Neutrino-pasta scattering: the opacity of nonuniform neutron-rich matter

Neutron-rich matter at subnuclear densities may involve complex structures displaying a variety of shapes, such as spherical, slablike, and/or rodlike shapes. These phases of the {\it nuclear pasta} are expected to exist in the crust of neutron stars and in core-collapse supernovae. The dynamics of core-collapse supernovae is very sensitive to the interactions between neutrinos and nucleons/nuclei. Indeed, neutrino excitation of the low-energy modes of the pasta may allow for a significant energy transfer to the nuclear medium, thereby reviving the stalled supernovae shock. The linear response of the nuclear pasta to neutrinos is modeled via a simple semi-classical simulation. The transport mean-free path for $\mu$ and $\tau$ neutrinos (and antineutrinos) is expressed in terms of the static structure factor of the pasta, which is evaluated using Metropolis Monte Carlo simulations.