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The B-spline basis-set method is applied to determining the rovibrational eigenspectrum of diatomic molecules. Particular attention is paid to a challenging numerical task of an accurate and efficient description of the vibrational levels near the dissociation limit (halo-state and Feshbach molecules). Advantages of using B-splines are highlighted by comparing the performance of the method with that of the commonly used discrete-variable representation (DVR) approach. Several model cases, including the Morse potential and realistic potentials with 1/[R.sup.3] and 1/[R.sup.6] long-range dependence of the internuclear separation are studied. We find that the B-spline method is superior to the DVR approach and it is robust enough to properly describe the Feshbach molecules. The developed numerical method is applied to studying the universal relation of the energy of the last bound state to the scattering length. We illustrate numerically the validity of the quantum-defect-theoretic formulation of such a relation for a 1/[R.sup.6] potential. PACS Nos.: 31.15.-p,34.50.Cx La methode utilisant une base de fonctions B-spline est utilisee pour determiner le spectre rovibrationnel des molecules diatomiques. Une attention toute particuliere est portee a la description numerique precise et efficace des niveaux vibrationnels proches de la limite de dissociation (etat halo et molecule de Feshbach). Nous soulignons l'avantage presente par l'utilisation de B-spline en comparant les performances de cette methode a celles de la methode de representation en variable discrete (DVR) communement utilisee. La methode developpee ici est utilisee pour etudier la relation universelle entre l'energie du dernier etat lie et la longueur de diffusion. Nous illustrons numeriquement la validite de cette relation obtenue dans le cadre de la theorie du defaut quantique sur l'exemple d'un potentiel en 1/[R.sup.6]., 1. Introduction The finite basis-set technique is an important numerical tool in solving quantum mechanical problems, for example, in quantum chemistry [1]. One of the popular recent developments is the [...]

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. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Develops numerical calculations of vibrational levels of alkali dimers close to the dissociation limit in the framework of a Fourier Grid Hamiltonian method. Interpretation of photoassociation experiments in cold atom samples; Proposal of a mapping procedure adapted to the asymptotic R[sup R-n] behavior of the long-range potentials.

Theoretical calculations for the ground state and for 83 excited states of the Na2 molecule are presented in the framework of two independent approaches. The electron–core interaction is represented either by a pseudopotential or by a model potential, and a core polarization potential is introduced in both cases. The basis set contains either Gaussian orbitals or two-center generalized Slater orbitals. The two methods appear to give similar results, one being more accurate for the ground and first excited states, the other being better adapted to the intermediate Rydberg states. A very good agreement is obtained with the experimental spectroscopic constants determined for 26 states, the mean deviation being ΔRe=0.05a0, Δωe=0.86 cm-1, and ΔDe=57 cm-1. [ABSTRACT FROM AUTHOR]