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, be tween the Hamiltonian matrix H and a Lanczos vector C. For highly exci ted states and/or strong perturbations the size of H grows fast leadin g to storage problems. By making-use of direct methods, i.e. avoidance of explicit construction on of large Hamiltonian matrices, such probl ems can be overcome. Utilizing the underlying analytical properties of the Laguerre basis e(-lambdar)L(k)2I+2(2lambdar) a direct RRGM (D-RRG M) for the unperturbed hydrogenic Hamiltonian is derived, changing the storage needs from scaling as N2 to 4N where N is the number of radia l functions for each factorized H-0(l, m) block with the possibility o f parallel processing. A further computational simplification is intro duced by putting the expression for the photoionization (PI) cross sec tion in the rational form conventionally used in the representation of density or states (DOS). This allows the construction of the PI cross section directly from the tridiagonal Lanczos matrix avoiding the exp licit calculation of individual eigenvalues and eigenvectors. To illus trate and verify the method the PI cross section for a hydrogen atom i n a static electric field, for both pi and cr polarization, was calcul ated for an electric field strength of F = 5714 V cm-1. Sufficiently l arge basis sets could be employed so that good comparison with experim ent and other theoretical work was obtained, including the field-induc ed modulations near the zero-field ionization limit.