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Evidence is given on the usefulness of the variational method to explore the nonseparable Schroedinger problem for the energy evolution of one-electron atoms and diatomic molecular ions confined by a hard prolate spheroidal cavity when the nuclear positions do not coincide with the foci. In this work, we study explicity the case of the hydrogen atom (H) and the H2+ and HeH++ under the aforementioned confinement conditions and obtain variationally the energy evolution as a function of nuclear positions along the major axis of a confining spheroid of fixed size and eccentricity. The particular case of an electron (e-) under the same confinement conditions is also addressed using the same methodology. Our calculations are restricted to the ground states of H (1sσ), HeH++ (1sσ), e-(1sσ) and the ground-state (1sσg) and first excited state (2pσu) of H2+. It is shown that a simple LCAO Dickinson-type variational ansatz wavefunction adapted for the confinement case of all systems treated in this work provides very rewarding results for the energy dependence on the size and shape of the confining cavity when compared with corresponding available exact calculations. For e- as well as for H, H2+ and HeH++ with “on-focus” nuclear positions excellent general quantitative agreement is observed. For the “off-focus” case, moderate quantitative agreement is obtained with available accurate B-spline variational calculations for H. For the molecular systems with “off-focus” nuclear positions, the results of this work are the first of this kind. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [ABSTRACT FROM AUTHOR]

We have developed an approach to continuously load ultracold 85Rb2 vibrational ground-state molecules into a crossed optical dipole trap from a magneto-optical trap. The technique relies on a single high-power light beam with a broad spectrum superimposed onto a narrow peak at an energy of about 9400 cm-1. This single laser source performs all the required steps: the short-range photoassociation creating ground-state molecules after radiative emission, the cooling of the molecular vibrational population down to the lowest vibrational level vX=0, and the optical trapping of these molecules. Furthermore, we probe by depletion spectroscopy and determine that 75% of the vX=0 ground-state molecules are in the three lowest rotational levels JX=0, 1, 2. The lifetime of the ultracold molecules in the optical dipole trap is limited to about 70 ms by off-resonant light scattering. The proposed technique opens perspectives for the formation of new molecular species in the ultracold domain, which are not yet accessible by well-established approaches. [ABSTRACT FROM AUTHOR]