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Journal of Physics B Atomic and Molecular Physics

Two-photon ionisation of atomic hydrogen in the presence of one-photon ionisation

M Aymar, Michele Crance

Published May 14, 1980• 61 citations
Publisher

Abstract

The authors propose a numerical method to calculate N-photon ionisation cross sections, when ionisation by N-1 photons is energetically possible. They present some results obtained for N=2. Cross sections obtained for two-photon ionisation of ns states of hydrogen by circularly polarised light are in excellent agreement with previous theoretical ones. As an example the method is also applied to lithium atoms.

DOI
10.1088/0022-3700/13/9/002

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Angular distributions and polarisation phenomena in non-resonant multiphoton ionisation of alkali-metal atoms. II. Two-photon ionisation of atomic caesium

G Laplanche, M. Jaouen, A. Rachman

For pt.I see ibid., vol.19, p.79 (1986). The authors study the two-photon ionisation of unpolarised target atoms of caesium in their ground state or in one of the two first excited states 6P 1/2 or 6P 3/2 in the non-resonant region. Circularly, linearly and unpolarised light are considered. For each case they give a systematic analysis of generalised transition probabilities, angular distributions and polarisation phenomena. In particular, it is shown that polarised electrons can be obtained even with linearly or unpolarised light.

Journal of Physics B Atomic and Molecular Physics•Jan 14, 1986•3 citations
The authors propose a numerical method to calculate N-photon ionisation cross sections, when ionisation by N-1 photons is energetically possible. They present some results obtained for N=2. Cross sections obtained for two-photon ionisation of ns states of hydrogen by circularly polarised light are in excellent agreement with previous theoretical ones. As an example the method is also applied to lithium atoms.
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.
Two-photon ionisation of atomic hydrogen is considered in the non-relativistic dipole approximation at the photoelectric threshold and above it. In this region are obtained convergent analytical expressions for the radial transitions matrix elements, necessary for the calculation of ionisation rates. Partial and total cross sections per unit intensity are calculated for two-photon ionisation of atomic hydrogen in excited states with 2<or=n<or=9 by linearly and circularly polarised light at the photoelectric threshold and above it. At the photoelectric threshold calculations are also carried out for the two-photon ionisation of atomic hydrogen in the ground state.
By using a perturbative treatment based on the central field approximation, the authors have calculated multiphoton ionisation probabilities in several cases of experimental interest (two-, three- and four-photon ionisation of the caesium and potassium ground states at the doubled Nd glass laser frequency and one-, two- and three-photon ionisation of some s, p, d and caesium Rydberg states). Some of these probabilities have been calculated beyond the minimum non-vanishing order. They have also performed some calculations for hydrogen. The comparison of their results with previous ones obtained by analytical methods provides a good test of the numerical techniques involved in the calculations.
The infinite summations over the complete set of unperturbed atomic states appearing in the NNNth-order perturbation theory for multiphoton ionization are performed using the Dalgarno-Lewis method. The relevant transition matrix elements are written in a closed integral form exhibiting all the analytic properties of the amplitude as a function of incident photon energy. The cross sections for two- and three-photon ionization for atomic hydrogen are calculated for both linearly and circularly polarized light with a wide range of photon energy spectrum including the near resonance, and numerical comparison is made with the values obtained by different methods.
For pt.I see ibid., vol.19, p.79 (1986). The authors study the two-photon ionisation of unpolarised target atoms of caesium in their ground state or in one of the two first excited states 6P 1/2 or 6P 3/2 in the non-resonant region. Circularly, linearly and unpolarised light are considered. For each case they give a systematic analysis of generalised transition probabilities, angular distributions and polarisation phenomena. In particular, it is shown that polarised electrons can be obtained even with linearly or unpolarised light.