Abstract
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.
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