Effect of electronic environment on neutrino-nucleus reactions at $r$-process sites

We discuss effects of the electron plasma on the charged-current neutrino-nucleus reaction $({\nu }_e,e^{-})$ in a core-collapse supernova environment. We first discuss the electron screening effect on the final state interaction between the outgoing electron and the daughter nucleus. To this end, we employ a schematic surface peaked transition density and solve the Dirac equation for the outgoing electron with the screened Coulomb potential obtained with the Thomas-Fermi approximation. In addition to the screening effect, we also discuss the Pauli blocking effect due to the environmental electrons on the spectrum of the outgoing electron. We find that both effects hinder the cross section of the charged-current reaction, especially at low incident energies.

Figure 1

Cross sections for the charged-current ${\nu }_e+$${}^{56}\mathrm{Fe}$ $\to e^{-}+$${}^{56}\mathrm{Co}$ reaction as a function of the energy of the outgoing electron for three densities of the environmental electrons, ${\rho }_e^0$. The Fermi transition to the $J^{\pi }=0^{+}$ state at $E_x=3.5$ MeV in ${}^{56}\mathrm{Co}$ is considered. Top, middle, and bottom panels are for ${\rho }_e^0={10}^{32},{10}^{33}$, and ${10}^{34}$ cm${}^{-3}$, respectively. Solid line shows the results in the absence of the environmental electrons; dotted line includes the electron screening effects. Dashed line takes into account both screening and Pauli blocking effects.

Figure 2

Same as Fig. 1, but for the ${\nu }_e+$${}^{208}\mathrm{Pb}$ $\to e^{-}+$${}^{208}\mathrm{Bi}$ reaction. The Fermi transition to the $J^{\pi }=0^{+}$ state at $E_x=15.0$ MeV in ${}^{208}\mathrm{Bi}$ is considered.

Figure 3

Total cross sections for the ${\nu }_e+$${}^{56}\mathrm{Fe}$ $\to e^{-}+$${}^{56}\mathrm{Co}$ reaction as a function of the density of the environmental electrons. These are given as the ratio to the cross sections in the absence of the environmental electrons, ${\sigma }_0$. The meaning of each line is the same as in Fig. 1.

Figure 4

Same as Fig. 3, but for the ${\nu }_e+$${}^{208}\mathrm{Pb}$ $\to e^{-}+$${}^{208}\mathrm{Bi}$ reaction.