Mapped grid methods for long-range molecules and cold collisions.

The paper discusses ways of improving the accuracy of numerical calculations for vibrational levels of diatomic molecules close to the dissociation limit or for ultracold collisions, in the framework of a grid representation. In order to avoid the implementation of very large grids, Kokoouline et al. [J. Chem. Phys. 110, 9865 (1999)] have proposed a mapping procedure through introduction of an adaptive coordinate x subjected to the variation of the local de Broglie wavelength as a function of the internuclear distance R. Some unphysical levels ("ghosts") then appear in the vibrational series computed via a mapped Fourier grid representation. In the present work the choice of the basis set is reexamined, and two alternative expansions are discussed: Sine functions and Hardy functions. It is shown that use of a basis set with fixed nodes at both grid ends is efficient to eliminate "ghost" solutions. It is further shown that the Hamiltonian matrix in the sine basis can be calculated very accurately by using an auxiliary basis of cosine functions, overcoming the problems arising from numerical calculation of the Jacobian J(x) of the R-->x coordinate transformation.

Resonant coupling in the formation of ultracold ground state molecules via photoassociation.

We demonstrate the existence of a new mechanism for the formation of ultracold molecules via photoassociation of cold cesium atoms. The experimental results, interpreted with numerical calculations, suggest that a resonant coupling between vibrational levels of the 0+u (6s+6p1/2) and (6s+6p3/2) states enables formation of ultracold molecules in vibrational levels of the ground state well below the 6s+6s dissociation limit. Such a scheme should be observable with many other electronic states and atomic species.

Spectroscopy and Lifetimes of the 1(2)Piu State of Na+2: A New Comparison between Theory and Experiment.

A detailed theoretical study of the spectroscopy of the 1(2)Piu state of Na+2 is presented, including the determination of Dunham coefficients from recent effective potential calculations of the Na+2 molecular potential curves. We emphasize the discrepancies existing among several experiments and among several theoretical models available in the literature. The radiative lifetime of the rovibrational levels of the 1(2)Piu state are also computed and are found in agreement within 20% with experiment. Copyright 1998 Academic Press.