Abstract
Abstract We generalize our virial approach to study spin-polarized neutron matter and the consistent neutrino response at low densities. In the long-wavelength limit, the virial expansion makes model-independent predictions for the density and spin response, based only on nucleon–nucleon scattering data. Our results for the neutrino response provide constraints for random-phase approximation or other model calculations, and we compare the virial vector and axial response to response functions used in supernova simulations. The virial expansion is suitable to describe matter near the supernova neutrinosphere, and this work extends the virial equation of state to predict neutrino interactions in neutron matter.
Highlights
Neutrinos radiate 99% of the energy in core-collapse supernovae
For low densities and high temperatures, the virial expansion provides a tractable approach to strong interactions, and in previous works we have presented the virial equation of state of low-density nucleonic matter [3, 4]
We have extended our virial approach to study spin-polarized neutron matter and the consistent longwavelength response
Summary
The scattering of neutrinos and the physics of the explosion are most sensitive to the properties of low-density nucleonic matter [1, 2], which is a complex problem due to strong coupling with large scattering lengths, clustering in nuclear matter and the non-central nature of nuclear interactions. The virial approach can be used to describe matter in thermal equilibrium around the neutrinosphere in supernovae. The temperature of the neutrinosphere is roughly T ∼ 4 MeV from about 20 neutrinos detected in SN1987a [6, 7], and the density follows from known cross sections of neutrinos with these energies n ∼ 1011 − 1012 g/cm. The virial approach makes model-independent predictions for the conditions of the neutrinosphere, based only on the experimental scattering data. We use the virial expansion to describe how neutrinos interact with low-density neutron matter. The free cross section per particle for neutrino-neutron elastic scattering is given by [8]
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