Theoretical treatment of channel mixing in excited ${\mathrm{Rb}}_2$ and ${\mathrm{Cs}}_2$ ultracold molecules: Perturbations in $0_u^{+}$ photoassociation and fluorescence spectra

The mapped Fourier grid method, using a coordinate adapted to the local de Broglie wavelength associated to the vibrational motion in a molecule, and recently developed by Kokoouline et al. [J. Chem. Phys. 110, 9865 (1999)], is used to compute the perturbed binding energies and rotational constants of the ${\mathrm{Cs}}_2{0}_u^{+}(6s+6p{}^2{P}_{1/2,3/2})$ photoassociation spectrum below the lower dissociation limit. The results are shown to be very sensitive to the molecular potential curves and spin-orbit coupling. In the case of ${\mathrm{Rb}}_2{0}_u^{+}(5s+5p{}^2{P}_{1/2,3/2}),$ a strong isotopic effect is also predicted. The results can be interpreted in the framework of generalized two-channel quantum defect theory, and generalized Lu-Fano plots are presented. This work suggests that parameters could easily be fitted to experimental spectra, eliminating the difficulties caused by limitations in the accuracy of the short-range molecular potentials.