Calculations of photodissociation and photoionization cross sections by using a recursive expansion of Green's operator with absorbing boundary conditions

Abstract

An iterative method for calculating total cross sections for molecular photodissociation and atomic photoionization is presented. It is based on the recursive expansion of Green's operator with absorbing boundary conditions, recently developed by Mandelshtam and Taylor. The method is tested by calculating cross sections for photodissociation of the molecule and another model problem, as well as for the photoionization of a hydrogen atom in the absence and presence of a strong magnetic field. In all applications the discrete variable representation is employed.

Excitation and ionization inp+ H collisions calculated by direct numerical solution using Laguerre meshes

“…We can find only a small number of atomic applications, i.e. for atomic structure calculation (Godefroid et al 1989, Vincke et al 1993, Demeur et al 1994, Malegat 1994, Malegat and Vincke 1994, Grozdanov and McCarroll 1996, Grozdanov et al 1997 and for the R-matrix method (Layton 1993, Layton andStade 1993). Very recently, the present author (Sakimoto (2000b), hereafter referred to as paper I) has employed the DVR to investigate the ionization of atomic hydrogen by antiproton (p) impact:p + H →p + p + e.…”

Calculation of electron transport in multiterminal systems using complex absorbing potentials

“…Numerical tests show that high-lying states do not contribute to the spectral decomposition in the desired energy range around the Fermi energy. One should also note that if the size of the Hamiltonian matrix does not allow direct diagonalization then one can use recursive methods, for example those based on damped Chebyshev polynomial expansions [50][51][52] or the Lanczos algorithm 53,54 . Using the spectral representation, one can rewrite the transmission coefficient in an explicitly energy dependent simple form…”

Photodynamics of Molecules in Space

“…Ionized regions (HII) 10000 10 8 -10 9 Ionized gas H + , C + , N + ,O + . Emission spectra (discrete and continuous Other important features of the observations, which are important for any theoretical interpretation, are listed below 1.…”

“…For that reason, we have developed several novel methods [9][10][11][12][13][14][15][16], which make it relatively easy to compute photodissociation cross sections whether resonances are present or not. To describe narrow resonances in the time dependent approach requires propagation of the wave packet for a long time, which affects the accuracy of the calculation.…”

“…When the Hamiltonian becomes large (of the order of 500 or more), it is preferable to calculate the Green function by recursive methods [9]. It should be noted that in the above the pseudo scalar product, without complex conjugation, is used as is appropriate for complex matrices.…”