Invariant-embedding and cognate kinetic descriptions of particle reflection/emission from surfaces

The invariant-embedding (IE) approach, originally developed by Ambartsumyan and Chandrasekhar, is revisited in this paper. The unified derivation and description presented are geared to particle backscattering/emission from surfaces and contain earlier treatments as special cases of the arising general theory that embraces a large variety of bombarding particles and collision-cascade types. A particular new development concerns the relationship between the half-space and infinite-medium solutions in terms of the resolvent of the underlying transport operator. The infinite-medium reformulation of the IE approach gives rise to new equations that are more transparent, highlight fundamental relationships underlying various descriptions of reflection/emission kinetics, and are very flexible for further analytical transformations or numerical studies of the solutions. The general discussion is illustrated by explicit distributions characterizing elastic electron backscattering from a solid; an efficient and powerful calculation technique is discussed and exemplified by various resulting dependencies.