Relationship between the albedo and scattering operators for the Boltzmann equation with semi-transparent boundary conditions

The albedo and scattering operators are central objects in the time-dependent transport theory. Their mutual relationship has recently been established by Arianfar and Emamirad for the case of transparent boundaries. In this paper, we extend the result to general boundary conditions. To allow for this extension, the scattering theory for a transport-like equation is generalized to include partially reflecting boundary conditions. The existence of the wave and scattering operators is directly inferred from the properties of the evolutions. operators that are determined, in turn, by the physics of collisions within and at the boundaries of the scattering domain.