COMPLEX COORDINATE L(2) CALCULATION OF PARTIAL PHOTOIONIZATION CROSS-SECTIONS - THEORY AND A MODEL COMPUTATION

It has been known for quire some time that L(2) methods can be used to obtain the total photoabsorption cross sections for atomic and molecular photo-detachment or ionization without explicit enforcement of coordinate space boundary conditions. Such methods use matrix manipulations followed by use of moment-imaging techniques or various implementations of analytic continuation to construct the total cross section from discretized input data. The present work extends these methods by giving a prescription for obtaining partial photoabsorption cross sections with no prior enforcement of coordinate space boundary conditions, and still retains the desirable feature that only L(2) basis functions are used. The problem of computation of the flux into non-degenerate two-body final states, even at intermediate energy where three- or many-body break-up channels are open, has thus been solved using analytic continuation of appropriate matrix elements of the full resolvent combined with analogous continuations of the Fredholm determinant.