The scattering of line radiation—I. A generalized redistribution function

The theory of the frequency redistribution of radiation during scattering is re-investigated with the aim of producing a generalized frequency redistribution function. The assumption, commonly made, that the atom performing the scattering of the radiation has a constant velocity for the duration of the scattering event is not made in the present investigation. As a result a formal theory is developed which does indeed lead to a generalized redistribution function. Two limiting cases are discussed: in one of the limits, we reconsider the case where the velocity of the atom is constant during the scattering event; the other limiting case describes the situation which occurs when the velocity at absorption, of the atom performing the scattering, is completely uncorrelated with its velocity at emission. This latter case is then more fully discussed with a view to overcoming one of the major difficulties encountered with the existing theories of frequency redistribution, i.e. that complete redistribution in the radiation scattered from an atmosphere being viewed by a distant observer can not be predicted.