A new approach to including doubly excited levels in the collisional radiative model

Abstract

A severe limitation on the application of the collisional radiative model is the need to include an exceedingly high number of relevant doubly excited and inner shell excited levels. The direct inclusion of all these levels is simply impractical. In a previous theory we have included doubly excited configurations as effective levels assuming statistical distribution of the populations within these configurations. In the present work we develop a new approach which minimizes even further the amount of effective levels, and leading, paradoxically, to weaker statistical assumptions. It is shown that the outer Rydberg orbital of the doubly excited configuration resembles a continuum electron, and is only weakly coupled to the internal core. This fact allows the application of the Factorization Interpolation method, reducing the cross-sections of the various collisional radiative processes to one electron multipole transitions between core states only. The radial integrals include the outer orbital and the summation over all the involved continuum orbitals. It is also shown that the assumption of a statistical distribution can be extended to groups of states with neighboring Rydberg orbitals. Each group then contains effective levels characterized by the core state designation and therefore has the same dimension as the original core. A convergence procedure is described that involves reducing the number of Rydberg orbitals within a group. It is shown that a small number of groups is sufficient for convergence, reducing drastically the number of effective levels in the model. The simple example of the Ne-like ion is discussed. The many thousands of relevant doubly excited states are reduced in this case to the 37 levels of the core multiplied by the small number of groups. This reduction is even more striking in more complex ions and in cases where the core is far from closed shell configurations.