Multiphoton Processes in Homopolar Diatomic Molecules

Within the framework of time-dependent perturbation theory and the Born—Oppenheimer approximation, general expressions are derived for the cross sections of multiphoton processes induced by radiation acting on a homopolar diatomic molecule. A Morse-type model of potential-energy curves of excited electronic states is proposed which gives a good representation of true curves. The procedure used to evaluate the sums over intermediate states is described. The method is based on the use of the internuclear potential Green's functions obtained in closed form. Analytic expressions are derived for one-photon and two-photon cross sections. The results for higher-order processes are presented in a form which is convenient for numerical computation. As an illustration, the cross section for one-photon dissociation of $\mathrm{H}_2^{}{}_{}{}^{+}$ from the $v=0\mathrm{}$ vibrational level is calculated as a function of wavelength. A comparison of cross sections calculated using the Morse-type model of potential curves with those using accurate wave functions of $\mathrm{H}_2^{}{}_{}{}^{+}$ shows a good precision of the model.