Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic Molecular and Optical Physics

Two-photon ionization of atomic hydrogen above the one-photon ionization threshold

A P Jayadevan, R. B. Thayyullathil

Published Feb 12, 2001• 17 citations
Publisher

Abstract

An alternative method is presented for the evaluation of the two-photon ionization transition amplitude and transition rates of atomic hydrogen in the ground state above the one-photon ionization threshold. In this approach it is straightforward to calculate the angular distribution of the emitted electrons. These angular distributions are plotted and calculated transition rates are compared with the previously reported results.

DOI
10.1088/0953-4075/34/4/317

Related papers

Non Resonant Two Photon Ionization of Atomic Hydrogen: Exact Expressions of Angular Distribution

M Faye, S T Wane, Seydi Ababacar Ndiaye

Within the framework of second order time dependent perturbation theory and non relativistic dipole approximation, the exact expressions of the radial transition amplitude from 3d, 3p and 3s excited states, were obtained from the integral representation of the Green Coulomb function. Below threshold and above one photon ionization threshold, it can be expressed as an analytic combination of three Appell hypergeometric functions of first order, one of which is degenerated; while at threshold, it can be obtained in terms of an expansion of Gauss confluent hypergeometric functions. The angular coefficients are numerically evaluated and analysed for some available laser wavelengths.

Physica Scripta•Jan 1, 2003•2 citations

Multiphoton Ionization of Atomic Hydrogen in the Ground State

Yves Gontier, M. Trahin

The general theory of multiphoton ionization of hydrogen atoms by simultaneous absorption of several photons is discussed. In the nonrelativistic dipole approximation, the calculations lead to a recursion relationship concerning angular functions and involve radial matrix elements containing many summations over intermediate states. A general method for exactly evaluating several sums is described in detail and applied to the photo-ionization of atomic hydrogen in the ground state. Numerical results are presented as dispersion curves of the transition rate $\frac{{\ensuremath{\sigma}}_{n}}{{I}^{N\ensuremath{-}1}}$ for a range of wavelengths from 1000 up to 7200 \AA{}.

Physical Review•Aug 5, 1968•133 citations

Two-colour three-photon ionization of hydrogen

Magda Fifirig, Aurelia Cionga, Viorica Florescu

Based on analytical equations valid in perturbation theory, we study the process of ionization of the ground state of the hydrogen atom by the absorption of three photons, two of them being of the same frequency. Results are given for the total ionization rate and for the angular distribution of the ejected electrons, in a regime of frequencies in which two-colour two-photon ionization is not possible. The case of orthogonal photon polarizations, investigated in some detail, displays a strong dependence on the electron direction.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 14, 1997•11 citations

The general expression for the transition amplitude of two-photon ionization of atomic hydrogen

Erna Karule, B. Moine

Two-photon ionization of atomic hydrogen with an excess photon is revisited. The non-relativistic dipole approximation and Coulomb Green function (CGF) formalism are applied. Using the CGF Sturmian expansion straightforwardly, one gets the radial transition amplitude in the form of an infinite sum over Gauss hypergeometric functions which are polynomials. It is convergent if all intermediate states are in the discrete spectrum. In the case of two-photon ionization with an excess photon, when photoionization is also possible, intermediate states are in the continuum. We performed the explicit summation over intermediate states and got a simple general expression for the radial transition amplitude in the form of a finite sum over Appell hypergeometric functions, which are not polynomials. An Appell function may be expressed as an infinite sum over Gauss functions. In the case of ionization by an excess photon, Gauss functions are transformed to give a convergent radial transition amplitude for the whole region. The generalized cross sections for two-photon above-threshold ionization of atomic hydrogen in the ground state and excited states calculated by us agree very well with results of previous calculations. Generalized cross sections for two-photon ionization of positronium in the ground state are obtained by scaling those for atomic hydrogen.

Journal of Physics B Atomic Molecular and Optical Physics•May 2, 2003•15 citations

Asymmetries in multiphoton ionization of the ground state of a hydrogen atom

Nilam Shrestha, Ramaswamy Radhakrishnan, R. B. Thayyullathil

This paper illustrates the study on asymmetry of the angular distribution of the ejected electrons in a multiphoton process from the ground state of a hydrogen atom. General expressions for the multiphoton ionization rates have been derived based on a variation of the Dalgarno–Lewis method for the evaluation of matrix elements in higher order perturbation theory. In addition, these analytical expressions for the various multiphoton transition rates and their variation as a function of polarization, phase, frequency and intensity of the incident radiation have been studied extensively. The general expression obtained can be used to analyse any number of incident beams with arbitrary polarization, phase and intensity.

Journal of Physics B Atomic Molecular and Optical Physics•May 1, 2014•1 citation

Two-photon ionisation of atomic hydrogen simultaneously with one-photon ionisation

Erna Karule

Two-photon ionisation of atomic hydrogen in the ground state with linearly and circularly polarised light is considered. In the region above the one-photon ionisation threshold expressions for the two-photon ionisation transition matrix elements are obtained using the non-relativistic dipole approximation. The two-photon ionisation rate is calculated above and below the one-photon ionisation threshold. Above threshold the total cross section for two-photon ionisation has no resonances and diminishes more rapidly than the photoionisation cross section as the wavelength decreases.

Journal of Physics B Atomic and Molecular Physics•Feb 14, 1978•73 citations
An alternative method is presented for the evaluation of the two-photon ionization transition amplitude and transition rates of atomic hydrogen in the ground state above the one-photon ionization threshold. In this approach it is straightforward to calculate the angular distribution of the emitted electrons. These angular distributions are plotted and calculated transition rates are compared with the previously reported results.
Within the framework of second order time dependent perturbation theory and non relativistic dipole approximation, the exact expressions of the radial transition amplitude from 3d, 3p and 3s excited states, were obtained from the integral representation of the Green Coulomb function. Below threshold and above one photon ionization threshold, it can be expressed as an analytic combination of three Appell hypergeometric functions of first order, one of which is degenerated; while at threshold, it can be obtained in terms of an expansion of Gauss confluent hypergeometric functions. The angular coefficients are numerically evaluated and analysed for some available laser wavelengths.
The general theory of multiphoton ionization of hydrogen atoms by simultaneous absorption of several photons is discussed. In the nonrelativistic dipole approximation, the calculations lead to a recursion relationship concerning angular functions and involve radial matrix elements containing many summations over intermediate states. A general method for exactly evaluating several sums is described in detail and applied to the photo-ionization of atomic hydrogen in the ground state. Numerical results are presented as dispersion curves of the transition rate $\frac{{\ensuremath{\sigma}}_{n}}{{I}^{N\ensuremath{-}1}}$ for a range of wavelengths from 1000 up to 7200 \AA{}.
Based on analytical equations valid in perturbation theory, we study the process of ionization of the ground state of the hydrogen atom by the absorption of three photons, two of them being of the same frequency. Results are given for the total ionization rate and for the angular distribution of the ejected electrons, in a regime of frequencies in which two-colour two-photon ionization is not possible. The case of orthogonal photon polarizations, investigated in some detail, displays a strong dependence on the electron direction.
Two-photon ionization of atomic hydrogen with an excess photon is revisited. The non-relativistic dipole approximation and Coulomb Green function (CGF) formalism are applied. Using the CGF Sturmian expansion straightforwardly, one gets the radial transition amplitude in the form of an infinite sum over Gauss hypergeometric functions which are polynomials. It is convergent if all intermediate states are in the discrete spectrum. In the case of two-photon ionization with an excess photon, when photoionization is also possible, intermediate states are in the continuum. We performed the explicit summation over intermediate states and got a simple general expression for the radial transition amplitude in the form of a finite sum over Appell hypergeometric functions, which are not polynomials. An Appell function may be expressed as an infinite sum over Gauss functions. In the case of ionization by an excess photon, Gauss functions are transformed to give a convergent radial transition amplitude for the whole region. The generalized cross sections for two-photon above-threshold ionization of atomic hydrogen in the ground state and excited states calculated by us agree very well with results of previous calculations. Generalized cross sections for two-photon ionization of positronium in the ground state are obtained by scaling those for atomic hydrogen.
This paper illustrates the study on asymmetry of the angular distribution of the ejected electrons in a multiphoton process from the ground state of a hydrogen atom. General expressions for the multiphoton ionization rates have been derived based on a variation of the Dalgarno–Lewis method for the evaluation of matrix elements in higher order perturbation theory. In addition, these analytical expressions for the various multiphoton transition rates and their variation as a function of polarization, phase, frequency and intensity of the incident radiation have been studied extensively. The general expression obtained can be used to analyse any number of incident beams with arbitrary polarization, phase and intensity.
Two-photon ionisation of atomic hydrogen in the ground state with linearly and circularly polarised light is considered. In the region above the one-photon ionisation threshold expressions for the two-photon ionisation transition matrix elements are obtained using the non-relativistic dipole approximation. The two-photon ionisation rate is calculated above and below the one-photon ionisation threshold. Above threshold the total cross section for two-photon ionisation has no resonances and diminishes more rapidly than the photoionisation cross section as the wavelength decreases.