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Physical Review A

Normalized line shapes for far-wing continuum spectra: The Rb-Xe satellite band

Ronald James Bieniek

Published Nov 1, 1985• 2 citations
Publisher

Abstract

Recent advances in experimental spectroscopy offer the promise of yielding much detailed information about molecular potentials and collisional interactions from a study of the light emitted or absorbed in the far wings of atomic lines. However, readily manipulable, accurate theoretical expressions and methods are needed to extract such knowledge. Straightforward formulas, based on the distorted-wave approximation, for the normalized emission intensity in the far wing of a pumped atomic line are given here. By normalizing theoretical spectra with respect to the strength of the atomic line, one obtains a convenient form for the analysis of experimental differential spectra that are reported in nonarbitrary units. Theoretical and experimental spectra are numerically consistent in the test case of the blue-wing satellite (\ensuremath{\sim}7610 A\r{}) of the Rb ${D}_{2}$ line (7800 A\r{}) broadened by Xe perturbers.

DOI
10.1103/physreva.32.3150

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Recent advances in experimental spectroscopy offer the promise of yielding much detailed information about molecular potentials and collisional interactions from a study of the light emitted or absorbed in the far wings of atomic lines. However, readily manipulable, accurate theoretical expressions and methods are needed to extract such knowledge. Straightforward formulas, based on the distorted-wave approximation, for the normalized emission intensity in the far wing of a pumped atomic line are given here. By normalizing theoretical spectra with respect to the strength of the atomic line, one obtains a convenient form for the analysis of experimental differential spectra that are reported in nonarbitrary units. Theoretical and experimental spectra are numerically consistent in the test case of the blue-wing satellite (\ensuremath{\sim}7610 A\r{}) of the Rb D2{D}_{2}D2​ line (7800 A\r{}) broadened by Xe perturbers.
Measurements are presented for the blue-wing satellite bands of the Rb first resonance line (780 nm) emitted in the presence of the noble gases Ne, Ar, Kr, and Xe. The continuum intensity per spectral interval and perturber density is expressed as a fraction of the total Rb (780 nm) fluorescence from optically thin vapor. Over the \ensuremath{\sim}1018{10}^{18}1018-1019{10}^{19}1019 cm3{\mathrm{cm}}^{3}cm3 density range investigated this normalized satellite-peak intensity is found to scale linearly with perturber density and approximately exponentially in $\frac{\ensuremath{-}1}{T},T$ being the absolute temperature. In the classically forbidden region beyond the satellite peak the intensity drops exponentially with frequency for Xe perturbers, but departs from exponential behavior in the Ar and Kr data. We observe undulations in the spectra between line center and the satellite. This is expected due to the possibility of interference between contributions to the transition probability at two internuclear separations, the separations at which the difference potential equals the photon energy.
When two atoms are in proximity, their resonance lines are broadened because of the formation of molecular potentials, between which photon transitions can occur. The level of experimental refinement in measuring excimer and collisional far-wing spectra calls for interpretive theoretical methods that accurately treat the observed structure in line shapes. Of particular interest are satellites and undulations, for they can give much information on intermolecular potentials. We derive an expression for TTT-matrix elements, based on JWKB wave functions and stationary-phase techniques, that is universally applicable to situations with one, two, or more Condon points. Each transition point is treated individually, with effects of potential shape, wave-function phases, and interference separately highlighted. The expression is tested against quantum-mechanical line shapes of the red and blue wings of the Rb DDD lines broadened by Xe perturbers. Agreement is quite good for both the red-wing undulations and the blue-wing satellite-supernumerary structure.
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 concept of Berry phase is included in an analysis of the intensity distribution in far wings of pressure-broadened spectral lines emitted or absorbed by atoms placed in an external cone-rotating electric field. Particular attention is focused on frequency regions where rainbow satellite bands appear. A classical-path treatment that employs the time-dependent Schr\"odinger equation is used to derive an expression for the line shape, and it uses a dipole transition moment calculated with quasimolecular wave functions given by the Berry version of the adiabatic approximation. It is found that in the presence of an external rotating electric field, the intensity distribution in far wings can be expressed in terms of the universal line shape function of the unified Franck-Condon theory once energy shifts due to Stark and Berry effects are taken into account. We show that the influence of Berry phase in the profiles of the far wings can be manifested either in the form of deviations of observed profiles from the quasistatic distribution or the appearance of additional features in the vicinity of the maximum of the rainbow satellite band. As an example, the modification of the rainbow satellite at 162.3 nm in the red wing of the self-broadened Lyman-$\ensuremath{\alpha}$ line of hydrogen, caused by an external rotating electric field, is considered.
When an atom emits or absorbs radiation in the presence of perturbing atoms, satellite bands frequently appear in the spectrum. Such bands may occur when the active atom is subject to equal forces in the two states involved in the transition for some particular configuration of perturbers. In this work a semiclassical approach is used to derive an approximate expression for the one-perturber spectrum in the two-state adiabatic approximation. The expression, which involves an average over Airy functions, is readily adapted for rapid numerical evaluation. Also, an analytic expression for the rate of decline in intensity on the classically forbidden far side of the satellite is found. The semiclassical one-perturber line shape for satellite bands is compared with the classical and quantum-mechanical counterparts for the case of resonance broadening of the Lyman-$\ensuremath{\alpha}$ line in absorption. The semiclassical line shape is found to be much more realistic than the classical shape in which the satellite appears as a singularity. The semiclassical treatment provides an interpretation of the shape of a satellite band in terms of the intermolecular potentials, a possibility not evident in the exact quantum-mechanical treatment.
We have measured the far-wing collisional redistribution line shape, the redistributed fluorescence polarization, and the collisional alignment decay rates for barium perturbed by argon and xenon. The experiment was performed with a heated gas cell ($T\ensuremath{\sim}900$ K) with perturber-gas densities in the 1---30-Torr range and laser light detuned \ifmmode\pm\else\textpm\fi{} 3--- 1000 ${\mathrm{cm}}^{\ensuremath{-}1}$ from the 5535-\AA{} Ba I $6^{1}S\ensuremath{-}6^{1}P$ resonance line. Metal-vapor densities were determined by a Rayleigh scattering technique, which is outlined in detail. By correlating structure in the line shape with that of the polarization, we are able to make definitive statements about the interatomic potentials. The Ba data show strong similarities with previous experimental results for similar two-electron atoms, namely Ca, Sr, and Hg, and so our conclusions are of relevance to these systems as well.