Lande subtraction method with finite integration limits and application to strong-field problems

Abstract

The Lande subtraction method has been widely used in Coulomb problems, but the momentum coordinate p∈(0,∞) is assumed. In past applications, a very large range of p was used for accuracy. We derive the supplementary formulation with p∈(0,p_{max}) at reasonably small p_{max} for practical calculations. With the recipe, accuracy of the hydrogenic eigenspectrum is dramatically improved compared to the ordinary Lande formula by the same momentum grids. We apply the present formulation to strong-field atomic above-threshold ionization and high-order harmonic generations. We demonstrate that the proposed momentum space method can be another practical theoretical tool for atomic strong-field problems in addition to the existing methods.

A theoretical study on the strong-field ionization of the lithium atom

“…In the finite-integration limit momentum space method [1], the TDSE of a model one-electron atom under a laser field in R-space is transformed into P-space through Fourier transformations. The eigenset of the unperturbed Hamiltonian is then employed for time-propagation [13].…”

“…Therefore, we modified the conventional Lande subtraction method and developed the finite integration limit P-TDSE. The improvement demonstrated that the method is efficient and accurate and is especially suitable for strong-field problems [1].…”

A simple method to construct eigenset of single-active-electron atom in momentum space with applications to solve time-dependent Schroedinger equation

“…Compared with N = 2048, p max = 100 of case I, Table I in Ref. [15] of our previous complicated Lande subtraction method, the present accuracy with half grid number has been competitive or even better. The results show that high accuracy in E(nl) was reached at a modest number of grids.…”

“…We showed that the time-dependent Schrödinger equation (TDSE) of a hydrogen atom under irradiating of intense laser pulse can be calculated by using the generated P-space eigenset of the hydrogen atom. The photoelectron spectra and high-order harmonic generations were obtained without cooperating to other approximations [15]. However, the Lande regularization method has never been straightforward in coding, and application was limited.…”

Ionization enhancement and suppression by phase-locked ultrafast pulse pairs

“…We performed the TDSE calculation in momentum space where the photoelectrons have finite momenta and localized wave functions. For the calculations, we used the time-dependent generalized pseudospectral method [37][38][39], in which the electron wave function is discretized on an optimized momentum grid (depending on a single-variable parameter) and propagated accurately using the split-operator scheme. The total ionization probability was calculated by projecting the postinteraction wave function onto the continuum states of the unperturbed Hamiltonian.…”