Theoretical treatment of channel mixing in excited Rb-2 and Cs-2 ultracoldmolecules: Determination of predissociation lifetimes with coordinate mapping - art. no. 032716

The treatment of the dynamics of ultracold molecules requires new theoretic al tools. Previous work of the present authors [J. Chem. Phys. 110, 9865 (1 999)] for calculation of vibrational levels by a Fourier grid representatio n with use of adaptative coordinates is generalized here to the treatment o f the bound-continuum interaction in a two-channel problem. Two numerical m ethods are presented: a time-dependent method using a Chebyshev propagator to compute the correlation function and a time-independent method with diag onalization of a Hamiltonian that includes an absorbing optical potential. In both eases the adaptative coordinate is defined by a numerical rather th an an analytical procedure. Lifetimes are reported for the predissociated l evels of the Rb-2 and Cs-2 0(u)(+) (ns+np(2)P(3/2)) spectra, where n=5,6. T he two numerical methods give similar results. The lifetimes increase with the vibrational quantum number proportionally to the classical vibration pe riod estimated from the Le Roy-Bernstein law for an asymptotic R-3 potentia l, and the energy variation can be fitted to an analytical formula. The res ults 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. [Ph ys. Rev. Lett. 73, 632 (1994)] for one predissociated level of Rb-87(2) is reproduced. A strong isotopic effect is found for the rubidium dimer, the l ifetimes of Rb-85(2) and Rb-87(2) levels differing by a factor of 3. Finall y, we present a third approach, in the framework of a generalized two-chann el quantum-defect theory, where lifetimes are determined by extrapolation o f parameters fitted to Lu-Fano plots of computed bound levels below the P-1 /2 dissociation limit. Excellent agreement is obtained with the numerical r esults, suggesting the possibility of fitting to experimental spectra.