New analytical expression for the rotational factor in Raman transitions

Abstract

The matrix elements of the polarizability anisotropy γ in the Raman spectra of diatomic molecules are investigated. These matrix elements are given by [Formula: see text] where Gνν′(m) is the rotational factor with m = [(J′(J′ + 1) − J(J + 1)]/2 and J′ − J = ±2. By using a nonconventional approach to the Rayleigh–Schrödinger perturbation theory the rotational factor can be written as Gνν′(m) = A0 + A1m + A2m2 where the coefficients A0, A1, and A2 are given by simple analytical expressions in terms of the integrals [Formula: see text] and [Formula: see text] where Y stands for Ψ(0) (the pure vibration wave function), or Ψ(0) (the first rotational perturbative correction to Ψ(0), or Ψ(2) (the second correction). A numerical application is presented for the ground states of CO and H2 molecules. A comparison with a numerical and direct calculation of the rotational factor Gνν′(m) shows the accuracy of the present formalism.