}}=0.38$ and $S_{2d\frac{5}{2}}=0.22$. A dashed light red band represents calculated cross sections for the $E_x=679$ keV case with spectroscopic factor $S_{nlj}=1$ (top, blue) and 0.1 (bottom, purple). The uncertainty of the cross section is $\approx 30\%$, similar to the uncertainties in the spectroscopic factors extracted here.