Exact solution of the transport equation for radiative transfer with scattering albedo ωO < 1 using the Laplace transform and the Wiener-Hopf technique and an expression ofH-function

We have considered the transport equation for radiative transfer to a problem in semi-infinite non-conservative atmosphere with no incident radiation and scattering albedo ₀ < 1. Usint the Laplace transform and the Wiener-Hopf technique, we have determined the emergent intensity and the intensity at any optical depth. We have obtained theH-function of Dasgupta (1977) by equating the emergent intensity with the intensity at zero optical depth.     

On transfer equation in a semi-infinite atmosphere with albedo ω>1

In this note we derive an exact solution of transfer equation in a plane-parallel semiinfinite atmosphere with albedo >1, by the method of Laplace transform and Wiener-Hopf technique. The emergent intensityI(0, ) is obtained in terms of theH ⁰-functionH ⁰() (Das Gupta, 1978) for which some good approximations are given. Intensity at any depth is also obtained.I(0, )/I(0, 0) is plotted in graphs against [0,1], and shows a maximum which drops and shifts towards the origin as increases.     

Exact solution of the equation for the problem of diffuse reflection and transmission with a scattering function ω0(1 +x cos⊙) by the method of laplace transform and theory of linear singular integral equation

Neutrinos couple through a weak neutral current to the density of matter, in particular to the neutron density. Density fluctuations, or phonons, in the neutron fluid may be emitted or absorbed by neutrinos passing through the matter. At high densities, temperatures and neutrino energies the neutrino mean free paths for phonon emission and absorption can be 10⁶ cm. Significant changes in the neutrino momentum and energy accompany these processes. We present a model calculation for neutrino scattering by phonons, and representative numerical results for the neutrino mean free path and mean energy and momentum changes fork _B T andE _v both ranging from 1 to 27 MeV.Research supported by the National Research Council of Canada.