Analogue of oscillation theorem for nonadiabatic diatomic states: application to the A(1)Sigma(+) and b(3)Pi states of KCs

Relative intensity measurements in the high resolution A ¹Σ⁺∼b³Π → 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 A¹Σ⁺ and b³Π states the number of nodes n_A and n_b of the non-adiabatic vibrational eigenfunctions φvA and φvb 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 φv1 and φv2 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 φv1 and φv2 never exceeds the ordering number v of eigenstate: (n₁ + n₂)/2 ≤ v.