Long-range interaction of two metastable rare-gas atoms

Motivated by cold-collision studies of metastable rare-gas atoms @1–4# and prospects of achieving Bose-Einstein condensation in these systems @5#, we present calculations of long-range dispersion ~van der Waals! coefficients for two atoms interacting in the ns(3/2)2 atomic states (n53 for Ne, n54 for Ar, n55 for Kr, and n56 for Xe!. The metastable states have long lifetimes, 43 s for Xe @6#, decaying to the ground S0 state by a weak magnetic-quadrupole transition. With such a long lifetime the metastable atom behaves as an effective ground state in experiments. Compared to alkalimetal systems, an attractive feature of the noble-gas atoms is the availability of isotopes with zero nuclear spin. The lack of hyperfine structure leads to a substantial simplification of molecular potentials, though some complexity arises due to the nonvanishing total electron angular momentum (J52) of the metastable state. The anisotropy leads to 15 distinct longrange molecular states connecting to the ns(3/2)2 1ns(3/2)2 asymptotic configuration. Our theoretical treatment of long-range interactions is similar to recent high-precision calculations of van der Waals coefficients for alkali-metal atoms @7#. By using many-body methods and accurate experimental matrix elements for the principal transitions, leading dispersion coefficients C6 were determined to an accuracy better than 1% for Na, K, and Rb, and of 1% for Cs and 1.5% for Fr. The semiempirical values of C6 coefficients for metastable noblegas atoms obtained here have an estimated uncertainty of 4%. The approach relies on the determination of dynamic polarizability functions. To construct the polarizabilities we combine experimental lifetime @8–15# and energy data of the excited states with accurate semiempirical dynamic polarizabilities of the ground states of noble-gas atoms @16#. The theoretical lifetimes and branching ratios @17# are adjusted to reproduce the measured static polarizabilities @18#, which are known with a 2% uncertainty. We estimated the additional small contributions within the Dirac-Hartree-Fock framework. The resulting polarizabilities satisfy the ThomasReiche-Kuhn ~TRK! oscillator strength sum rule. The Racah notation for atomic levels is used. The particle-hole states are labeled as nl(K)J or nl8(K)J , where n and l are the principal and the orbital angular momentum quantum numbers of the valence electron and K5Jc1l , where Jc is the angular momentum of the core. The primed configurations converge to a Rydberg series limit with a hole in the (n21)p1/2 state, and the unprimed to a hole in the (n21)p3/2 state. The manifold of the lowest ns valence