A NEW APPROACH TO INCLUDING DOUBLY-EXCITED LEVELS IN THE COLLISIONAL RADIATIVE MODEL

A severe limitation on the application of the collisional radiative mo del is the need to include an exceedingly high number of relevant doub ly excited and inner shell excited levels. The direct inclusion of all these levels is simply impractical. In a previous theory we have incl uded doubly excited configurations as effective levels assuming statis tical distribution of the populations within these configurations. In the present work we develop a new approach which minimizes even furthe r the amount of effective levels, and leading, paradoxically, to weake r statistical assumptions. It is shown that the outer Rydberg orbital of the doubly excited configuration resembles a continuum electron, an d is only weakly coupled to the internal core. This fact allows the ap plication of the Factorization Interpolation method, reducing the cros s-sections of the various collisional radiative processes to one elect ron multipole transitions between core states only. The radial integra ls include the outer orbital and the summation over all the involved c ontinuum orbitals. It is also shown that the assumption of a statistic al distribution can be extended to groups of states with neighboring R ydberg orbitals. Each group then contains effective levels characteriz ed by the core state designation and therefore has the same dimension as the original core. A convergence procedure is described that involv es 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 e xample 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 th e core multiplied by the small number of groups. This reduction is eve n more striking in more complex ions and in cases where the core is fa r from closed shell configurations.