While the photon forward-scattering amplitude on free magnetic dipoles (e.g. free neutrons) vanishes, the nucleon magnetic moments still contribute significantly to the photon dispersion relation in a supernova (SN) core where the nucleon spins are not free due to their interaction. We study the frequency dependence of the relevant spin susceptibility in a toy model with only neutrons which interact by one-pion exchange. Our approach amounts to calculating the photon absorption rate from the inverse bremsstrahlung process γn→nnn, and then deriving the refractive index nrefr with the help of the Kramers-Kronig relation. In the static limit (→ω0) the dispersion relation is governed by the Pauli susceptibility χPauli so that nrefr²-1≈χPauli>0. For {ω} somewhat above the neutron spin-relaxation rate Γ_σ we find nrefr²-1<0, and for ωΓ_σ the photon dispersion relation acquires the form ω²-k²=m_γ². An exact expression for the ``transverse photon mass'' m_γ is given in terms of the f-sum of the neutron spin autocorrelation function; an estimate is m_γ²≈χPauliTΓ_σ. The dominant contribution to nrefr in a SN core remains the electron plasma frequency so that the Cherenkov processes γν↔ν remain forbidden for all photon frequencies.
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Kopf et al. (1998) studied this question.