The hyperfine pressure shift of the metastable helium (
1s2s: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{} ${10}^{\ensuremath{-}9}$/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.
The interaction of two excited hydrogen atoms in metastable states constitutes a theoretically interesting problem because of the quasidegenerate
2P1/2 levels that are removed from the
2S 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<100a0, where
a0 is the Bohr radius) and one may thus restrict the discussion to the levels with
n=2 and
J=1/2 to a good approximation. Because each
S or
P state splits into an
F=1 triplet and an
F=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/R3 and
1/R6 and are evaluated within the hyperfine manifolds. When both atoms are metastable
2S states, we find an interaction energy of order ${E}_{h}\ensuremath{\chi}{({a}_{0}/R)}^{6}$, where
Eh and
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.
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.
Pressure shifts inside an atomic beam are among the more theoretically challenging effects in high-precision measurements of atomic transitions. A crucial element in their theoretical analysis is the understanding of long-range interatomic interactions inside the beam. For excited reference states, the presence of quasi-degenerate states leads to additional challenges, due to the necessity to diagonalize large matrices in the quasi-degenerate hyperfine manifolds. Here, we focus on the interactions of hydrogen atoms in reference states composed of an excited nD state (atom A), and in the metastable 2S state (atom B). We devote special attention to the cases n=3 and n=8. For n=3, the main effect is generated by quasi-degenerate virtual P states from both atoms A and B and leads to experimentally relevant second-order long-range (van-der-Waals) interactions proportional to the sixth inverse power of the interatomic distance. For n=8, in addition to virtual states with two states of P symmetry, one needs to take into account combined virtual P and F states from atoms A and B. The numerical value of the so-called C6 coefficients multiplying the interaction energy was found to grow with the principal quantum number of the reference D state; it was found to be of the order of 1011 in atomic units. The result allows for the calculation of the pressure shift inside atomic beams while driving transitions to nD states.
We present semiempirical calculations of long-range van der Waals interactions for two interacting metastable rare-gas atoms Ne through Xe. Dispersion coefficients
C6 are obtained for homonuclear molecular potentials asymptotically connecting to the
ns(3/2)2+ns(3/2)2 atomic states. The estimated uncertainty of the calculated
C6 dispersion coefficients is 4%.