Theoretical treatment of channel mixing in excitedRb2andCs2ultracold molecules: Determination of predissociation lifetimes with coordinate mapping

The treatment of the dynamics of ultracold molecules requires new theoretical tools. Previous work of the present authors [J. Chem. Phys. 110, 9865 (1999)] for calculation of vibrational levels by a Fourier grid representation with use of adaptative coordinates is generalized here to the treatment of the bound-continuum interaction in a two-channel problem. Two numerical methods are presented: a time-dependent method using a Chebyshev propagator to compute the correlation function and a time-independent method with diagonalization of a Hamiltonian that includes an absorbing optical potential. In both cases the adaptative coordinate is defined by a numerical rather than an analytical procedure. Lifetimes are reported for the predissociated levels of the ${\mathrm{Rb}}_2$ and ${\mathrm{Cs}}_2{0}_u^{+}{(ns+np}^2{P}_{3/2})$ spectra, where $n=5,6.\mathrm{}$ The two numerical methods give similar results. The lifetimes increase with the vibrational quantum number proportionally to the classical vibration period estimated from the Le Roy–Bernstein law for an asymptotic $R^{-3}$ potential, and the energy variation can be fitted to an analytical formula. The results are shown to be very sensitive to the molecular parameters, potentials, and couplings. The measured width of 8.5 GHz reported by Cline et al. [Phys. Rev. Lett. 73, 632 (1994)] for one predissociated level of ${}^{87}{\mathrm{Rb}}_2$ is reproduced. A strong isotopic effect is found for the rubidium dimer, the lifetimes of ${}^{85}{\mathrm{Rb}}_2$ and ${}^{87}{\mathrm{Rb}}_2$ levels differing by a factor of 3. Finally, we present a third approach, in the framework of a generalized two-channel quantum-defect theory, where lifetimes are determined by extrapolation of parameters fitted to Lu-Fano plots of computed bound levels below the $P_{1/2}$ dissociation limit. Excellent agreement is obtained with the numerical results, suggesting the possibility of fitting to experimental spectra.