NUMERICAL ANALYSIS OF THE AB INITIO COMPUTATION OF THE EFFECTS OF IONIZATION ON THE NONLINEAR SUSCEPTIBILITY COEFFICIENTS OF THE HYDROGEN ATOM*

Patrick O. Kano, Moysey Brio, Jerome V. Moloney

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

This paper provides a numerical analysis of a procedure for determining the effects of ionization on the nonlinear susceptibility coefficients of the hydrogen atom. To solve the relevant system of Schrodinger-type equations, we have developed a multidomain pseudospectral code with high accuracy symmetric finite differences to update cell boundary points. Using a conservative time stepping, one is then able to resolve the oscillatory solutions to the underlying equations, compute the ionization probability, and accurately determine the polarization. To gain insight into the physical mechanisms involved, we have calculated the full susceptibility and one which depends solely on the electronic bound-bound transitions. Our analysis reveals that saturation of the susceptibility occurs without including bound-continuum transitions. We have also found that a linear extrapolation of the total susceptibility versus the ionization probability to obtain the instantaneous susceptibility is quantitatively unreliable.

Original languageEnglish (US)
Pages (from-to)53-80
Number of pages28
JournalCommunications in Mathematical Sciences
Volume4
Issue number1
DOIs
StatePublished - 2006

Keywords

  • Numerical analysis
  • nonlinear susceptibility
  • time dependent Schroedinger equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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