Methods for Coulomb Few-Body Problems

Department of Physics, University of Utah, Salt Lake City, UT 84112, USA Quantum Theory Project, P.O. Box 118435, University of Florida, Gainesville, FL 32611, USA 

This contribution examines current approaches to Coulomb few-body problems mainly from a methodological perspective, in contrast to recent reviews which have focused on the results obtained for benchmark problems. The methods under discussion here employ wavefunctions which explicitly involve all the interparticle coordinates and use functional forms appropriate to nonadiabatic systems in which all the particles are of comparable mass. The use of such wavefunctions for states of arbitrary angular symmetry is reviewed, and the kinetic-energy operator, written in the interparticle coordinates, is presented in a convenient form. Evaluation of the resultant angular matrix elements is discussed in detail. For exponentially correlated wavefunctions, problems of integral evaluation are surveyed, the relatively new analytical procedures are summarized, and relations among matrix elements are presented. The current status of Gaussian-orbital and Hylleraas methods is also reviewed. 

Appendix A. Angular Momentum Identities Appendix B. Differential Properties of the References 

ADVANCES IN QUANTUM CHEMISTRY, VOLUME 47 ISSN 0065-3276 DOI I0.I0I6/S0065-3276(04)47008-7 

The next significant advance in the area after these early investigations did not occur for about a decade, perhaps awaiting a growth in the power of digital computers. In 1977, Thakkar and Smith (an Uppsala alumnus) 

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Harris, F.E. Current methods for Coulomb few-body problems, Adv. Quant. Chem. 2004,47,129-... 

Current Methods for Coulomb Few-Body Problems interchanging I and l, we reach... 

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