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Physical Review A

Hyperfine Pressure Shift of Helium ( 1s2s:S3 ) Atoms in Helium ( 1s2:S1 )

Chizuko M. Dutta, N. C. Dutta, T. P. Das

Published Jan 1, 1973• 5 citations
Publisher

Abstract

The hyperfine pressure shift of the metastable helium ($1s2s:^{3}S$) in a buffer gas consisting of ground-state helium atoms is studied by the linked-cluster many-body perturbation approach. Owing to the existence of the repulsive barrier in the intermolecular potential of this system at sizable intermolecular separation, the main contribution to the hyperfine pressure shift comes from the long-range attractive region of the van der Waals potential and the contribution from the short- and intermediate-range region may be neglected. We calculate a shift of -15.0 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$/torr, in essential agreement with the experimental value of (-7.4 \ifmmode\pm\else\textpm\fi{} 3.0) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$/torr.

DOI
10.1103/physreva.7.60

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Physical Review A•May 5, 2021•5 citations
The hyperfine pressure shift of the metastable helium (1s2s:3S1s2s:^{3}S1s2s:3S) in a buffer gas consisting of ground-state helium atoms is studied by the linked-cluster many-body perturbation approach. Owing to the existence of the repulsive barrier in the intermolecular potential of this system at sizable intermolecular separation, the main contribution to the hyperfine pressure shift comes from the long-range attractive region of the van der Waals potential and the contribution from the short- and intermediate-range region may be neglected. We calculate a shift of -15.0 \ifmmode\times\else\texttimes\fi{} 10\ensuremath−9{10}^{\ensuremath{-}9}10\ensuremath−9/torr, in essential agreement with the experimental value of (-7.4 \ifmmode\pm\else\textpm\fi{} 3.0) \ifmmode\times\else\texttimes\fi{} 10\ensuremath−9{10}^{\ensuremath{-}9}10\ensuremath−9/torr.
Long-range interaction studies of the system ${\mathrm{He}}_{2}(^{3}\ensuremath{\Sigma}^{+})$ based on the multiconfiguration self-consistent-field formalism are reported. In this formalism the long-range contribution to the hyperfine pressure shift of metastable He(23S)\mathrm{He}(2^{3}S)He(23S) in buffer gas of ground-state He is discussed. It is found by actual computation to be an order of magnitude smaller than that predicted by the many-body perturbation theoretic approach. Possible explanations of the discrepancy are discussed.
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.
The interaction of two excited hydrogen atoms in metastable states constitutes a theoretically interesting problem because of the quasidegenerate 2P1/22{P}_{1/2}2P1/2​ levels that are removed from the 2S2S2S states only by the Lamb shift. The total Hamiltonian of the system is composed of the van der Waals Hamiltonian, the Lamb shift, and the hyperfine effects. The van der Waals shift becomes commensurate with the $2S\ensuremath{-}2{P}_{3/2}$ fine-structure splitting only for close approach (R<100a0R<100{a}_{0}R<100a0​, where a0{a}_{0}a0​ is the Bohr radius) and one may thus restrict the discussion to the levels with n=2n=2n=2 and J=1/2J=1/2J=1/2 to a good approximation. Because each SSS or PPP state splits into an F=1F=1F=1 triplet and an F=0F=0F=0 hyperfine singlet (eight states for each atom), the Hamiltonian matrix a priori is of dimension 64. A careful analysis of the symmetries of the the problem allows one to reduce the dimensionality of the most involved irreducible submatrix to 12. We determine the Hamiltonian matrices and the leading-order van der Waals shifts for states that are degenerate under the action of the unperturbed Hamiltonian (Lamb shift plus hyperfine structure). The leading first- and second-order van der Waals shifts lead to interaction energies proportional to 1/R31/{R}^{3}1/R3 and 1/R61/{R}^{6}1/R6 and are evaluated within the hyperfine manifolds. When both atoms are metastable 2S2S2S states, we find an interaction energy of order ${E}_{h}\ensuremath{\chi}{({a}_{0}/R)}^{6}$, where Eh{E}_{h}Eh​ and L\mathcal{L}L are the Hartree and Lamb shift energies, respectively, and $\ensuremath{\chi}={E}_{h}/\mathcal{L}\ensuremath{\approx}6.22\ifmmode\times\else\texttimes\fi{}{10}^{6}$ is their ratio.
We present results of the pressure broadening and shift of the rubidium 5s2S1∕2–6p2P3∕25s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\text{--}6p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}5s2S1∕2​–6p2P3∕2​ (420.2 nm) spectral line by argon and helium buffer gases at pressures below 10 torr. High-resolution absorption measurements were performed with a single-mode external cavity diode laser, having 20-GHz tuning range and a linewidth of about 1 MHz. Pressure broadening and shift parameters of Lorentzian hyperfine components have been determined. We obtained the redshift of hyperfine spectral lines for He and the blueshift for Ar.
We propose the explanation of a small yet finite frequency shift of a hyperfine transition in two-dimensional atomic hydrogen bound to the surface of superfluid helium at T < 0.1 K. The nonzero shift is caused, first, by the interaction between adsorbed atoms, which effectively reduces their binding energy to the helium surface by a value proportional to their density and, consequently, reduces the deviation of the hyperfine constant from the free-atom value. Second, the transition between the hyperfine states b and c is shifted owing to a difference in the interaction of the b and c atoms with the residual atoms in the state a that appear due to one and two-body nuclear relaxation. This shift is also linear in the density of the two-dimensional gas. The net effect of the two contributions qualitatively agrees with the experimentally observed value of the shift.
Low-energy properties of spin-polarized electron-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) and spin-polarized positronium-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering are calculated using the modified confined variational method. To take the van der Waals interaction into consideration, the van der Waals coefficient between positronium and helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) is calculated using the explicitly correlated Gaussian basis. Compared with the ground state noble gases, the larger scattering length and zero pickoff annihilation rate indicates that He(23S)\mathrm{He}(2\phantom{\rule{0.16em}{0ex}}^{3}S)He(23S) may be a more suitable cooling gas. In the energy range we considered, no similarity is found for the SSS-wave cross sections between these two scatterings. A Ramsauer-Townsend minimum is observed in spin-polarized electron-helium(23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering due to the large polarization of metastable helium. This may open a new way to find and study the Ramsauer-Townsend effect.