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Physical Review

Pressure Shifts of High-Series Spectral Lines and Cross Sections for Scattering of Very Slow Electrons from Rare-Gas Atoms

M. H. Choudhury

Published Oct 5, 1969• 13 citations
Publisher

Abstract

A completely quantum-mechanical theory of the pressure shift of high-series spectral lines of alkali atoms by foreign gases (usually inert gases) is presented. In this version of the theory, the Schr\"odinger equation for the whole system consisting of the excited alkali atom and the foreign gas is written, the interaction terms simplified, and the resulting equation solved by the methods of perturbation theory. The main qualitative results of Fermi's theory are reproduced, together with contributions from other terms which have no analog in Fermi's theory, and whose interpretation leads to interesting physical consequences justified by experimental observations. In particular, values of the total cross section for the scattering of very slow electrons at effective electron kinetic energies between 0.034 and 0.21 eV are obtained, and found to be in fair agreement with those obtained directly from experiment. For argon, krypton, and xenon, these results indicate the existence of the Ramsauer-Townsend effect.

DOI
10.1103/physrev.186.66

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Pressure Shifts of High-Series Spectral Lines and Cross Sections for Scattering of Very Slow Electrons from Rare-Gas Atoms. II

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In an earlier paper, one of the authors gave a completely quantum-mechanical treatment of the pressure shift, due to foreign atoms, of high-series spectral lines of alkali-metal atoms. The same basic method of solving the Schr\"odinger equation for the system using perturbation techniques is adopted again. However, in the present paper, the center-of-mass motion is treated separately, allowing the use of more realistic distribution functions when averaging over the center-of-mass motion of the foreign atoms. By using a Boltzmann-type distribution law, it is shown that, for foreign atoms exhibiting a red shift, the observed shift decreases with increase in temperature, but no analogous result is found for atoms exhibiting a blue shift.

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Semiclassical calculations of the quasi-elastic l-mixing and inelastic n,l-changing processes in thermal collisions of a Rydberg sodium atom with rare-gas atoms (Ne, Ar, Kr and Xe) as well as and atoms with Ne are presented in a wide range of principal quantum numbers. The main emphasis is put on the study of the effects in the Rydberg-atom - rare-gas-atom collisions associated with both the short- and long-range (polarization) parts of the electron - perturber interaction. It is shown that the polarization interaction between the highly excited electron and the Ne atom provides the major contribution to the cross section of the l-mixing and n, l -changing transitions. We show that the Ramsauer - Townsend effect in slow electron scattering by the heavy rare-gas atoms significantly affects the values of the cross sections, particularly for the inelastic transitions with large energy transfer. A quantitative explanation of these phenomena is given using the recently developed semiclassical normalized perturbation theory for the Rydberg-atom - neutral collisions combined with the modified effective range theory for scattering of slow electrons by the rare-gas atoms.

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A theory of inelastic n,l-changing and quasielastic l-mixing collisions of Rydberg atoms with the heavy rare-gas atoms is developed. It is based on the semiclassical impact-parameter approach combined with the normalized perturbation theory. Semiclassical formulas for scaled transition probabilities and cross sections as functions of the inelasticity parameter and the collision strength are analyzed. This approach gives a general description of collisional nl\ensuremath{\rightarrow}${\mathit{n}}^{\ensuremath{'}}$ transitions independently of the specific values of the principal quantum number, the relative velocity, and the type of colliding atoms. The energy and angular dependence of the electron-atom scattering amplitude is included in the theory by incorporating the impulse-approximation results in the weak-coupling limit. The Ramsauer-Townsend effect affects significantly the values of the cross sections, especially for the inelastic transitions with large energy transfer. The results obtained are used in calculations of the quenching cross sections for the Rb(nS,nD,nF) atoms in collisions with Ar, Kr, and Xe. Comparison of theory and experiment is made in a wide range of the principal quantum numbers and transition energy defects. \textcopyright{} 1996 The American Physical Society.

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Temperature dependence of spectral lineshifts in pressure broadening

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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.

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SENSITIZED FLUORESCENCE IN VAPORS OF ALKALI METALS: VI. ENERGY TRANSFER IN COLLISIONS BETWEEN RUBIDIUM AND INERT GAS ATOMS

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The total cross sections for inelastic collisions between rubidium and inert gas atoms, leading to a transfer of excitation between the 5 2P1/2 and 5 2P3/2 levels in rubidium, have been determined in a study of sensitized fluorescence in rubidium – inert gas mixtures. The experiments were performed at a rubidium vapor pressure of 1.5 × 10−6 mm Hg, at which there is no imprisonment of resonance radiation, and over a range of inert gas pressures extending from 1 to 350 mm Hg. The cross sections Q1(5 2P1/2 → 5 2P3/2) and Q2(5 2P1/2 ← 5 2P3/2) are as follows: Rb–He: 7.6 × 10−18 and 10.3 × 10−18 cm2; Rb–Ne: 1.7 × 10−19 and 2.3 × 10−19 cm2; Rb–A: 1.0 × 10−19 and 1.6 × 10−19 cm2; Rb–Kr: 6.4 × 10−20 and 1.5 × 10−19 cm2; Rb–Xe: 7.9 × 10−20 and 2.1 × 10−19 cm2. The cross sections are subject to two apparent anomalies: they do not vary monotonically with the polarizabilities of the inert gases and not all of their ratios Q1/Q2 have values predicted by the principle of detailed balancing. These properties of the cross sections, as well as a partial disagreement with Franck's rule, are interpreted qualitatively in terms of a "free particle" interaction between the inert gas atoms and the 5 2P orbital electron in rubidium. A competing process involving three-body collisions and the possible formation of Rb – inert gas van der Waals' molecules is also suggested.

Canadian Journal of Physics•Apr 1, 1966•38 citations

Frequency Shifts in Hyperfine Splitting of Alkalis Caused by Foreign Gases

Henry Margenau, P. Fontana, Lewis S. Klein

The difference in the dispersion force between an alkali atom in a particular hyperfine level belonging to the groundstate and a perturbing molecule is computed. These asymptotic forces, if active alone, generally produce red shifts and suffice to account for the results obtained for the heavier buffer gases. Experimental data exhibit blue shifts for the lighter gases and therefore indicate that the net frequency shifts are the result of exchange as well as dispersion forces. The former cannot be determined theoretically. Therefore, a simple model is devised in which the difference in the forces is given a positive trend at distances of separation smaller than $d$, while beyond $d$ it is given the calculated form. The experimental data for all alkali-rare gas interactions can then be fitted by values of $d$ which, for the different foreign gases, are of the order of their gas-kinetic diameters.

Physical Review•Jul 1, 1959•40 citations
A completely quantum-mechanical theory of the pressure shift of high-series spectral lines of alkali atoms by foreign gases (usually inert gases) is presented. In this version of the theory, the Schr"odinger equation for the whole system consisting of the excited alkali atom and the foreign gas is written, the interaction terms simplified, and the resulting equation solved by the methods of perturbation theory. The main qualitative results of Fermi's theory are reproduced, together with contributions from other terms which have no analog in Fermi's theory, and whose interpretation leads to interesting physical consequences justified by experimental observations. In particular, values of the total cross section for the scattering of very slow electrons at effective electron kinetic energies between 0.034 and 0.21 eV are obtained, and found to be in fair agreement with those obtained directly from experiment. For argon, krypton, and xenon, these results indicate the existence of the Ramsauer-Townsend effect.
In an earlier paper, one of the authors gave a completely quantum-mechanical treatment of the pressure shift, due to foreign atoms, of high-series spectral lines of alkali-metal atoms. The same basic method of solving the Schr\"odinger equation for the system using perturbation techniques is adopted again. However, in the present paper, the center-of-mass motion is treated separately, allowing the use of more realistic distribution functions when averaging over the center-of-mass motion of the foreign atoms. By using a Boltzmann-type distribution law, it is shown that, for foreign atoms exhibiting a red shift, the observed shift decreases with increase in temperature, but no analogous result is found for atoms exhibiting a blue shift.
Semiclassical calculations of the quasi-elastic l-mixing and inelastic n,l-changing processes in thermal collisions of a Rydberg sodium atom with rare-gas atoms (Ne, Ar, Kr and Xe) as well as and atoms with Ne are presented in a wide range of principal quantum numbers. The main emphasis is put on the study of the effects in the Rydberg-atom - rare-gas-atom collisions associated with both the short- and long-range (polarization) parts of the electron - perturber interaction. It is shown that the polarization interaction between the highly excited electron and the Ne atom provides the major contribution to the cross section of the l-mixing and n, l -changing transitions. We show that the Ramsauer - Townsend effect in slow electron scattering by the heavy rare-gas atoms significantly affects the values of the cross sections, particularly for the inelastic transitions with large energy transfer. A quantitative explanation of these phenomena is given using the recently developed semiclassical normalized perturbation theory for the Rydberg-atom - neutral collisions combined with the modified effective range theory for scattering of slow electrons by the rare-gas atoms.
A theory of inelastic n,l-changing and quasielastic l-mixing collisions of Rydberg atoms with the heavy rare-gas atoms is developed. It is based on the semiclassical impact-parameter approach combined with the normalized perturbation theory. Semiclassical formulas for scaled transition probabilities and cross sections as functions of the inelasticity parameter and the collision strength are analyzed. This approach gives a general description of collisional nl\ensuremath{\rightarrow}${\mathit{n}}^{\ensuremath{'}}$ transitions independently of the specific values of the principal quantum number, the relative velocity, and the type of colliding atoms. The energy and angular dependence of the electron-atom scattering amplitude is included in the theory by incorporating the impulse-approximation results in the weak-coupling limit. The Ramsauer-Townsend effect affects significantly the values of the cross sections, especially for the inelastic transitions with large energy transfer. The results obtained are used in calculations of the quenching cross sections for the Rb(nS,nD,nF) atoms in collisions with Ar, Kr, and Xe. Comparison of theory and experiment is made in a wide range of the principal quantum numbers and transition energy defects. \textcopyright{} 1996 The American Physical Society.
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.
The total cross sections for inelastic collisions between rubidium and inert gas atoms, leading to a transfer of excitation between the 5 2P1/2 and 5 2P3/2 levels in rubidium, have been determined in a study of sensitized fluorescence in rubidium – inert gas mixtures. The experiments were performed at a rubidium vapor pressure of 1.5 × 10−6 mm Hg, at which there is no imprisonment of resonance radiation, and over a range of inert gas pressures extending from 1 to 350 mm Hg. The cross sections Q1(5 2P1/2 → 5 2P3/2) and Q2(5 2P1/2 ← 5 2P3/2) are as follows: Rb–He: 7.6 × 10−18 and 10.3 × 10−18 cm2; Rb–Ne: 1.7 × 10−19 and 2.3 × 10−19 cm2; Rb–A: 1.0 × 10−19 and 1.6 × 10−19 cm2; Rb–Kr: 6.4 × 10−20 and 1.5 × 10−19 cm2; Rb–Xe: 7.9 × 10−20 and 2.1 × 10−19 cm2. The cross sections are subject to two apparent anomalies: they do not vary monotonically with the polarizabilities of the inert gases and not all of their ratios Q1/Q2 have values predicted by the principle of detailed balancing. These properties of the cross sections, as well as a partial disagreement with Franck's rule, are interpreted qualitatively in terms of a "free particle" interaction between the inert gas atoms and the 5 2P orbital electron in rubidium. A competing process involving three-body collisions and the possible formation of Rb – inert gas van der Waals' molecules is also suggested.
The difference in the dispersion force between an alkali atom in a particular hyperfine level belonging to the groundstate and a perturbing molecule is computed. These asymptotic forces, if active alone, generally produce red shifts and suffice to account for the results obtained for the heavier buffer gases. Experimental data exhibit blue shifts for the lighter gases and therefore indicate that the net frequency shifts are the result of exchange as well as dispersion forces. The former cannot be determined theoretically. Therefore, a simple model is devised in which the difference in the forces is given a positive trend at distances of separation smaller than ddd, while beyond ddd it is given the calculated form. The experimental data for all alkali-rare gas interactions can then be fitted by values of ddd which, for the different foreign gases, are of the order of their gas-kinetic diameters.