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Journal of Physics B Atomic Molecular and Optical Physics

Temperature dependence of spectral lineshifts in pressure broadening

W. C. Kreye, John F. Kielkopf

Published Jan 14, 1991• 3 citations
Publisher

Abstract

An exact quantum adiabatic evaluation of the shift of an isolated spectral line is applied to the potassium 7s-4p transition perturbed by argon. The long-range interaction of excited alkali states with noble gases is computed with a large basis set of unperturbed atomic states, a multipole interaction and a pseudopotential to compare with a measurement of the dependence of the shift on temperature. The parameters of the theoretical potassium-argon excited-state potential are determined by adjusting the theoretical temperature dependence to fit the observations. Previous pseudopotential models, fitted to ground-state interactions derived from scattering experiments, show weaker long-range interactions than the authors find. The conclusions are consistent with independent line wing experiments on this and other alkali-noble-gas systems that reveal significant interactions at long range.

DOI
10.1088/0953-4075/24/1/010

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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
An exact quantum adiabatic evaluation of the shift of an isolated spectral line is applied to the potassium 7s-4p transition perturbed by argon. The long-range interaction of excited alkali states with noble gases is computed with a large basis set of unperturbed atomic states, a multipole interaction and a pseudopotential to compare with a measurement of the dependence of the shift on temperature. The parameters of the theoretical potassium-argon excited-state potential are determined by adjusting the theoretical temperature dependence to fit the observations. Previous pseudopotential models, fitted to ground-state interactions derived from scattering experiments, show weaker long-range interactions than the authors find. The conclusions are consistent with independent line wing experiments on this and other alkali-noble-gas systems that reveal significant interactions at long range.
Theoretical pseudopotentials and dispersion potentials are used to study ground-state hyperfine splitting frequencies of alkali-metal atoms (Li, Na, K, Rb, and Cs) in noble gases (He, Ne, Ar, Kr, and Xe) in all combinations. With a single fitting parameter, calculations based on first-order perturbation theory qualitatively present each temperature dependence of the measured frequency shift. With this parameter and excitation energies of alkali-metal and noble-gas atoms, the hyperfine splitting frequency of alkali-metal atoms is suitable for investigating the properties of noble-gas atoms, such as the s-wave scattering length of electrons, the electric-dipole polarizability, and the van der Waals radius. This study suggests the possibility of improving excitation energies and van der Waals potentials of colliding pairs.
Experiments have revealed that pressures of noble gases cause bands to appear in both the red and violet wings of the alkali doublet lines. The present paper is devoted to the explanation of these bands and to the shift and shape of the doublet lines which they accompany. In order to examine various qualitative proposals previously put forth to this end, we first ascertain the validity of the statistical theory as applied to the magnetic substates of the alkali resonance lines and develop a criterion for adiabaticity. This criterion indicates that the earlier theories are inadequate. Shift and broadening of the two components of the alkali doublet lines are then calculated as functions of noble gas density by considering the van der Waals energy perturbation due to n simultaneously acting perturbers. The conclusion, which is in agreement with experiments, is that the P322 resonance line is shifted and broadened more than the 2P½ resonance line at moderate pressures. A phenomenological approach is used to construct a more reasonable theory of the ``satellite'' bands. In the absence of reliable knowledge concerning the repulsive portions of the interaction curves, only a semiquantitative understanding of the data is achieved.
The normalized fluorescence spectrum of the Li 6708-\AA{} resonance line perturbed by the noble gases has been measured for 100 \AA{} either side of the resonance line, at a temperature of 400 \ifmmode\pm\else\textpm\fi{} 10\ifmmode^\circ\else\textdegree\fi{}C. The noble-gas pressure range of 100-1800 Torr was investigated. It was observed that the line wings scale linearly with this pressure for $2<|\ensuremath{\Delta}\ensuremath{\lambda}|<100$ \AA{}, and it was was demonstrated that a Lorentzianbroadened line core can be observed for this pressure range. The Li density was \ensuremath{\sim} 1010{10}^{10}1010/cm3{\mathrm{cm}}^{3}cm3 and was varied to establish the fluorescence spectrum in the limit of no radiation entrapment. The central region of the line has been measured with high resolution and compared to calculated profiles due to the various fine structure and isotopic line components, each broadened by a convolution of Lorentz, Doppler, and instrumental profiles. The shift and Lorentz broadening rates, as well as the wavelengths for transition to non-Lorentzian behavior, are reported. In contrast to the heavier alkali-metal-noble-gas cases, no distinctive far-wing features such as satellites or sharp inflections are observed. This is consistent with the much larger collision velocities for the Li case.
Normalized emission spectra of the optically excited Rb resonance lines (7800 \AA{}, 7948 \AA{}) have been measured in the presence of He, Ne, Ar, Kr, and Xe for about 50 \AA{} on either side of the lines. The perturber gas pressures were in the range 100-1100 Torr and the temperature was 318 \ifmmode^\circ\else\textdegree\fi{}K. The spectra, normalized to the total emission, are shown to be due to binary collisions. Shifts and widths of the Lorentzian cores of the lines were obtained, at pressures sufficiently low for impact theory to apply. The widths are corrected for the Rb hfs and the instrument function. Various power-law fits to the near-wing intensities are presented and compared to theoretical expectations. The red satellites reported by other authors are found to be, in the low-pressure limit, mere shoulders on the line wing for Ar and Kr, while Xe barely produces an actual peak. The measured linewidths and shifts are compared to previous measurements.
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