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An efficient mapped pseudospectral method for weakly bound states: vibrational states of He-2, Ne-2, Ar-2 and Cs-2

TitleAn efficient mapped pseudospectral method for weakly bound states: vibrational states of He-2, Ne-2, Ar-2 and Cs-2
Publication TypeJournal Article
Year of Publication2008
AuthorsLo, JQW, Shizgal, BD
JournalJournal of Physics B-Atomic Molecular and Optical Physics
Volume41
Pagination13
Date PublishedSep
Type of ArticleArticle
ISBN Number0953-4075
KeywordsBASIS FUNCTIONS, DIATOMIC-MOLECULES, DIMERS, DISCRETE, HELIUM DIMER, LAGRANGE-MESH METHOD, LONG-RANGE MOLECULES, NONCLASSICAL, QUADRATURE DISCRETIZATION METHOD, QUANTUM-MECHANICAL PROBLEMS, RARE-GAS, ULTRAVIOLET-LASER SPECTROSCOPY, VARIABLE REPRESENTATION
Abstract

This paper reports the application of pseudospectral methods to the calculation of the bound states of He-2, Ne-2, Ar-2 and Cs-2. The calculation of the uppermost loosely bound states, only one for He-2, presents a challenge for most numerical methods. We employ the quadrature discretization method which is a collocation based on quadrature points defined with weight functions that approximate the ground states. A mapping procedure is proposed that greatly improves the convergence of the uppermost states that are very loosely bound and characterized by very diffuse eigenfunctions. Comparisons with the results with other methods and experiment are also carried out wherever possible.
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