Temperature effects on neutron-capture cross sections and rates through electric dipole transitions in hot nuclei

The temperature evolution of electric dipole transition strengths of Sn isotopes is studied using self-consistent quasiparticle random phase approximation (QRPA) and finite-temperature RPA models based on a relativistic density functional. For tin isotopes lighter than ${}^{132}\mathrm{Sn}$, temperature only shows its effect at high values of 2 MeV, while for neutron-rich tin isotopes heavier than ${}^{132}\mathrm{Sn}$, the low-lying strength distributions get fragmented and spread to the lower-energy region already at temperature of 1 MeV. Using these electric dipole transition strengths as inputs for the talys code, the temperature effects on $(n,\gamma )$ cross sections are studied. For tin isotopes lighter than ${}^{132}\mathrm{Sn}$, temperature causes an enhancement of neutron-capture cross section at high temperatures of 2 MeV, while for neutron-rich tin isotopes heavier than ${}^{132}\mathrm{Sn}$, the cross section is largely enhanced already at temperature $T=1.0$ MeV, and the bump of cross section caused by the pygmy dipole resonance also becomes broader. The change in neutron-capture rate can be as large as 70% for ${}^{136}\mathrm{Sn}$, considering the temperature effects on electric dipole transition strength in the final compound nucleus with a temperature of 0.86 MeV (corresponding to $T=10$ GK in the astrophysical environment). The change is around 20% for tin isotopes lighter than ${}^{132}\mathrm{Sn}$ and above 40% for those heavier than ${}^{132}\mathrm{Sn}$.

Figure 1

Electric dipole transition strength $R$ of even-even Sn isotopes as a function of excitation energy $E$, for temperatures $T=0$ MeV calculated by RQRPA model and $T=1,2$ MeV calculated by FTRRPA model, based on the energy density functional DD-ME2. Each slice represents a different Sn isotope, with the mass number $A$ annotated to the right.

Figure 2

Transition densities of neutrons and protons for the low-lying peaks of three Sn isotopes at $T=0$ MeV, including the peak at (a) $E=8.33$ MeV in ${}^{126}\mathrm{Sn}$, the peaks at (b) $E=6.04$ MeV, and (c) $E=8.28$ MeV in ${}^{136}\mathrm{Sn}$, as well as the peaks at (d) $E=5.11$ MeV and (e) $E=7.54$ MeV in ${}^{146}\mathrm{Sn}$, calculated by RQRPA model based on the energy density functional DD-ME2.

Figure 3

Electric dipole transition strength $R$ as a function of excitation energy $E$ (left column) and the corresponding $(n,\gamma )$ cross section as a function of neutron energy $E_n$ (right column), for $T=0$ (top row), 1 (middle row), and 2 MeV (bottom row). The three lines in each panel correspond to different nuclei: ${}^{126}\mathrm{Sn}$ (black solid), ${}^{136}\mathrm{Sn}$ (blue dotted), and ${}^{146}\mathrm{Sn}$ (red dashed).

Figure 4

Electric dipole transition strength $R$ as a function of excitation energy $E$ (left column) and the corresponding $(n,\gamma )$ cross section as a function of neutron energy $E_n$ (right column), for ${}^{126}\mathrm{Sn}$ (top row), ${}^{136}\mathrm{Sn}$ (middle row), and ${}^{146}\mathrm{Sn}$ MeV (bottom row). The three lines in each panel correspond to different temperatures: $T=0$ (black solid), 1 (blue dotted), and 2 MeV (red dashed).

Figure 5

The ratio between neutron-capture rate using the electric dipole strength of $T=0.86$ MeV and neutron-capture rate using the electric dipole strength of $T=0.0$ MeV for tin isotopes in astrophysical environment with temperature $astroT={10}^{10}$ K as a function of mass number $A$ of the final compound nucleus.