## Physics & Astronomy ETDs

## Publication Date

11-1-1968

## Abstract

Theoretical calculations of the rotational-vibrational constants of the B^{1}Σ^{+}_{u} state of H_{2} were made using the Dunham analysis and by fitting equations to energy eigenvalues. The potential energy function for the nuclei used in the calculations was computed by W. Kolos and L. Wolniewicz using the variational technique. The power series used in the Dunham analysis made use of Stirling's central difference interpolation polynomial. The equilibrium separation R_{e} found from the Born-Oppenheimer potential is 2. 42916_{5} atomic units, differing from the Kolos-Wolniewicz value of 2.4288. Adiabatic corrections were taken into account through a perturbation series. This yielded R_{e} = 2.4341_{1.4} a.u. or 1.28805_{7} Ȧ. The Dunham analysis yielded adiabatically corrected constants as follows:

The constants obtained from the energy levels are:

B_{V}, D_{V}, and H_{V }were calculated from v=0 to v=25 using the energy levels and a cubic-order in J(J+1) leastsquares procedure. Graphs of these quantities, as well as ΔG_{V+1/2 }are included. The reason for the discrepancy in the values for ω_{e} from the two methods is not understood. The D values from the two methods is not understood. The D_{V} values that were found are believed to be more reliable than experimental values since the effect of H_{V} was taken into account when the D_{V} values were calculated. Both D_{V} and H_{V} values show a continuous decrease up to v= 25. The theoretical constants are compared with the experimental values of G. Herzberg and L. L. Howe, T. Namioka, G. H. Dieke, and P. G. Wilkinson.

## Degree Name

Physics

## Level of Degree

Masters

## Department Name

Physics & Astronomy

## First Committee Member (Chair)

Charles Leroy Beckel

## Second Committee Member

Mohammed Shafi

## Third Committee Member

John Root Green

## Fourth Committee Member

Lawrence Fred Shampine

## Language

English

## Document Type

Thesis

## Recommended Citation

Moody, Sandra Zink. "Theoretical Analysis of the Vibrations and Rotations of the B¹[Sigma][Mu] State of the Hydrogen Molecule." (1968). https://digitalrepository.unm.edu/phyc_etds/294