Solution of a set of population balance equations for atomic and molecular quantum levels in some particular cases

Astronomy and Astrophysics – Astrophysics

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Diatomic Molecules, Equilibrium Flow, Quantum Mechanics, Rotational States, Radiation Distribution, Atomic Energy Levels, Radiative Transfer, Astrophysics

Scientific paper

Recursion solutions of population balance equations for levels of a quantum system were obtained. The solutions generalize Seaton's ones for the case when there is an outward leak of populations and an influx of populations from outside, and populations of levels are affected by either an equilibrium field of external radiation or stimulated collisional transitions. A recursion solution was also obtained for populations of rotational levels of a diatomic molecule in a nonequilibrium radiation field with an account for populations' outward leak and influx from outside (in particular, by means of radiative association and dissociation). The solutions suggested are compact; they allow us to quickly and conveniently calculate populations of atomic and molecular quantum levels in various astrophysical problems.

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