Analogue of oscillation theorem for nonadiabatic diatomic states: application to the A 1Σ+ and b 3Π states of KCs

Abstract

Relative intensity measurements in the high resolution A (1)Sigma(+) approximately b (3)Pi--> X (1)Sigma(+) laser induced fluorescence spectra of the KCs molecule highlighted a breakdown of the conventional one-dimensional oscillation theorem (L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Pergamon, New York, 1965). For strongly spin-orbit coupled A (1)Sigma(+) and b (3)Pi states the number of nodes n(A) and n(b) of the non-adiabatic vibrational eigenfunctions phi and phi corresponding to the v-th eigenstate differs essentially from their adiabatic counterparts. It is found, however, that in the general case of two-component states with wavefunctions phi and phi coupled by the sign-constant potential operator V(12) not equal 0: (1) the lowest state v = 0 is not degenerate; and (2) the arithmetic mean of the number of nodes n(1) and n(2) of phi and phi never exceeds the ordering number v of eigenstate: (n(1) + n(2))/2 <or=v.