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Journal of Physics B Atomic and Molecular Physics

Two-photon ionisation of the potassium atom

Michael Stuart Pindzola, A B Chen, Burke Ritchie

Published Jan 28, 1981• 4 citations
Publisher

Abstract

The two-photon ionisation cross section of potassium is calculated from a quasi-degenerate perturbation theory expansion in the atom-radiation field interaction. The authors assume a narrow bandwidth radiation field of moderate photon flux (1025-1029 photons/cm2 s). Resonances are treated by first diagonalising the Hamiltonian among the strongly coupled resonant states and then applying perturbation theory to include nonresonant background effects. All bound and continuum atomic states are calculated in the non-relativistic Hartree-Fock approximation and the various summations over intermediate states are handled by the inhomogeneous differential equation technique. Results for potassium show that resonance structures, including fine structure, are well resolved for a photon flux of 1027 photons/cm2 or less. As the flux increases to 1029, the resonance enhancement is substantially quenched.

DOI
10.1088/0022-3700/14/2/006

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The two-photon ionisation cross section of potassium is calculated from a quasi-degenerate perturbation theory expansion in the atom-radiation field interaction. The authors assume a narrow bandwidth radiation field of moderate photon flux (1025-1029 photons/cm2 s). Resonances are treated by first diagonalising the Hamiltonian among the strongly coupled resonant states and then applying perturbation theory to include nonresonant background effects. All bound and continuum atomic states are calculated in the non-relativistic Hartree-Fock approximation and the various summations over intermediate states are handled by the inhomogeneous differential equation technique. Results for potassium show that resonance structures, including fine structure, are well resolved for a photon flux of 1027 photons/cm2 or less. As the flux increases to 1029, the resonance enhancement is substantially quenched.
For pt.I see ibid., vol. 17, p.4643 (1984). The authors apply the theoretical results obtained in a previous paper in order to study the two-photon resonant ionisation of atomic caesium in the neighbourhood of the fine-structure doublet 7P 1/2 -7P 3/2 when the incident light is right-hand circularly polarised. This formalism allows one to consider these two resonant states on an equal footing and it includes the effects of the infinite summations involved in higher-order perturbation theory. The numerical results show that the two-photon resonant ionisation of caesium takes place through an anticrossing of levels, at least in the intensity range studied. The temporal behaviour of the probability exhibits two distinct temporal regimes: linear for long interaction times and cubic for the shorter ones. The intermediate regime is characterised by quantum beats. At high intensity values, it is found that the induced light shift of the resonances is time dependent. It is also shown that the contribution of the higher-order effects may explain the slight departures between the theoretical and experimental results in the off-resonant two-photon ionisation of atomic caesium.
Non-resonant k-photon ionisation cross sections may be calculated by kth order perturbative treatment. This method is generally considered to be good when the detuning from the closest resonance is much larger than the expected shift and width of this resonance. The aim of this paper is to discuss the validity of this criterion for several realistic cases. By diagonalising an effective Hamiltonian built on a few quasi-resonant states, we have calculated multiphoton ionisation cross sections for ground state caesium by linearly polarised light in frequency ranges containing the tuning range of the ruby laser, the Nd glass laser and its first harmonic. The study is carried out up to an intensity of 10 11 W cm -2 .
Perturbation theory of multiphoton ionisation due to a classical electromagnetic field is modified to allow for intermediate resonances with bound states. Complex energies, generally associated with resonances, do not enter into this formalism. For a monochromatic field of frequency u, a constant ionisation rate can then be defined unambiguously and only such continuum states are excited which correspond to the absorption of energy in integral multiples of hu. As an application, differential and total cross sections for the two-photon ionisation of hydrogen, for frequencies below the n = 3 resonance region, are obtained in closed form. Existing data for generalised cross sections, calculated numerically using the complex coordinate method, are in good agreement with the present results. Finally, the mean fractional ionisation resulting from a pulse of finite duration is estimated on the basis of the associated power spectrum. For short pulses, the time dependence of ionisation exhibits a departure from that expected of a time-independent rate.
Investigates theoretically a new aspect of radiative collisions on two-photon ionisation of colliding atoms of different species A and B. The authors derive the main characteristics of the resonance appearing in the two-photon ionisation cross section of atom B when the laser frequency is tuned on a resonance transition of atom A which cannot itself be ionised by two-photon absorption. Under some realistic conditions and for reasonable values of the light energy density flux F ( approximately 1 MW cm -2 ), the cross section of the process considered varies as F 2/5 while its width varies as F 1/2 . These predictions are in reasonable agreement with a recent observation on the mixture Sr(A)-Cs(B) by Brechignac et al. (1980).
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.