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 ¹Σ⁺∼b ³Π → X ¹Σ⁺ 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 ¹Σ⁺ and b ³Π states the number of nodes n_A and n_b of the non-adiabatic vibrational eigenfunctions φ^v_A and φ^v_b 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 φ^v₁ and φ^v₂ coupled by the sign-constant potential operator V₁₂ ≠ 0: (1) the lowest state v = 0 is not degenerate; and (2) the arithmetic mean of the number of nodes n₁ and n₂ of φ^v₁ and φ^v₂ never exceeds the ordering number v of eigenstate: (n₁ + n₂)/2 ≤ v.