Pumping of OH Main-Line Masers in Star-Forming Regions
Pumping routes of masers can in principle be recovered from a small matrix of master equations, at an advanced stage of elimination, by tracing back the coefficients to a set of unmodified all-process rate coefficients, drawn from those which appeared in the original set of master equations, prior to any elimination operations. The traceback is achieved by logging the operations carried out on each coefficient. There is no guarantee that a pumping scheme can be represented as a small set of important routes in this way. In the present work, the traceback method is applied to a model which is typical of a large volume of parameter space which produces very strong inversions in the main lines of the rotational ground state of OH, at 1665- and 1667-MHz. For both lines, the pumping scheme is largely restricted to the $^{2}Π_{3/2}$ stack of rotational levels, and it is possible to list a comparatively small set of routes (less than ten) which provide more than 80 per cent of the inversion. In both cases, the strongest, and simplest, route consists of a radiative upward stage, to the $^{2}Π_{3/2}, J=5/2$ rotational level, followed by a collisional de-excitation to the rotational ground state.