DIATOMIC ROVIBRATIONAL MATRIX-ELEMENTS - ANALYTIC-EXPRESSION OF THE ROTATIONAL FACTOR FOR ANY POTENTIAL

The problem of the rotational effect in the rovibrational matrix elements M(vJ)v'J' = [PSI(vJ)\f(r)\PSI(v'J')] is considered. Rayleigh-Schrodinger perturbation theory is used to show that, for any diatomic electronic potential U(r) (even of the RKR type) and for any operator f(r), the rotational factor G(vv')(J,J') = M(vJ)v'J'/M(v0)v'0 is given by G(vv')(J, J') = G(vv)(0) + G(vv)(1)m + G(vv)(2)m2 + ... with m = [J'(J' + 1)-J(J + 1)]/2. The coefficients G(vv')(0), G(vv)(1) and G(vv)(2) are simply deduced from the integrals [Y(v) Absolute value of f Y(v')], in which Y denotes the pure vibrational wavefunction PSI(v)(0), or a successive perturbative correction PSI(v)(1), PSI(v)(2), ... Numerical application to the RKR potential of the X 0g+ state of I2 (for the transitions v = 0 and DELTAv less-than-or-equal-to 8 with m = -5, -10, -15) and to the Dunham potentials of the ground states of HCl (for the transitions v = 0 and DELTAv less-than-or-equal-to 7 with m = -2, -4, -6, -8) and HF molecules (for the transitions v = 0 and DELTAv less-than-or-equal-to 5 with m = -2, -4, -6, -8) shows the satisfactory accuracy of the present formulation.