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Physical Review A

Calculations on laser-induced collisional energy transfer

S. Geltman

Published Apr 1, 1992• 21 citations
Publisher

Abstract

We examine theoretically the behavior of cross sections for laser-induced collisional energy transfer (LICET) over a wide range of detunings and laser intensities for the two-atom pairs Li-Sr and Eu-Sr which have been previously studied experimentally. These two cases are complementary in that the laser and collisional interactions enter in opposite orders, and their level structures are such as to give weak-field line shapes of opposite asymmetry and intensity shift. A three-state model is used and the Bambini-Berman formula for the weak-field quasistatic wing is verified. At high intensities the peak cross section is found to go through a maximum and the LICET profile is found to become symmetric about a shifted center with notable departures from a uniform falloff in the far quasistatic wing, apparently arising from radiative collisional interference effects.

DOI
10.1103/physreva.45.4792

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We examine theoretically the behavior of cross sections for laser-induced collisional energy transfer (LICET) over a wide range of detunings and laser intensities for the two-atom pairs Li-Sr and Eu-Sr which have been previously studied experimentally. These two cases are complementary in that the laser and collisional interactions enter in opposite orders, and their level structures are such as to give weak-field line shapes of opposite asymmetry and intensity shift. A three-state model is used and the Bambini-Berman formula for the weak-field quasistatic wing is verified. At high intensities the peak cross section is found to go through a maximum and the LICET profile is found to become symmetric about a shifted center with notable departures from a uniform falloff in the far quasistatic wing, apparently arising from radiative collisional interference effects.
A four-state model considering the relative velocity distribution function for calculating the cross section of laser-induced collisional energy transfer in a Sr—Li system is presented and profiles of laser-induced collision cross section are obtained. The resulting spectra obtained from different intermediate states are strongly asymmetrical in an opposite asymmetry. Both of the two intermediate states have contributions to the final state, and none of the intermediate states should be neglected. The peak of the laser-induced collisional energy transfer (LICET) profile shifts toward the red and the FWHM becomes narrower obviously with laser field intensity increasing. A cross section of 1.2 × 10−12 cm2 at a laser field intensity of 2.17 × 107 V/m is obtained, which indicates that this collision process can be an effective way to transfer energy selectively from a storage state to a target state. The existence of saturation for cross section with the increase of the laser intensity shows that the high-intensity redistribution of transition probabilities is an important feature of this process, which is not accounted for in a two-state treatment.
The theory of light-induced collisional energy transfer (LICET) in the Eu-Sr system is extended to include all the degenerate M states that occur in the separated-atom basis states. Previous treatments were restricted to only the M=0 substates. Numerical solutions are obtained for the resulting nine-state dynamic coupled system to determine transitions probabilities on a given straight-line path. Intense laser fields of linear and circular polarization are treated. It is found that the full M-state treatment results in dependences on the trajectory orientation angles which are much more complex than in the M=0 treatment. The exact and quasisymmetries involving these orientation angles are described in simple group-theoretic terms. The resulting spectral line shapes (LICET transition cross sections as a function of laser detuning) are seen to have structures that are understood in terms of the coupling matrix elements, as well as appreciable Stark shifts. These shifts, which appear to be an essential outcome of the theory, are not yet seen in measurements of the LICET line shape.
The behavior of the quasistatic wing of the light-induced collisional-energy-transfer (LICET) line shape is analyzed. The reaction can be written as A∗{A}^{\mathrm{*}}A∗+B+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}A+B∗∗{B}^{\mathrm{*}\mathrm{*}}B∗∗. The two-level model is found to be inadequate to describe the falloff of the spectral line shape in the quasistatic wing. The three-level model, on the other hand, leads to the prediction of a cross section that depends on the detuning in various ways, according to the strength of the collisional coupling and the influence of the van der Waals shifts on the levels under consideration. Good agreement with existing experimental results is found. To check the approximations made in the derivation of these results, numerical evaluation of the transition probability has been performed for several cases. A Monte Carlo simulation of the full LICET spectrum is also presented.
It is shown that the conventional two-state theory of laser-induced collisional energy transfer (LICET) cannot be expected to provide an adequate description of the quasistatic wing behavior observed in a number of high-resolution LICET experiments. The theory breaks down whenever the detuning parameter \ensuremath{\Delta} of the LICET reaction is comparable to some frequency mismatch \ensuremath{\delta}\ensuremath{\omega} between either the initial or final state and a (virtual) intermediate state in the reaction. A simple extension of the conventional two-state theory is presented which leads to good agreement with experiment. For a van der Waals collisional interaction, the quasistatic wing is shown to fall off as \ensuremath{\Vert}\ensuremath{\Delta}${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}1/2}$(\ensuremath{\delta}\ensuremath{\omega}+\ensuremath{\Vert}\ensuremath{\Delta}\ensuremath{\Vert}${)}^{\mathrm{\ensuremath{-}}3/2}$ instead of \ensuremath{\Vert}\ensuremath{\Delta}${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}1/2}$ predicted by the two-state theory.
Based on the four-state model of laser-induced collisional energy transfer,the cross section of the collisional energy transfer in the Sr-Ca system is obtained.Various factors,including field intensity,relative speed,and temperature,which influence the collisional cross section,are discussed for illustrating the features of the Sr-Ca laser-induced collisional energy transfer(LICET) process.The calculated results show that the LICET spectral profiles obviously become narrower when the laser field intensity increases.The collision cross section rises with laser intensity and tends to saturate.In the vicinity of the spectral profile center,the cross section at fixed laser detuning becomes smaller as the relative speed and system temperature increase.The results indicate that the intermediate states strongly affect the spectral profile of LICET.
We report a measurement of the excitation spectrum of the laser-induced collisional energy transfer process for the Eu-Sr system in the weak-field regime. The measurement has been performed in a detuning range extending up to 85 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in the static wing, providing a wider check of existing theoretical models. The frequency resolution of the measurement (0.1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) was suitable for a quantitative study of the core of the line spectrum, where a comparison with the results of numerical calculations based on an effective three-level model gives complete evidence for a cooperative decay from the Sr(5p2{\mathit{p}}^{2}p2)1{)}^{1})1D2{\mathit{D}}_{2}D2​ final level.