Polarizability of Rydberg atoms and the dominant long-range interactions -art. no. 042703

The dominant long-range interaction of an alkali-metal atom with charged pa rticles at low energies is given for large separation R by the dispersive p otential W similar or equal to - alpha(d)/R-4 in terms of the dipole polari zability alpha(d). For atoms prepared initially in Rydberg states of quantu m numbers (n, l), the potential assumes a more complicated form due to the complete or near degeneracy of the n manifold. Contributions to the polariz ability are treated in two parts, (a) one for the: nondegenerate states and (b) the other for the degenerate or near degenerate cases. It is shown tha t <(alpha)over tilde>((b))(d) for case (b) is in general R dependent, and i n the limit of complete degeneracy, diverges as R-2. That is, for a small e nergy gap Delta between a pair of nearly degenerate states which are dipole coupled, the dispersion potential W-(b) similar or equal to D/R-2 for R<R- x and W-(b) similar or equal to- alpha(d)((b))/R-4 for R>R-x, where D is th e dipole moment, R-x = [2\D/Delta\](1/2), and alpha(d)((b)) similar or equa l to D-2/Delta. They may also compete with a 1/R-3 potential for Rydberg at oms with l>0. The total alpha(d) can be very large in magnitude For small D elta and even assume negative values, but the corresponding R, also increas es as Delta decreases. The validity region in R of the R-4 behavior of the potential recedes to larger R as the polarizability grows. A general formul a for alpha(d) is given, taking into account the effects of tine-structure splitting, the Lamb shift, and quantum defects.