Interatomic interactions and thermally induced shifts and broadenings of energy levels of atoms in circular Rydberg states

Analytical expressions are obtained for the constants determining the energy of the long-range (at large distances exceeding the LeRoy radius R_LR ≈ 4n²) polarisation interaction of the multipole electric moments of two atoms in identical Rydberg states with large principal (n) and maximum orbital (l ) and magnetic (m) quantum numbers (|m| = l = n – 1). Asymptotic expansions in powers of n are found for the components of the van der Waals interaction tensor, which determine the dependence of the dispersion energy on the orientation of the interatomic axis. The spontaneous and thermally induced broadenings of the energy levels of circular states are represented analytically as functions of the principal quantum number and temperature. It is found that analytical formulae for the sum of spontaneous and thermally induced line widths in the region of high temperatures and large principal quantum numbers (assuming n³k_BT ≫ 1) do not contain a temperature-independent contribution of the spontaneous part of the broadening. Closed analytical expressions are also obtained for the Farley–Wing function and for the n- and T-dependent corrections to the asymptotic behaviour of the thermally induced shift.