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Diffuse reflection and transmission coefficients in a plane parallel medium are calculated for a Rayleigh phase-function averaged over polarization and Rayleigh polarized phase-function. This is calculated by imbedding the finite medium into a semi-infinite scattering and absorbing medium. Numerical calculations for semi-infinite albedo are compared with Pomraning results. The albedos for finite medium are calculated via the imbedding equations which converge for large t to the value of semi-infinite medium.

Radiation transfer problem in the slowing-down region is solved for a spherical geometry. Modelled kernels are used to represent the slowing-down kernel. Calculations are performed for the radiation flux at the boundary of the sphere for two cases: (i) in the presence of internal source, (ii) if the radiation is incident on the sphere. Numerical results are obtained by using the Padé approximant technique.

The problem of radiation transfer in a cylinder with diffuse reflectivity and containing an energy source is connected with the source-free radiation transfer problem with isotropic boundary condition. Equation for the radiation heat flux is obtained for a polynomial source. In the special case of isotropic scattering, the radiation heat flux is given in terms of the albedo of the second problem. An expression is also given for the net radiation heat flux.

Equations for the angular density of radiation, reflected and transmitted intensities associated with radiation scattered by inhomogeneous dispersive media are obtained. The Padé approximant technique is used to calculate these intensities in inhomogeneous and homogeneous media. The results for the [0/1] Padé approximant lead to numerical results that compared with the exact results.

The particle escape probability from a spherical region containing an internal source is defined in terms of a functional relation for the diffuse scattering problem. The bivariational method is used to obtain numerical results for homogenous and inhomogeneous sphere.

Exact relations for radiation heat flux at the boundaries of a slab with diffusely reflecting boundary conditions and internal source are obtained in terms of the reflection and transmission coefficients of a source free slab with isotropic boundary conditions. The integral equation defining the radiation heat flux contains explicitly the internal source. So, the particular solution for radiative transfer equation is not required. Available exact values for albedos give exact values of radiation heat flux. Padé approximant technique is used to obtain numerical values for homogenous media.

The equation of radiative transfer for an inhomogenous dispersive finite medium subject to general boundary conditions is solved. The Padé approximation technique is used to calculate the angular distribution of radiation. Numerical results for the [0/1] Padé approximant lead to numerical results that compared with the exact results.

The Padé approximants is used to estimate the albedo for an inhomogeneous semi-infinite medium. The single-scattering albedo is assumed to fall off exponentially with optical depth.

Asymptotic calculations for reflection and transmission coefficients for particles incident on an inhomogeneous plane parallel medium are performed. The medium is assumed to consist of several different optically thick homogeneous layers. Functional relations between the reflection and transmission coefficients for the sublayers are obtained. The invariant embedding concepts are used to calculate the albedo for sublayers. Numerical calculations and comparisons are performed.

The slowing-down Boltzmann equation for generalized boundary conditions is considered and transformed to one-speed equation in Laplace space. Exact relations between energy reflection and transmission coefficients for a problem with diffuse reflecting boundary conditions and the albedos for the problem with isotropic boundary conditions are obtained. The Galerkin method is used to calculate the energy reflection coefficient for a finite slab for different thicknesses at different mass ratiosA, target to projectile mass, at different synthetic-scattering kernels. The results for partial heat fluxes for isotropic and anisotropic-scattering dispersive medium are given. The results obtained for isotropic boundary conditions are compared well with the exact results.

The problem of heat flux at the critical surfaces and the surfaces of a pellet of deuterium and tritium (conduction zone) heated by laser have been considered. Ion-electron collisions are only allowed for: i.e., the linear transport equation is used to describe the problem with boundary conditions consists of isotropic and diffuse boundary conditions. The bi-variational technique has been used to calculate the electron density and temperature across the conduction zone as well as the heat flux. Numerical results are given and compared with those of Rouse and Williams (1981) results.

The reflectivity and transmissivity of a linear anisotropically scattering plane-parallel slab with a stepwise variation of the single scattering albedo and anisotropic coefficient of the scattering kernel within the medium are determined for an isotropically-incident radiation. The slab under consideration is devided intoM sub-layers and the invariant embedding concepts are used to get the reflection and transmission coefficients for the sub-layers. Tabulated results, covering a wide range of albedos at different values of the anisotropic coefficient, are presented.

In this note, we connect the problem of radiation transfer in a sphere with diffuse reflectivity and containing an energy source with the problem of source free radiation transfer with isotropic boundary condition. The equation for the radiative heat flux is obtained for a polynomial source. In the special case of a uniform source, the radiation heat flux and the angular flux are given in terms of the albedo of the second problem.

Equations for radiation, scattered anisotropically from dispersive media are obtained for general boundary conditions. The Padé approximant technique is used to calculate the reflection coefficients for these media. Numerical results are given for diffuse reflected boundary condition.

The mean number of particle scattering in a semi-infinite and finite slab for arbitrary energy sources are calculated by Padé approximants. Uniform source distribution is considered for the finite slab. For the semi-infinite medium we calculatethe number of particles due external radiation and at a particular point in the medium. Numerical calculations and comparisons were performed.

The emergent flux for radiation transfer in an inhomogeneous half-space with internal source is obtained in terms of the source-function of the diffuse reflection problem. Modified Eddington method is used to calculate the diffuse problem and, hence, the emergent flux. Numerical result are given and compared with previous work.

Equations connecting the transmission and reflection functions of a finite medium to the reflection function of a semi-infinite one are used to get the albedos in the slowing-down region. The transport equation is solved by the modified Eddington method using Fermi's backward-forward scattering model, modulated to allow for different orders of backward-forward and isotropic scattering. Numerical results for the energy albedos are obtained and compared.

An asymptotic solution for the equation of radiative transfer in an inhomogeneous medium was obtained on the basis of the corresponding solutions for homogeneous sub-layers in the slowing down region. Function relations between the reflection and transmission coefficients for the whole slab and those of the sublayers are given. The invariant embedding concepts are used to get the reflection and transmission coefficients for the sub-layers. We assumed different models for the slowing-down kernels. Laplace transform was used to transform the Boltzmann equation to one velocity approximation with re-scaled mean-free path and single-scattering albedo. Numerical results are given for energy albedo as a function of the mass number of the host medium.