PHOTON DISPERSION IN A SUPERNOVA CORE

While the photon forward-scattering amplitude on free magnetic dipoles (e.g. free neutrons) vanishes, the nucleon magnetic moments still con tribute significantly to the photon dispersion relation in a supernova (SN) core where the nucleon spins are not free due to their interacti on. We study the frequency dependence of the relevant spin susceptibil ity in a toy model with only neutrons which interact by one-pion excha nge. Our approach amounts to calculating the photon absorption rate fr om the inverse bremsstrahlung process gamma nn-->nn, and then deriving the refractive index n(refr) with the help of the Kramers-Kronig rela tion. In the static limit (omega-->0) the dispersion relation is gover ned by the Pauli susceptibility chi(Pauli) so that n(refr)(2)-1 approx imate to chi(Pauli)>0. For omega somewhat above the neutron spin-relax ation rate Gamma(sigma) we find n(refr)(2)-1<0, and for omega much gre ater than Gamma(sigma) the photon dispersion relation acquires the for m omega(2)-k(2)=m(gamma)(2). An exact expression for the ''transverse photon mass'' m(gamma) is given in terms of the f-sum of the neutron s pin autocorrelation function; an estimate is m(gamma)(2) approximate t o chi(Pauli)T Gamma(sigma). The dominant contribution to n(refr) in a SN core remains the electron plasma frequency so that the Cherenkov pr ocesses gamma nu<->nu remain forbidden for all photon frequencies.