On the anomalous A1–A2 splittings in the ν2-ν4 manifold of PH3

Abstract

The anomalous k dependence of the A1–A2 splittings in the ν2-ν4 manifold of PH3 has been reported in several papers. We have studied this anomaly by taking into account the strong vibration-rotation mixings between various levels with k − l ≡ 0 (mod. 3). The anomalous k dependence is caused because usual perturbation treatment can not be applied to the manifold due to the near degeneracy of ν2 and ν4. We treat the problem by solving a 4 × 4 matrix which involves |ν4, J, k = 1, l = 1〉, |ν4, J, k = 2, l = −1〉, |ν2, J, k = 3, l = 0〉, and |ν4, J, k = 4, l = 1〉. A least-squares fitting of the observed A1–A2 splittings gives the splitting parameters for the ν4 state to be Δ(k=1,l=1) = 5268.48(40) − 9.57(12)J(J + 1) + 0.0377(21)J2(J + 1)2 MHz, Δ(k=2,l=−1) = 553(65) kHz, and Δ(k=4,l=1) = 1(2) Hz, and for the ν2 state to be Δ(k=3,l=0) = 291(38)Hz.