Microscopic folding model analysis of the radiative $(n,\gamma )$ reactions near the $Z=28$ shell closure and the weak $s$ process

Radiative thermal neutron capture cross sections over the range of thermal energies from 1 keV to 1 MeV are studied in the statistical Hauser-Feshbach formalism. The optical model potential is constructed by folding the density-dependent M3Y nucleon-nucleon interaction with radial matter densities of target nuclei obtained from relativistic-mean-field (RMF) theory. The standard nuclear reaction code talys1.8 is used for calculation of cross sections. The nuclei studied in the present work reside near the $Z=28$ proton shell closure and are of astrophysical interest, taking part in $p,s$, and $r$ processes of nucleosynthesis. The Maxwellian-averaged cross-section (MACS) values for energies important for astrophysical applications are presented.

Figure 1

Charge density profiles of ${}^{59}\mathrm{Co},{}^{65}\mathrm{Cu},{}^{70}\mathrm{Zn}$, and ${}^{72}\mathrm{Ge}$, from the relativistic-mean-field theory, are compared with the Fourier-Bessel parameter fit to the elastic electron scattering data, taken from DeVries et al. [23]. The solid lines represent theoretical results and the discrete points represent the Fourier-Bessel parameter fit to the scattering data.

Figure 2

Nucleosynthesis path from Fe to Ga. Shaded rectangles represent the stable isotopes. The $p$-only and $r$-only nuclei are designated by rectangles with thick borders.

Figure 3

Comparison of $(n,\gamma )$ cross sections of the present calculation with experimental measurements for ${}^{56,57,58,60}\mathrm{Fe}$. The solid lines indicate the theoretical results. For the convenience of viewing, we have multiplied the cross sections of ${}^{56,58,60}\mathrm{Fe}$ by factors of 10, 0.005, and 0.1, respectively.

Figure 4

Comparison of $(n,\gamma )$ cross sections of the present calculation with experimental measurements for ${}^{59}\mathrm{Co}$ and ${}^{63,65}\mathrm{Cu}$. The solid lines indicate the theoretical results. For the convenience of viewing, we have multiplied the cross sections of ${}^{63}\mathrm{Cu}$ and ${}^{65}\mathrm{Cu}$ by factors of 10 and 5, respectively.

Figure 5

Comparison of $(n,\gamma )$ cross sections of the present calculation with experimental measurements for ${}^{58,60,61}\mathrm{Ni}$. The solid lines indicate the theoretical results. For the convenience of viewing, we have multiplied the cross sections of ${}^{58}\mathrm{Ni}$ and ${}^{61}\mathrm{Ni}$ by factors of 0.1 and 2.0, respectively.

Figure 6

Comparison of $(n,\gamma )$ cross sections of the present calculation with experimental measurements for ${}^{62,63,64}\mathrm{Ni}$. The solid lines indicate the theoretical results. For the convenience of viewing, we have multiplied the cross sections of ${}^{63}\mathrm{Ni}$ and ${}^{64}\mathrm{Ni}$ by factors of 10 and 0.1, respectively.

Figure 7

Comparison of $(n,\gamma )$ cross sections of the present calculation with experimental measurements for ${}^{64,66,68}\mathrm{Zn}$ and ${}^{69,71}\mathrm{Ga}$. The solid lines indicate the theoretical results. For the convenience of viewing, we have multiplied the cross sections of ${}^{64}\mathrm{Zn}$ and ${}^{68}\mathrm{Zn}$ by factors of 10 and 0.1, respectively.

Figure 8

Predicted cross section values for ${}^{69}\mathrm{Ga}(n,\gamma ){}^{70}\mathrm{Ga}$ reaction with two different density-folded microscopic potentials based on two different nucleon-nucleus interactions. The red solid line represents a calculation with optical model potential based on the DDM3Y $\mathit{NN}$ interaction and the blue dotted line represents calculations with the JLM optical model potential.

Figure 9

Cross sections for the reaction ${}^{58}\mathrm{Fe}(n,\gamma ){}^{59}\mathrm{Fe}$ with different combinations of real and imaginary potential well depths.