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Physical Review A

Calculated pressure broadening and shift for alkali-metal atoms perturbed by rare gases: Two-photon S−S transitions

Chao Wu, William C. Stwalley

Published Sep 1, 1978• 16 citations
Publisher

Abstract

The broadening and shift of two-photon $S\ensuremath{-}S$ transitions (e.g., in alkali-metal atoms perturbed by rare gases) are shown to be readily calculable. These calculations employ (a) newly available expressions for alkalimetal-rare-gas long-range potential coefficients ${C}_{6}$, ${C}_{8}$, and ${C}_{10}$; and (b) the (herein discussed) appropriate form of impact theory (particularly simple since only a single potential curve is involved and inelastic processes are not usually important). It is demonstrated in particular that the influence of ${C}_{8}$ and ${C}_{10}$ terms on the broadening and shift is significant though not dominant. Comparison with recent experimental data on the Na-rare-gas pairs shows reasonable agreement for the heavy rare gases.

DOI
10.1103/physreva.18.1066

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Calculated pressure broadening and shift for the sodium atom perturbed by rare gases. II. Two-photon 3S−nS transitions ( n=6−9 )

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Our recent treatment [Phys. Rev. A 18, 1066 (1978)] of the broadening and shift of alkali-metal-atom two-photon $S\ensuremath{-}S$ transitions is applied to the Na $3S\ensuremath{-}\mathrm{nS}$ transitions ($n=6\ensuremath{-}9$) perturbed by Ar, Kr, and Xe rare gases. Comparison with recent experimental data [A. Flusberg et al., Phys. Rev. A 19, 1607 (1979)] on the Na-Ar pair for $n\ensuremath{\le}7$ shows good agreement. However, for transitions to $n>8$ the calculated pressure effects no longer agree well with experimental data; presumably the pressure effects cannot be adequately described by a simple two-body long-range impact theory.

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In this paper we present the results and discuss the applicability of an impact theory of lineshapes, developed by Henry and Herman for the pressure-induced broadening and shifting of transitions from the ground state to various Rydberg states of alkalis, to the situation in which the perturbing atoms are ground-state rare gas atoms. This theory, which has successfully described the collisional broadening of Rydberg states by alkali atoms, can without major alterations predict the widths and shifts of Doppler-free two-photon transitions to n S and n D states of Rb and Na, 6⩽ n ⩽30, perturbed by He, Ne, Ar, Kr and Xe. The results in all cases show reasonable agreement with experiment, with the transitions to Na**( n D) states being somewhat less satisfactory than the others.

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Collisional broadening and shift of Doppler-free two-photon thallium lines perturbed by rare-gas atoms

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The extended Omont-Ueda-Kaulakys treatment of collisional effects on quasi-Rydberg states, in which the perturbation of the lower state is taken into account is applied to thallium-rare gas systems. The pressure broadening and shift coefficients of two-photon transitions in thallium involving the 6P 1/2 -n P 1/2,3/2 (n = 9-14) states are calculated and compared with experimental data obtained by Hermann et al. [Eur. Phys. J. D 1, 129 (1998)].

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Broadening and Shifting of the Alkali-Metal Resonance Lines by Collisions of Like Monatoms

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The purpose of this work is the evaluation of the linewidth w and lineshift d of the sodium resonance line 3p − → 3s when the excited atoms are evolving in their parent gas. Assuming the Baranger impact approximation, these two quantities are given in terms of the phase shifts of the ground Na(3s) + Na(3s) and the excited Na(3p)+Na(3s) states. The quantal calculations and the semi-classical method, developed by Mott and Massey and Landau and Lifshitz, show that the cross sections σ and λ vary with the energy like E−1/2, the width w and the shift d do not depend on the temperature, the long-range interactions have a big influence on w and d, and the rate coefficients depend on the dispersion coefficients like w/n ≈ +7.298 × 10−8C3(Σ) and d/n ≈ +8.893 × 10−9C3(Σ). The study also shows that the sodium results can be extended to the other alkali-metal atoms (Li, K, Rb, Cs, and Fr) by a simple scaling. Keywords: potential energy curve, broadening cross section, rate coefficient, linewidth, lineshift, dispersion coefficient

•Jan 1, 2006•0 citations

Broadening and shift of Rydberg levels by elastic collisions with rare-gas atoms

B. Kaulakys

The author obtains expressions for Rydberg level broadening and shift cross sections and rates suitable for elastic collisions of ground-state rare-gas atoms with Rydberg atoms. The semiclassical impact broadening theory is used. The interaction of a Rydberg atom with a rare-gas atom is approximated by the superposition of polarisation potentials and the Fermi pseudopotential. It is shown that similar expressions for the broadening and shift cross sections due to the perturber-Rydberg-electron interaction can be obtained in the JWKB approximation for the Rydberg-electron wavefunctions and for the square-well model potential. Consequently the shift and width of the Rydberg level are not very sensitive to the shape of the potential but only to its normalisation. Expressions for the shift and width in the square-well potential approximation suitable in the high-density limit of the perturbing atoms are obtained. Limits of the applicability of the expressions for the broadening and shift cross sections are discussed. Calculated broadening and shift rates agree well with experimental results for the broadening and shift of Rydberg levels with small, medium and large principal quantum numbers by all rare gases excepting neon.

Journal of Physics B Atomic and Molecular Physics•Nov 28, 1984•41 citations
The broadening and shift of two-photon S\ensuremath−SS\ensuremath{-}SS\ensuremath−S transitions (e.g., in alkali-metal atoms perturbed by rare gases) are shown to be readily calculable. These calculations employ (a) newly available expressions for alkalimetal-rare-gas long-range potential coefficients C6{C}_{6}C6​, C8{C}_{8}C8​, and C10{C}_{10}C10​; and (b) the (herein discussed) appropriate form of impact theory (particularly simple since only a single potential curve is involved and inelastic processes are not usually important). It is demonstrated in particular that the influence of C8{C}_{8}C8​ and C10{C}_{10}C10​ terms on the broadening and shift is significant though not dominant. Comparison with recent experimental data on the Na-rare-gas pairs shows reasonable agreement for the heavy rare gases.
Our recent treatment [Phys. Rev. A 18, 1066 (1978)] of the broadening and shift of alkali-metal-atom two-photon $S\ensuremath{-}S$ transitions is applied to the Na $3S\ensuremath{-}\mathrm{nS}$ transitions ($n=6\ensuremath{-}9$) perturbed by Ar, Kr, and Xe rare gases. Comparison with recent experimental data [A. Flusberg et al., Phys. Rev. A 19, 1607 (1979)] on the Na-Ar pair for $n\ensuremath{\le}7$ shows good agreement. However, for transitions to n>8n>8n>8 the calculated pressure effects no longer agree well with experimental data; presumably the pressure effects cannot be adequately described by a simple two-body long-range impact theory.
In this paper we present the results and discuss the applicability of an impact theory of lineshapes, developed by Henry and Herman for the pressure-induced broadening and shifting of transitions from the ground state to various Rydberg states of alkalis, to the situation in which the perturbing atoms are ground-state rare gas atoms. This theory, which has successfully described the collisional broadening of Rydberg states by alkali atoms, can without major alterations predict the widths and shifts of Doppler-free two-photon transitions to n S and n D states of Rb and Na, 6⩽ n ⩽30, perturbed by He, Ne, Ar, Kr and Xe. The results in all cases show reasonable agreement with experiment, with the transitions to Na**( n D) states being somewhat less satisfactory than the others.
The purpose of this work is the evaluation of the linewidth w and lineshift d of the sodium resonance line 3p − → 3s when the excited atoms are evolving in their parent gas. Assuming the Baranger impact approximation, these two quantities are given in terms of the phase shifts of the ground Na(3s) + Na(3s) and the excited Na(3p)+Na(3s) states. The quantal calculations and the semi-classical method, developed by Mott and Massey and Landau and Lifshitz, show that the cross sections σ and λ vary with the energy like E−1/2, the width w and the shift d do not depend on the temperature, the long-range interactions have a big influence on w and d, and the rate coefficients depend on the dispersion coefficients like w/n ≈ +7.298 × 10−8C3(Σ) and d/n ≈ +8.893 × 10−9C3(Σ). The study also shows that the sodium results can be extended to the other alkali-metal atoms (Li, K, Rb, Cs, and Fr) by a simple scaling. Keywords: potential energy curve, broadening cross section, rate coefficient, linewidth, lineshift, dispersion coefficient
The author obtains expressions for Rydberg level broadening and shift cross sections and rates suitable for elastic collisions of ground-state rare-gas atoms with Rydberg atoms. The semiclassical impact broadening theory is used. The interaction of a Rydberg atom with a rare-gas atom is approximated by the superposition of polarisation potentials and the Fermi pseudopotential. It is shown that similar expressions for the broadening and shift cross sections due to the perturber-Rydberg-electron interaction can be obtained in the JWKB approximation for the Rydberg-electron wavefunctions and for the square-well model potential. Consequently the shift and width of the Rydberg level are not very sensitive to the shape of the potential but only to its normalisation. Expressions for the shift and width in the square-well potential approximation suitable in the high-density limit of the perturbing atoms are obtained. Limits of the applicability of the expressions for the broadening and shift cross sections are discussed. Calculated broadening and shift rates agree well with experimental results for the broadening and shift of Rydberg levels with small, medium and large principal quantum numbers by all rare gases excepting neon.