Classical theory of transitions between degenerate states of excited hydrogen atoms in plasmas

The authors present a general classical theory of transitions between degenerate states of hydrogen-like atoms and ions, with particular application to multiple overlapping collisions with the charged particles of an isotropic plasma. They classify individual collisions as either Stark adiabatic or Stark sudden. The combined effects lead to a combination of diffusion and Poisson randomisation of the angular momentum, for which an explicit time-dependent solution is obtained in terms of elementary functions. The time constants, lambda D for the diffusion process and lambda P for the Poisson process, are given in terms of elementary functions of nuclear charge and principal quantum number, reduced mass, charge and density of incident particles and temperature. The equilibration rate for angular momentum, l, in the absence of other processes is equal to the sum over lambda D+ lambda P for all charged species.