General explicit pure rotational effect for infrared, Raman and higher (ΔJ) spectra for a diatomic molecule

The problem of the pure rotational transitions nu J <-> nu J' for any spectra \ J-J'\ greater than or equal to 1 for a diatomic molecule is considered. It is proved that, the wave functions Psi(nu J) and Psi(nu J') are expanded in terms of the running number m =[J'(J' + 1) - J(J + 1)]/2 as Psi(nu J) = Sigma(n=0)pi(n)m(n) and Psi(nu J') = Sigma(n=0) pi(n)(-m)(n) where pi(n) are expressed in terms of the pure vibrational wave function phi(0) and its rotational corrections phi(n) (defined in the conventional perturbation theory). By using this m-representation of the wave functions the pure rotational matrix elements of the considered transitions are given by M-nu J(nu J') =< Psi(nu J)\gamma \Psi(nu J') >= Sigma(n=0)mu(2n)m(2n) where mu(2n) are simple combinations of simple integrals of the form < phi(i)\gamma \phi(n) >. This formulation is valid for any potential (either numerical or analytical), any vibrational level nu and any operator gamma. The numerical application to the Dunham potential of the molecule H-2 in the Raman transitions and to the Huffaker potential of the molecule CO in the infrared transitions shows the validity and the high accuracy of the present formulation.