An L² Method for Continuum States

Abstract

The recent development of laser and synchrotron technology has led to a large amount of detailed experimental information about the continuous spectra of atoms and molecules. The theoretical interpretation of these results often requires a very careful treatment of the continuum, because interesting features like the resonances’ shapes and widths arise uniquely from the electron correlation, and hence can be reproduced only by accurate wavefunctions. These calculations are generally performed by close-coupling or related methods, mainly through the numerical integration of the radial equation for the electron wave. These techniques, although quite adequate to the purpose, lie outside the usual framework of the computational quantum chemistry, where several methods have been developed to treat carefully the correlation problem; in fact, pratically all these methods rely on the use of L² basis functions. It is therefore highly desirable to develop methods for extracting the properties belonging to the continuum from computations performed entirely on L² bases without the limits of the standardly used techniques, such as the Stieltjes (moment) /1/ and the R-matrix /2/ methods. The Stieltjes technique is a valuable tool for computing slowly varying photoionization cross-sections, but cannot reproduce their features at narrow resonances; moreover it does not yield the states or many other interesting quantities. The R-matrix method, instead, can be usefully employed when the continuum states are fairly approximated by a single ionic configuration coupled to one electron wave. Its multiconfigurational extension, however, leads to intractable bielectronic integrals.