Astrophysics and Space Science

, Volume 62, Issue 2, pp 309–333 | Cite as

Neutrino chemical potential and neutrino heat conductivity with allowance for neutrino scattering

  • V. S. Imshennik
  • D. K. Nadyozhin
Article

Abstract

The equations of neutrino hydrodynamics are derived in two different approximations taking into consideration the neutrino scattering from stellar material. In a thermal-conductivity approximation which holds good when neutrino optical depth with respect to absorption exceeds 1, the neutrino scattering is taken into account, analogously with photon radiative conductivity, by introducing the transport cross-section in the neutrino mean free path. In a practically important case when the neutrino optical thickness with respect to scattering is high enough, whereas that concerning absorption is sufficiently low, another approximation of ‘Comptonized’ neutrinos is valid. In this case, the neutrino and antineutrino chemical potentials are independent of each other. They have to be calculated from equations of continuity established for neutrino and antineutrino alongside with the diffusion equation expressing the law of lepton-charge conservation. The equations of neutrino hydrodynamics are written out both with and without inclusion of muon neutrinos and antineutrinos.

The equations obtained are established to deal properly with neutrino diffusion inside collapsing stars.

Keywords

Heat Conductivity Free Path Diffusion Equation Optical Depth Optical Thickness 

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Copyright information

© D. Reldel Publishing Co 1979

Authors and Affiliations

  • V. S. Imshennik
    • 1
  • D. K. Nadyozhin
    • 1
  1. 1.Institute of Applied MathematicsU.S.S.R. Academy of SciencesMoscowU.S.S.R.

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