Neutron capture reactions relevant to the $s$ and $p$ processes in the region of the $N=50$ shell closure

The radiative neutron capture cross sections for nuclei participating in the $s$-process and the $p$-process nucleosynthesis in and around the $N=50$ closed neutron shell have been calculated in a statistical semimicroscopic Hauser-Feshbach approach for the energy range of astrophysical interest. A folded optical-model potential is constructed utilizing the standard DDM3Y real nucleon-nucleon interaction. The folding of the interaction with target radial matter densities, obtained from the relativistic mean-field theory, is done in coordinate space using the spherical approximation. The standard nuclear reaction code talys1.8 is used for cross-section calculation. The cross sections are compared with experimental results. Maxwellian-averaged cross sections and astrophysical reaction rates for a number of selected nuclei are also presented.

Figure 1

Charge-density profiles from theoretical RMF model (green solid line) compared with experimental density distributions obtained from Fourier-Bessel parameter fitting (red points) of elastic electron scattering distribution [22].

Figure 2

The $s$-process path near the shell closure at $N=50$. The colored rectangles represent stable and extremely long-lived isotopes. The $p$-nuclei and $s$-only isotopes are designated by rectangles with thick borders.

Figure 3

Comparison of results of the present calculation (solid lines) with experimental measurements for ${}^{84}\mathrm{Sr}$ [24], ${}^{85}\mathrm{Rb}$ [25], ${}^{86}\mathrm{Sr}$ [26], and ${}^{87}\mathrm{Sr}$ [26, 27], with $N=46,48,49$. For the convenience of viewing, cross-section values for ${}^{85}\mathrm{Rb}$ and ${}^{86}\mathrm{Sr}$ have been multiplied by factors of 2 and 0.5, respectively.

Figure 4

Comparison of results of the present calculation (solid lines) with experimental measurements for ${}^{87}\mathrm{Rb}$ [28], ${}^{88}\mathrm{Sr}$ [29], ${}^{89}\mathrm{Y}$ [28], ${}^{90}\mathrm{Zr}$ [30, 31], and ${}^{92}\mathrm{Mo}$ [38, 39], with $N=50$. For the convenience of viewing, cross-section values for ${}^{87}\mathrm{Rb}, {}^{89}\mathrm{Y}$, and ${}^{92}\mathrm{Mo}$ have been multiplied by factors of 0.1, 10, and 0.1, respectively.

Figure 5

Comparison of results of the present calculation (solid lines) with experimental measurements for ${}^{91}\mathrm{Zr}$ [32, 33], ${}^{92}\mathrm{Zr}$ [32, 34], ${}^{93}\mathrm{Nb}$ [37], and ${}^{94}\mathrm{Mo}$ [38], with $N=51,52$.

Figure 6

Comparison of results of the present calculation (solid lines) with experimental measurements for ${}^{93}\mathrm{Zr}$ [36], ${}^{95}\mathrm{Mo}$ [38], ${}^{94}\mathrm{Zr}$ [31], and ${}^{96}\mathrm{Mo}$ [38], with $N=53$, 54. For the convenience of viewing, cross-section values for ${}^{93}\mathrm{Zr}$ have been multiplied by a factor of 0.1.

Figure 7

Comparison of results of the present calculation (solid lines) with experimental measurements for ${}^{97}\mathrm{Mo}$ [38], ${}^{96}\mathrm{Zr}$ [31], ${}^{98}\mathrm{Mo}$ [40], and ${}^{99}\mathrm{Tc}$ [41, 42], with $N=55,56$. For the convenience of viewing, cross-section values for ${}^{99}\mathrm{Tc}$ have been multiplied by a factor of 2.

Figure 8

Cross sections calculated with DDM3Y and JLM interactions compared with experimental data for ${}^{85}\mathrm{Rb}$.