Low-energy enhancement in the $\gamma$-ray strength functions of ${}^{73,74}\mathrm{Ge}$

The $\gamma$-ray strength functions and level densities of ${}^{73,74}\mathrm{Ge}$ have been extracted up to the neutron-separation energy $S_n$ from particle-$\gamma$ coincidence data using the Oslo method. Moreover, the $\gamma$-ray strength function of ${}^{74}\mathrm{Ge}$ above $S_n$ has been determined from photoneutron measurements; hence these two experiments cover the range of ${\mathrm{E}}_{\gamma }\approx 1$–13 MeV for ${}^{74}\mathrm{Ge}$. The obtained data show that both ${}^{73,74}\mathrm{Ge}$ display an increase in strength at low $\gamma$ energies. The experimental $\gamma$-ray strength functions are compared with $M1$ strength functions deduced from average $B\left(M1\right)$ values calculated within the shell model for a large number of transitions. The observed low-energy enhancements in ${}^{73,74}\mathrm{Ge}$ are adopted in the calculations of the ${}^{72,73}\mathrm{Ge}\left(n,\gamma \right)$ cross sections, where there are no direct experimental data. Calculated reaction rates for more neutron-rich germanium isotopes are shown to be strongly dependent on the presence of the low-energy enhancement.

Figure 1

(a) Excitation energy-$\gamma$ matrix from the ${}^{74}\mathrm{Ge}({}^3\mathrm{He},{}^3\mathrm{He}\gamma ){}^{74}\mathrm{Ge}$ reaction. The NaI spectra are unfolded with the NaI response functions. (b) The first generation matrix from the same reaction. The area within the dashed lines is used in the further analysis.

Figure 2

Cross sections for the ${}^{74}\mathrm{Ge}\left(\gamma ,n\right)$ reaction from the current experiment (blue crosses) together with existing photoneutron data [36].

Figure 3

Experimental level density of ${}^{74}\mathrm{Ge}$. The data are normalized to known discrete levels at low excitation energy and to the level density extracted at $S_n$ from neutron-capture resonance spacings $D_0$. The two sets of arrows indicate where the data are normalized.

Figure 4

Level density of (a) ${}^{73}\mathrm{Ge}$ and (b) ${}^{74}\mathrm{Ge}$ normalized according to norm-1 and norm-2.

Figure 5

$\gamma \mathrm{SF}$ for the different normalization procedures together with photoneutron data on ${}^{74}\mathrm{Ge}$ from the present experiment and from already existing photoneutron data from Ref. [36] for (a) ${}^{73}\mathrm{Ge}$ and (b) ${}^{74}\mathrm{Ge}$. Note that ${}^{74}\mathrm{Ge}\gamma \mathrm{SF}$ above $S_n$ has been compared with both ${}^{73,74}\mathrm{Ge}$ data from the current experiment. The green lines represent the upper and lower limits of norm-1.

Figure 6

$\gamma \mathrm{SF}$ of ${}^{74}\mathrm{Ge}$ obtained from photon scattering reactions utilizing electron beams of 7 and 12.1 MeV (red and green circles, respectively) [56], from a statistical analysis of primary $\gamma$-ray spectra (black squares), and from $\left(\gamma ,n\right)$ reactions (blue crosses).

Figure 7

Shell-model calculations of the $M1$ component of the $\gamma \mathrm{SF}$ of ${}^{74}\mathrm{Ge}$ (blue dashed line) and ${}^{73}\mathrm{Ge}$ (green solid line).

Figure 8

Shell-model calculations of the $M1$ component of the $\gamma \mathrm{SF}$ of ${}^{80}\mathrm{Ge}$.

Figure 9

Neutron capture cross section as a function of neutron energy for the ${}^{72}\mathrm{Ge}$(n, $\gamma$)${}^{73}\mathrm{Ge}$ and ${}^{73}\mathrm{Ge}$(n, $\gamma$)${}^{74}\mathrm{Ge}$ reactions. The calculations are performed using Talys. In panels (a) and (b) resulting $\left(\mathrm{n},\gamma \right)$ cross sections from using the $\gamma \mathrm{SFs}$ from Fig. 5 combined with the experimentally constrained NLD, are shown. In panel (b) the electromagnetic type of the $\gamma \mathrm{SF}$ is either $E1$ or $M1$, while the level density type is kept constant. In panel (d) the level density input is varied, while the $\gamma \mathrm{SF}$ input is kept constant. See text for details.

Figure 10

Final neutron-capture cross sections for the ${}^{72}\mathrm{Ge}\left(n,\gamma \right){}^{73}\mathrm{Ge}$ and ${}^{73}\mathrm{Ge}\left(n,\gamma \right){}^{74}\mathrm{Ge}$ reactions including all uncertainties.

Figure 11

Ratio of Maxwellian-averaged $\left(n,\gamma \right)$ reaction rates including and excluding the upbend for the Ge isotopic chain up to the neutron drip line for temperatures (a) $T=1$ GK and (b) $T=0.15$ GK.