Nonuniform neutron-rich matter and coherent neutrino scattering

Abstract

Nonuniform neutron-rich matter present in both core-collapse supernovae and neutron-star crusts is described in terms of a semiclassical model that reproduces nuclear-matter properties and includes long-range Coulomb interactions. The neutron-neutron correlation function and the corresponding static structure factor are calculated from molecular dynamics simulations involving 40,000 to 100,000 nucleons. The static structure factor describes coherent neutrino scattering which is expected to dominate the neutrino opacity. At low momentum transfers the static structure factor is found to be small because of ion screening. In contrast, at intermediate momentum transfers the static structure factor displays a large peak due to coherent scattering from all the neutrons in a cluster. This peak moves to higher momentum transfers and decreases in amplitude as the density increases. A large static structure factor at zero momentum transfer, indicative of large density fluctuations during a first-order phase transition, may increase the neutrino opacity. However, no evidence of such an increase has been found. Therefore, it is unlikely that the system undergoes a simple first-order phase transition. Further, to compare our results to more conventional approaches, a cluster algorithm is introduced to determine the composition of the clusters in our simulations. Neutrino opacities are then calculated within a single heavy nucleus approximation as is done in most current supernova simulations. It is found that corrections to the single heavy nucleus approximation first appear at a density of the order of 10 13 g/cm 3 and increase rapidly with increasing density. Thus, neutrino opacities are overestimated in the single heavy nucleus approximation relative to the complete molecular dynamics simulations.

Nuclear “pasta” formation

“…For one, neutrino-pasta scattering helps determine the neutrino opacity in core collapse supernovae [6,7]. This is because supernova neutrinos have wavelengths comparable to pasta sizes and can scatter coherently from the pasta.…”

Ising Analogue to Compact-Star Matter

“…Such a coherent neutrino-matter scattering is not only expected at low temperature, but even more in the possible occurrence of a critical point in the post-bounce supernova explosion, with the associated phenomenon of critical opalescence [4,5]. At variance with usual-matter properties, the expected increase in the static form factor was not observed in molecular-dynamics simulation of stellar matter at finite temperature [6]. This might be an effect of the Coulomb interaction which also acts in finite nuclei.…”

Exploring the Nuclear Pasta Phase in Core-Collapse Supernova Matter

“…Horowitz et al [18,19] studied these effects using the QMD technique but did not get a conclusive answer because they did not reproduce all the classical pasta shapes in their model. Sonoda et al [11] showed how pasta phases affect the neutrino transport cross section via weak neutral current using several nuclear models.…”