# General theory for Rydberg states of atoms: nonrelativistic case

## TL;DR

This paper provides a comprehensive derivation of nonrelativistic energies for atomic Rydberg states, including finite nuclear mass effects, correcting previous discrepancies and offering detailed energy level data.

## Contribution

It introduces a complete derivation of Rydberg state energies with finite nuclear mass corrections, resolving past inconsistencies in the literature.

## Key findings

- Identification of missing terms in previous derivations
- Confirmation of discrepancies in earlier works
- Provision of detailed energy level tables

## Abstract

We carry out a complete derivation on nonrelativistic energies of atomic Rydberg states, including finite nuclear mass corrections. Several missing terms are found and a discrepancy is confirmed in the works of Drachman [in Long Range Casimir Forces: Theory and Recent Experiments on Atomic Systems, edited by F. S. Levin and D. A. Micha (Plenum, New York, 1993)] and Drake [Adv. At., Mol., Opt. Phys. 31, 1 (1993)]. As a benchmark, we present a detailed tabulation of different energy levels.