Proc. Neutrino Astrophysics - MPP Theory Group

Supernova Neutrino Opacities
G.G. Raffelt
Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)
Föhringer Ring 6, 80805 München, Germany
The collapsed cores of supernovae are so dense and hot that neutrinos are trapped. Therefore,
the transport of energy and lepton number is governed by the neutrino transport coefficients,
i.e. by their effective scattering and absorption cross sections. While electrons cannot
be entirely ignored, it is the interaction with nucleons which is thought to dominate the neutrino
opacities. The cross sections can be dramatically modified by medium effects; strong
magnetic fields which can also be important will not be considered here.
Final-state blocking by degenerate nucleons is one obvious modification of the vacuum
cross sections [1]. Even this trivial effect depends sensitively on the nucleon dispersion relation;
a reduced effective nucleon mass increases the degree of degeneracy. Moreover, depending
on the equation of state the composition may deviate from a naive proton-neutron mixture in
that there may be a significant fraction of hyperons. Studies of opacities with self-consistent
compositions and dispersion relations reveal large modifications [2].
The neutrino interaction with nucleons is dominated by the axial vector current, i.e. it
is a spin-dependent phenomenon. At supernuclear densities one thus expects a dominant
role for spin-spin correlations [3]; the use of uncorrelated single-particle states for an opacity
calculation amounts to an uncontrolled approximation.
A less intuitive effect is the cross-section reduction by the nucleon spin fluctuations which
are described by the dynamical dependence of the spin-density structure function [4, 5, 6].
In Fig. 1 the reduction of the average neutrino-nucleon axial-vector cross section is shown
as a function of the assumed nucleon spin fluctuation rate Γσ. A perturbative calculation
yields Γσ/T ≈ 20–50 for a SN core, but the true value is not known. Still, spin fluctuations
(dynamical correlations) certainly have a significant impact on the neutrino opacities.
Figure 1: Variation of the thermally averaged axial-current neutrino scattering cross section
on nucleons as a function of the nucleon spin-fluctuation rate. The curve marked “Lorentzian”
is obtained from a “resummed” dynamical structure function [6].
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