Finite Space Complete Basis Method: Precision Computation of High-Resolution Spectrum near Ionization Threshold

Abstract

A new method is proposed to describe quantum dynamical processes in finite space by using of a set of discretized complete bases. In this method, the finite space complete basis is obtained by solving the self-consistent field equation with reflecting boundary conditions. Hence, both negative and positive orbital energies can be obtained. Such method can be used in systems which involve dynamics only in the reaction zone, i.e., in a finite space. To illustrate the validity of the method, we present two examples: theoretical calculation of the high excited states spectra including the continuum of sodium and barium.

Coulomb effect on the dynamics of atoms in a strong elliptical laser field: Unification of the excitation and ionization

“…In experiments, the energy resolution is finite, so the measured oscillator strength is actually the oscillator strength density near the threshold, which is smoothly connected to the photoionization spectra [1,55]. In the numerical calculation of the oscillator strength density df l /dE using a basis set, we have shown that it can be calculated by two equivalent methods [55]. One is to calculate the density of state directly by finite difference (including the pseudo states) and using Eq.…”

Application of a numerical-basis-state method to strong-field excitation and ionization of hydrogen atoms

“…We have used a square grid with a higher concentration of grid points near the nucleus, i.e., r i = i 2 R 0 /N 2 . Furthermore, in the present application of the method, the outer boundary (R 0 ) and the total number of grid points (N ) are chosen to be adaptive for different n and l. Larger R 0 and N are chosen for larger n and l. This kind of numerical-basis set has been used before to calculate atomic photoabsorption spectra for highly excited states as well as continuum states [33,34]. These previous results indicate that the atomic energy levels and dipole transition matrix elements can be well reproduced using the numerical-basis set.…”

“…To this end, we numerically obtain finite-space energy eigenstates for the hydrogen atom in a box [33,34], represent the numericalbasis set on a grid, and propagate the system under the influence of an intense laser pulse. As examples, we calculate the transition probabilities to excited bound states and into the continuum as well as electron momentum spectra.…”