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The Journal of Chemical Physics

Theory of Pressure Effects on Alkali Doublet Lines

Lewis S. Klein, Henry Margenau

Published Jun 1, 1959• 42 citations
Publisher

Abstract

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.

DOI
10.1063/1.1730237

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It is pointed out that the usual theories of pressure broadening disagree with direct experimental measurements of the widths of resonance-broadened alkali doublet lines, although the theories are at least qualitatively confirmed for the wings of resonance lines and for foreign-gas broadening. There are also two conflicting sets of experimental data (both in strong disagreement with theory). Some qualitative arguments are given for doubting the validity, near the center of a resonance line, of the "two-body" approximation generally used in theoretical treatments, and some formal objections to the usual procedure are also presented. The basic equation relating the susceptibility to a resolvent operator matrix element is derived from a more fundamental point of view than usual; the result contains in principle all effects due to translational motion, to the quantized nature of the radiation field, and to "spatial dispersion." In the limit of large absorber mass it is proved rigorously that the two-body approximation can never be valid near the center of a line, even for very low densities. By using different approximations for the wings and the line center, we obtain satisfactory agreement with experiments in both regions for the alkali doublet lines. We are also able to decide between the two conflicting experiments, favoring the square-root density dependence of the line-width observed by Lauriston and Welsh.

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For pt.I, see ibid., vol.17, p.2599 (1984). General expressions for the line profile produced by an emitting atom embedded in a sea of randomly distributed identical perturbers, on the assumption that the interaction between the emitter and a perturber is of the type 1/R p , were presented in Paper I. The basic assumptions of the theory are that all emitter-perturber interactions are additive and that the trajectory of the perturber is a straight line. The profile is expressed in terms of a 'universal' function that does not depend explicitly on any parameters associated with the particular spectral line or perturbing gas considered. Explicit results are given for the cases p=6 and p=7; these are relevant to the analysis of the broadening of atomic and molecular lines by atoms and molecules. For the case of p=6, the sensitivity of the line parameters to the direction assumed for the quantisation axis of the emitter is examined. It is also shown that the degree of asymmetry depends significantly upon the thermal average being correctly evaluated, and good agreement with experiment is obtained for the asymmetries of the sodium resonance lines perturbed by the heavier rare gases.

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Broadening of the Rb resonance lines by the noble gases

Ch. Ottinger, Richard Scheps, George W. York +1 more

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Noble-gas broadening of the Li resonance line

Alan C. Gallagher

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} ${10}^{10}$/${\mathrm{cm}}^{3}$ 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.

Physical Review A•Jul 1, 1975•39 citations
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.
It is pointed out that the usual theories of pressure broadening disagree with direct experimental measurements of the widths of resonance-broadened alkali doublet lines, although the theories are at least qualitatively confirmed for the wings of resonance lines and for foreign-gas broadening. There are also two conflicting sets of experimental data (both in strong disagreement with theory). Some qualitative arguments are given for doubting the validity, near the center of a resonance line, of the "two-body" approximation generally used in theoretical treatments, and some formal objections to the usual procedure are also presented. The basic equation relating the susceptibility to a resolvent operator matrix element is derived from a more fundamental point of view than usual; the result contains in principle all effects due to translational motion, to the quantized nature of the radiation field, and to "spatial dispersion." In the limit of large absorber mass it is proved rigorously that the two-body approximation can never be valid near the center of a line, even for very low densities. By using different approximations for the wings and the line center, we obtain satisfactory agreement with experiments in both regions for the alkali doublet lines. We are also able to decide between the two conflicting experiments, favoring the square-root density dependence of the line-width observed by Lauriston and Welsh.
The displacement, asymmetry, and broadening of the second doublet of the rubidium principal series perturbed by pure helium, neon and argon up to 13 atmospheres are observed. The displacement as well as the broadening of the doublet components are not the same. The 2P12^{2}P_{\frac{1}{2}}2P21​​ component shifts and broadens more conspicuously than the 2P112^{2}P_{1\frac{1}{2}}2P121​​ component (an exception being the broadening by argon). The departure from linear relationship between the shift and the density of the perturbing gas is quite manifest. Both for helium and for neon the line contour shows a distinct asymmetry towards the violet, while for argon the line contour shows a very strong red asymmetry. For helium and neon the violet asymmetries of the 2P12^{2}P_{\frac{1}{2}}2P21​​ component are stronger than that of the 2P112^{2}P_{1\frac{1}{2}}2P121​​ component; the reverse is true for argon. The relationship between the half-width and the relative density is linear for foreign gas concentrations of relative densities up to 8 so far applied.
For pt.I, see ibid., vol.17, p.2599 (1984). General expressions for the line profile produced by an emitting atom embedded in a sea of randomly distributed identical perturbers, on the assumption that the interaction between the emitter and a perturber is of the type 1/R p , were presented in Paper I. The basic assumptions of the theory are that all emitter-perturber interactions are additive and that the trajectory of the perturber is a straight line. The profile is expressed in terms of a 'universal' function that does not depend explicitly on any parameters associated with the particular spectral line or perturbing gas considered. Explicit results are given for the cases p=6 and p=7; these are relevant to the analysis of the broadening of atomic and molecular lines by atoms and molecules. For the case of p=6, the sensitivity of the line parameters to the direction assumed for the quantisation axis of the emitter is examined. It is also shown that the degree of asymmetry depends significantly upon the thermal average being correctly evaluated, and good agreement with experiment is obtained for the asymmetries of the sodium resonance lines perturbed by the heavier rare gases.
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 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.