On the Rydberg-Ritz Formula in Quantum Mechanics
Abstract
A derivation is given of the Rydberg-Ritz formula for series spectra. Simple expressions are obtained for the Rydberg and Ritz coefficients. It is shown that the Ritz coefficient is proportional to the difference between the radial period of the electron and the period of the hypothetical orbit, with the same energy which would exist if the atomic core were to contract to zero radius. The derivation necessitates a study of the confluent hypergeometric function. An expansion in powers of the energy is obtained for this function. The coefficients in the expansion are found to be simple combinations of Bessel functions. Calculations of the Rydberg and Ritz coefficients are carried out for the S series of Na, K, and Cs and show satisfactory agreement with observation. The comparison with experiment yields information concerning the relative accuracy of different types of central fields employed to approximate the effect of the atomic core upon the valence electron. It is concluded that the Hartree-Fock field is not a convenient starting point for this purpose.
- Publication:
-
Physical Review
- Pub Date:
- January 1948
- DOI:
- 10.1103/PhysRev.73.60
- Bibcode:
- 1948PhRv...73...60J