Perturbation Theory in Closed Form for Heteronuclear Diatomic Molecules

Within the framework of the Born---Oppenheimer approximation questions are considered involving application of time-dependent perturbation theory to diatomic heteronuclear molecules. A potential-energy model of the form Vᵢ(r)=Aᵢ(r-rᵢ)²-Bᵢ(r-rᵢ)+Qᵢ is proposed which gives a good representation of the true curves of the ground and excited states of a molecule. The relation ωₑxₑ=6D²m=3ωₑ4/32m1/3 has been obtained between the dissociation energies into free ions D, vibrational frequencies ωₑ, and vibrational anharmonicity parameters ωₑxₑ of the ground state of polar molecules. Analytical expressions are derived for vibration-rotation spectra, wave functions, and radial matrix elements considered in the first-order perturbation theory. An explicit expression obtained for the Green's function of the model enables a closed form to be given for matrix elements appearing in the higher-order perturbation theory involved in calculation of multiphoton molecular transitions.