NEW ANALYTICAL EXPRESSIONS FOR THE HERMAN-WALLIS COEFFICIENTS OF INFRARED TRANSITIONS UP TO THE 3RD-ORDER

The rotational dependence of dipole moments M(vj)v'J' = <PSI(vJ)\f\PSI(v'J'>) in infrared transitions (vJ <--> v'J') is considered. Analytic theoretical expressions of the Herman-Wallis coefficients for the infrared transitions are investigated by using an unconventional approach of the Rayleigh-Schrodinger perturbation theory. The rotational factor G(vJ)v'J' = M(vJ)v'J'/M(v0)v'0 is expressed, in terms of the Bouanich-Herman-Wallis coefficients, by G(w')(m) = 1 + C'm + D'm2 + E'm3 +... with m = [J'(J'+1) - J(J + 1)]/2 and J' - J = +/- 1. The coefficients C', D', and E' are given in terms of the intergrals <PHI,(v)\f]PHI(p')> and <PHI(v)\PHI(p'> where PHI stands for the pure-vibrational wavefunction PSI(v) or for one of its successive perturbative corrections B(v), D(v), ..... These expressions are valid for any potential, whether empirical or of the RKR type, and for any operator f of the form x = (r - r(e))/r(e), x(l), exp(ax) and others. Numerical application of the present formulation in terms of the Dunham potential in the ground state of CO (for transitions nu V 0, 10, 20 and nu' - nu less-than-or-equal-to 4) and the ground state of HCl (for the transitions nu = 0 and DELTAnu less-than-or-equal-to 7) shows the good accuracy.