Supernova Neutrino Opacity from Nucleon‐Nucleon Bremsstrahlung and Related Processes

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Abstract
Elastic scattering on nucleons, νN → Nν, is the dominant supernova (SN) opacity source for μ and τ neutrinos. The dominant energy- and number-changing processes were thought to be νe- → e-ν and ν↔e+e− until Suzuki showed that the bremsstrahlung process νNN↔NN was actually more important. We find that for energy exchange, the related "inelastic scattering process" νNN↔NNν is even more effective by about a factor of 10. A simple estimate implies that the νμ and ντ spectra emitted during the Kelvin-Helmholtz cooling phase are much closer to that of e than had been thought previously. To facilitate a numerical study of the spectra formation we derive a scattering kernel that governs both bremsstrahlung and inelastic scattering and give an analytic approximation formula. We consider only neutron-neutron interactions; we use a one-pion exchange potential in Born approximation, nonrelativistic neutrons, and the long-wavelength limit, simplifications that appear justified for the surface layers of an SN core. We include the pion mass in the potential, and we allow for an arbitrary degree of neutron degeneracy. Our treatment does not include the neutron-proton process and does not include nucleon-nucleon correlations. Our perturbative approach applies only to the SN surface layers, i.e., to densities below about 1014 g cm-3.

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