Neutrino breakup of $A=3$ nuclei in supernovae

We extend the virial equation of state to include ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ nuclei, and predict significant mass-three fractions near the neutrinosphere in supernovae. While alpha particles are often more abundant, we demonstrate that energy transfer cross sections for muon and tau neutrinos at low densities are dominated by breakup of the loosely-bound ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ nuclei. The virial coefficients involving $A=3$ nuclei are calculated directly from the corresponding nucleon-${}^3\mathrm{H}$ and nucleon-${}^3\mathrm{He}$ scattering phase shifts. For the neutral-current inelastic cross sections and the energy transfer cross sections, we perform ab initio calculations based on microscopic two- and three-nucleon interactions and meson-exchange currents.

Figure 1

Mass fractions of nucleons and $A=3,4$ nuclei in chemical equilibrium as a function of temperature $T$. The top and bottom rows correspond to a density of ${10}^{11}\hspace{1em}\text{g}/{\text{cm}}^3$ and ${10}^{12}\hspace{1em}\text{g}/{\text{cm}}^3$ respectively, and from left to right the proton fractions are $Y_p=0.1,0.3,$ and $0.5$. For this temperature range, at ${10}^{11}\hspace{1em}\text{g}/{\text{cm}}^3$ the neutron fugacity is $z_n<0.1,0.05,0.01$ for $Y_p=0.1,0.3,$ and $0.5$ respectively, all other fugacities are $<0.01$ for all shown proton fractions. At the higher density, ${10}^{12}\hspace{1em}\text{g}/{\text{cm}}^3$, the neutron fugacity is $z_n<0.7,0.35,0.04$ for $Y_p=0.1,0.3,$ and $0.5$ respectively, all other fugacities are $<0.06$ for all shown proton fractions.

Figure 2

Neutrino energy loss ${\mathit{dE}}_{\nu }/\mathit{dx}$ for inelastic excitations of $A=3,4$ nuclei as a function of the matter temperature $T$ at a density of ${10}^{12}\text{g}/{\text{cm}}^3$. We assume that the neutrino energies are characterized by a Fermi-Dirac distribution with a temperature $T_{\nu }=6\hspace{1em}\text{MeV}$. The contributions from ${}^3\mathrm{H}$, ${}^3\mathrm{He}$, and ${}^4\mathrm{He}$ nuclei, and the total neutrino energy loss are shown for proton fractions $Y_p=0.1,0.3,$ and $0.5$.