A direct recursive residue generation method: application to photoionization of hydrogen in static electric fields

In studies of hydrogenic systems via the recursive residue generation method (RRGM) the major bottleneck is the matrix vector product HC, between the Hamiltonian matrix H and a Lanczos vector C. For highly excited states and/or strong perturbations the size of H grows fast leading to storage problems. By making use of direct methods, i.e. avoidance of explicit construction of large Hamiltonian matrices, such problems can be overcome. Utilizing the underlying analytical properties of the Laguerre basis e-λrLk2l+2(2λr) a direct RRGM (D-RRGM) for the unperturbed hydrogenic Hamiltonian is derived, changing the storage needs from scaling as N2 to 4N where N is the number of radial functions for each factorized Ho(l,m) block with the possibility of parallel processing. A further computational simplification is introduced by putting the expression for the photoionization (PI) cross section in the rational form conventionally used in the representation of density of states (DOS). This allows the construction of the PI cross section directly from the tridiagonal Lanczos matrix avoiding the explicit calculation of individual eigen values and eigenvectors. (Author)