Effective-potential model for high-LRydberg atoms

Abstract

A description of fine-structure patterns in nonpenetrating high-$L$ Rydberg atoms and ions is derived in a perturbative model in which the energy denominators occurring in the second-order perturbation theory are evaluated using the adiabatic expansion. The patterns of Rydberg energies that result are dominated by the expectation value of an effective potential containing a range of tensor orders and increasing negative powers of the Rydberg electron's radial coordinate. The coefficients of each term in the effective potential are expressed in terms of matrix elements and energies of the free ion at the core of the Rydberg system. Smaller corrections to these patterns due to application of the effective potential in second order and due to relativistic and spin contributions are also described. The effective potential provides a framework for extracting ion properties from measurements of high-$L$ fine-structure patterns.