Diatomic molecule in a strong infrared laser field: level-shifts and bond-length change due to laser-dressed Morse potential

We present a general mathematical procedure to handle interactions described by a Morse potential in the presence of a strong harmonic excitation. We account for permanent and field-induced terms and their gradients in the dipole moment function, and we derive analytic formulae for the bond-length change and for the shifted energy eigenvalues of the vibrations, by using the Kramers-Henneberger frame. We apply these results to the important cases of ${\mathrm{H}}_2$ and $\mathrm{L}\mathrm{i}\mathrm{H}$, driven by a near- or mid-infrared laser in the ${10}^{13}$ $\mathrm{W}\mathrm{/}\mathrm{c}{\mathrm{m}}^2$ intensity range.