COUPLING OF ROTATION AND ELECTRONIC MOTION IN CASES COVERING NEAR HUND'S CASE b THROUGH NEAR HUND'S CASE $d^{\ast}$

Abstract

General perturbed energy expressions for A-doubling are derived up to the fourth order for a near Hund's case b diatomic molecule using as perturbation the term $-2B(N_{x}L_{x} + N_{y}L_{y})$ and as parameter the electronic energy $E_{A}$ for a state of given A dispensing with the early restriction of electronic energy to the form of $A \cdot A^{2}$. Specific examples are given for Rydberg p-term $(L=1)$ and d-term $(L=2)$ complexes. For these term complexes the intermediate case is approached from case b, the $3 \times 3$ secular equation resulted in factoring the d-term complexes is expanded in infinite series to show its N-dependence. For Hund's case d, the rotation-electronic wavefunction is expressed by angular momenta coupling as follows $\Psi_{R, 0} = \Sigma_{A} C(N.L.R;A.-A,0) D_{NA} \Phi_{L,A}$ where the rotational wavefunction $D_{NA}$ may be identified to be the rotation $matrix.^{1}$ Instead of the Hill and Van Vleck's perturbation A $\cos^{2}\alpha$, the electric multipole perturbation on a united $atom^{2}$ due to the separation of the nuclei is taken as the perturbation on the Hund's case d wavefunction. The selection rules for the matrix elements are shown to be $\delta R=0, \pm 2$. These matrix elements are used to express the general perturbed energies up to the second order for a near Hund's case d diatomic molecule and to construct secular equations for intermediate cases approached from case d. The approaches from cases b and d are shown to give identical results. Special emphasis is given to the power of angular momenta coupling and the physical basis for our new point of view.