Fast theorems to identify the multiplet peaks and the link to the factor equivalent to Rydberg's constant for H-I

Abstract

In the quantum frame and dipole approximation for the Hydrogen atom, the paper provides a spectral model (QS-Model) based on the concept of the multiplet-peaks and also on the theorems of multiplets (BMT). These theorems show the transitions and their associated peaks in their multiplets. On the other hand, in this model, starting from the expression of energy levels of atomic structure in Dirac’s theory, the wavelengths of multipletpeaks in fine structure-approximation (fs-apx) are calculated. Based on the available NIST-data for the first five spectral series, the QS-Model is validated. This validation contains an observed-computed (O-C) type-analysis during which the improving-problem of the data for Balmer to Pfund series is examined. We give an analytical method and calculate the proportionality factor equivalent to the Rydberg constant in this model.