Abstract
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.
Highlights
Optical frequency measurements of nD–2S transition in hydrogen are of significant interest in high-precision spectroscopy [1,2,3,4]
For the interpretation of experimental data, the pressure shift experienced by atoms inside the atomic beam is of particular interest [5,6] and its description requires considerable theoretical effort
This is because the pressure shift is generated by interatomic long-range interactions
Summary
Optical frequency measurements of nD–2S transition in hydrogen are of significant interest in high-precision spectroscopy [1,2,3,4]. The treatment of the long-range (van-der-Waals) interaction of two excited atoms proceeds differently from that of ground-state atoms and from that of the excited-ground-state system This statement applies in particular to atoms where the virtual transitions to the quasidegenerate states are of low multipole order, e.g., in the case of dipole-allowed transitions. There are dipole-allowed virtual transitions to 2P and nP, as well as nF states (the latter are present for n = 8) The presence of these quasi-degenerate states makes a full diagonalization of the van-der-Waals Hamiltonian in the hyperfine-resolved basis necessary. Since = 2 for D states, there are 2` + 1 possible projections of orbital angular momentum along the axis of quantization, in addition to the spin projections This aspect enhances the dimensionality of the Hamiltonian matrices in the hyperfine-resolved basis, which describes the virtual transitions among the energetically quasi-degenerate states.
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