Physical Review

Frequency Shifts in Hyperfine Splitting of Alkalis Caused by Foreign Gases

Henry Margenau, P. Fontana, Lewis S. Klein

Published Jul 1, 1959• 40 citations

Abstract

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.

DOI: 10.1103/physrev.115.87

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Physical Review

Frequency Shifts in Hyperfine Splitting of Alkalis Caused by Foreign Gases

Henry Margenau, P. Fontana, Lewis S. Klein

Published Jul 1, 1959• 40 citations

Publisher

Abstract

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.

DOI: 10.1103/physrev.115.87

Related papers

Pseudopotential analysis on hyperfine splitting frequency shift of alkali-metal atoms in noble gases, revisited

Kiyoshi Ishikawa

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.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.

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

Chao Wu, William C. Stwalley

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Rare-Gas-Induced gJ Shifts in the Ground States of Alkali Atoms

Roger M. Herman

Based on the formal similarity between perturbations governing gyromagnetic ratio shifting and spin relaxation of alkali atoms in collisions with rare-gas atoms, a relatively direct semiempirical estimate of the ${g}_{j}$ shift as a function of buffer-gas density can be achieved. The expression $\frac{\ensuremath{\Delta}{g}_{J}}{{g}_{J}}=\ensuremath{-}{(\frac{4}{3\ensuremath{\pi}})}^{\frac{1}{2}}n{{\ensuremath{\sigma}}_{\mathrm{dis}}}^{\frac{1}{2}}{\ensuremath{\sigma}}_{\mathrm{kin}}$ is obtained for the fractional shift in ${g}_{J}$ , where $n$ is the rare-gas number density, ${\ensuremath{\sigma}}_{\mathrm{kin}}$ the alkali-rare-gas kinetic cross section, and ${\ensuremath{\sigma}}_{\mathrm{dis}}$ the cross section for alkali spin disorientation. With this relationship, we predict a fractional ${g}_{J}$ shift for Rb by He equal to -5. 3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ ${\mathrm{Torr}}^{\ensuremath{-}1}$, as compared with a recent value, -(5\ifmmode\pm\else\textpm\fi{}3) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ ${\mathrm{Torr}}^{\ensuremath{-}1}$, obtained through measurement by Hayne, Robinson, and their co-workers.Based on the formal similarity between perturbations governing gyromagnetic ratio shifting and spin relaxation of alkali atoms in collisions with rare-gas atoms, a relatively direct semiempirical estimate of the ${g}_{j}$ shift as a function of buffer-gas density can be achieved. The expression $\frac{\ensuremath{\Delta}{g}_{J}}{{g}_{J}}=\ensuremath{-}{(\frac{4}{3\ensuremath{\pi}})}^{\frac{1}{2}}n{{\ensuremath{\sigma}}_{\mathrm{dis}}}^{\frac{1}{2}}{\ensuremath{\sigma}}_{\mathrm{kin}}$ is obtained for the fractional shift in ${g}_{J}$, where $n$ is the rare-gas number density, ${\ensuremath{\sigma}}_{\mathrm{kin}}$ the alkali-rare-gas kinetic cross section, and ${\ensuremath{\sigma}}_{\mathrm{dis}}$ the cross section for alkali spin disorientation. With this relationship, we predict a fractional ${g}_{J}$ shift for Rb by He equal to -5. 3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ ${\mathrm{Torr}}^{\ensuremath{-}1}$, as compared with a recent value, -(5\ifmmode\pm\else\textpm\fi{}3) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ ${\mathrm{Torr}}^{\ensuremath{-}1}$, obtained through measurement by Hayne, Robinson, and their co-workers.

Physical ReviewNov 5, 196815 citations

Magnetic resonance frequency shifts upon spin-exchange collisions of alkali atoms

Victor A. Kartoshkin

Optics and SpectroscopyJun 1, 201013 citations

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.

{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.

{g}_{j}

shift as a function of buffer-gas density can be achieved. The expression $\frac{\ensuremath{\Delta}{g}_{J}}{{g}_{J}}=\ensuremath{-}{(\frac{4}{3\ensuremath{\pi}})}^{\frac{1}{2}}n{{\ensuremath{\sigma}}_{\mathrm{dis}}}^{\frac{1}{2}}{\ensuremath{\sigma}}_{\mathrm{kin}}$ is obtained for the fractional shift in

{g}_{J}

, where

n

is the rare-gas number density, ${\ensuremath{\sigma}}_{\mathrm{kin}}$ the alkali-rare-gas kinetic cross section, and ${\ensuremath{\sigma}}_{\mathrm{dis}}$ the cross section for alkali spin disorientation. With this relationship, we predict a fractional

{g}_{J}

shift for Rb by He equal to -5. 3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ ${\mathrm{Torr}}^{\ensuremath{-}1}$, as compared with a recent value, -(5\ifmmode\pm\else\textpm\fi{}3) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ ${\mathrm{Torr}}^{\ensuremath{-}1}$, obtained through measurement by Hayne, Robinson, and their co-workers.