Speaker
Description
In analyzing the dynamics of core-collapse supernovae and astrophysical phenomena, neutrino absorption and scattering cross sections are essential features to characterize. To obtain these measurements, we study nuclear response functions, whose imaginary part is related to these scattering rates. These functions are used to qualify the change in a measurable quantity in a medium responding to an external probe. In the shock wave of a supernovae, much of the energy is carried out as neutrinos escape. The neutrinos that stay within the neutrinosphere are able to interact with the nucleons that exist within the proto-neutron star. We aim to calculate both density-density and spin-spin response functions of neutrons and protons within these high-density media in the charged-current reactions that occur as a result of these interactions.
The imaginary part of this response correlates to dynamical structure functions, a function of momentum and energy transfer. An order-by-order calculation of response functions can lead to unphysical properties in these dynamical structure functions. Previously, our group has employed the technique of random phase approximation (RPA) to calculate these response functions. RPA is a many-body, conserving approximation derived from linear response theory. It builds off of the Hartree-Fock ground state, the lowest energy state achieved by assuming an independent particle in an average field. In RPA, bubble diagrams representing particle-hole excitations are summed infinitely, to calculate the response function from this ground state and the interaction potentials.
However, because it is computationally expensive, RPA is limited to first-order perturbations. In an attempt to achieve “beyond-RPA” measurements, incorporating second-order interactions, we employ Fermi Liquid Theory for calculating these response functions. Fermi Liquid Theory is framed around interacting fermions, at low temperature and occurring close to the Fermi surface. It estimates these fermions as very weakly interacting quasiparticles, or collective excitations, with a modified effective mass and Landau parameters that represent interaction strength. While FLT can help incorporate these higher order perturbations in the calculations of response functions, it is limited. We found that the regime at which FLT is valid includes lower momenta transfer and low energy transfer in the scattering interactions, where it correlates with RPA. In this regime, FLT offers an alternative, more comprehensive, measurement.