Stars as Laboratories for Fundamental Physics - MPP Theory Group

Processes in a Nuclear Medium 151
The axion emission and the neutrino scattering rates begin to be
suppressed at high density if Γ σ exceeds a few T . The numerical value
Eq. (4.34) that was derived in a simple OPE calculation indicates that
such large Γ σ may be expected in a nuclear medium. Of course, one
may well ask if a perturbative calculation of the spin-fluctuation rate is
adequate if such a calculation fails for the neutrino scattering rate. Nucleon
spins fluctuate because of their spin-dependent interaction with
other nucleons and thus are themselves subject to spin averaging effects.
The question of the true value of Γ σ in a nuclear medium (as opposed
to the OPE-calculated one) can be addressed empirically by virtue of
the SN 1987A neutrino signal and theoretically by the f-sum rule.
Because the axial-vector current contribution to the standard neutral-current
scattering rate dominates (the cross section is proportional
to CV 2 + 3CA), 2 it would be much easier for neutrinos to diffuse out of
the hot SN core if the axial-current scattering rate were significantly
suppressed. The observed SN 1987A neutrino signal would have been
much shorter than predicted in standard cooling calculations. The
impact of reduced neutrino opacities on the SN 1987A signal has been
studied by Keil, Janka, and Raffelt (1995); see Sect. 13.6. The main
conclusion is that a suppression of the axial-vector current opacity by
more than about a factor of 2 is not compatible with the SN 1987A
signal duration. This result would indicate that the effective Γ σ never
becomes much larger than a few T .
Theoretically, the f-sum rule Eq. (4.58) allows one to relate Γ σ to
the average spin-spin interaction energy in the medium. According to
Sigl’s (1995b) estimate one concludes, again, that Γ σ does not exceed
a few T in a nuclear medium.
These results imply that even in a dense medium the axial-vector
scattering rate is not suppressed as strongly as one may have expected
on the basis of a naive estimate of Γ σ . It still remains impossible to calculate
its exact magnitude from first principles. Therefore, the neutralcurrent
neutrino opacity remains an adjustable function of density for
practical SN cooling calculations much as the equation of state.
4.7 Effective Nucleon Mass and Coupling
In a dense medium it is not necessarily possible to use the vacuum
masses and coupling constants to determine interaction rates. The
axial-vector neutrino couplings are probably suppressed somewhat (Appendix
B). For the pion-nucleon coupling, Turner, Kang, and Steigman