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The Journal of Chemical Physics

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

Kiyoshi Ishikawa

Published Feb 9, 2023• 4 citations
Publisher

Abstract

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.

DOI
10.1063/5.0138434

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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.
We report an experimental and theoretical study on the shift of the hyperfine splitting frequency of ground-state Li atoms in noble gases, He, Ne, Ar, and Xe. The frequency shift is due to the change in the electron-spin density at the Li nuclei induced by collisions to the noble-gas atoms. The electron density is calculated along the interatomic distance in a pseudopotential and a dispersion potential. Based on the measured and the calculated frequency shifts, we find the importance of attractive force in collisions to helium as well as heavy noble-gas atoms. Taking advantage of the simple energy structure of the Li atom, we obtain the s wave scattering length for free electrons on noble-gas atoms by using the hyperfine splitting frequency as a precise measure.
Collisions with chemically inert atoms or molecules change the hyperfine coupling $A\phantom{\rule{0.16em}{0ex}}\mathbf{I}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}$ of an alkali-metal atom through the hyperfine-shift interaction $\ensuremath{\delta}A\phantom{\rule{0.16em}{0ex}}\mathbf{I}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}$. This interaction is responsible for the pressure shifts of the microwave resonances of alkali-metal atoms in buffer gases, is an important spin interaction in alkali-metal--noble-gas van der Waals molecules, and is anticipated to enable the magnetoassociation of ultracold molecules such as RbSr. An improved estimate is presented for the long-range asymptote of this interaction for Na, K, Rb, and Cs. To test the results, the change in hyperfine coupling due to a static electric field is estimated and reasonable agreement is found.
We demonstrate that the microwave resonant frequencies of ground-state 87Rb and 133Cs atoms have a nonlinear dependence on the pressure of the buffer gas Xe. Surprisingly, though the frequency shifts of Rb and Cs in the heavy noble gases Ar, Kr, and Xe are all negative, the nonlinearity in Xe is of the opposite sign to the nonlinearities in Ar and Kr. This discrepancy suggests that the frequency shifts due to alkali-noble van der Waals molecules in Xe are opposite in sign to the those in Ar and Kr. The nonlinearity in Xe shows a reproducible deviation from a simple model used to describe the shifts in Ar and Kr, which suggests that the spin-rotation interaction plays a significant role in the frequency shifts due to molecules. No nonlinearities were observed with the gases He and N 2 , as expected, and also Ne to within experimental error, which suggests that molecules do not form in Ne. Additionally, we present improved measurements of the shifts of Rb in Ar and Kr and of Rb and Cs in He and N 2 .
We report the first quantitative theoretical and experimental studies of frequency shifts of nuclear-magnetic-resonance (NMR) lines of noble-gas atoms and the corresponding frequency shifts of electron-paramagnetic-resonance (EPR) lines of alkali-metal atoms in mixtures of nuclear spin-polarized noble gases and vapors of spin-polarized alkali-metal atoms. The shifts are primarily due to the Fermi-contact hyperfine interaction. For the heavier noble gases there can be relatively large (\ensuremath{\approxeq}10%) contributions to the shifts from van der Waals molecules. The NMR frequencies of polarized 83Kr^{83}\mathrm{Kr}83Kr and 129Xe^{129}\mathrm{Xe}129Xe were measured in a vapor of spin-polarized alkali-metal atoms oriented parallel and antiparallel to the external magnetic field. The shift in the EPR frequency of the alkali-metal vapor due to the polarized noble-gas nuclei was measured simultaneously, thus providing a measurement of the absolute noble-gas nuclear polarization. The frequency shifts can be used as a convenient way to measure the absolute nuclear spin polarization of noble gases.
We demonstrate that the microwave resonant frequencies of ground-state87Rb and133Csatoms have a nonlinear dependence on the pressure of the buffer gas Xe. Surprisingly, though the frequency shifts of Rb and Cs in the heavy noble gases Ar, Kr, and Xe are all negative, the nonlinearity in Xe is of the opposite sign to the nonlinearities in Ar and Kr. This discrepancy suggests that the frequency shifts due to alkali-noble van der Waals molecules in Xe are opposite in sign to the those in Ar and Kr. The nonlinearity in Xe shows a reproducible deviation from a simple model used to describe the shifts in Ar and Kr, which suggests that the spin-rotation interaction plays a significant role in the frequency shifts due to molecules. No nonlinearities were observed with the gases He and N2, as expected, and also Ne to within experimental error, which suggests that molecules do not form in Ne. Additionally, we present improved measurements of the shifts of Rb in Ar and Kr and of Rb and Cs in He and N2.