Integral of a product of three 6-dimensional spherical harmonics

✍ Scribed by A. Amaya; E. Chacón

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 834 KB
• Volume: 71
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(92)90081-9

✦ Synopsis

A FORTRAN program is presented for the evaluation of the integral of a product of three 6-dimensional spherical harmonics over the surface of the unit 6-sphere. The functions have a classification according to the chain of groups 0(6) ~Sd'(2) x SU(3) ~SO(3) i SO(2), introduced originally by Dragt. This scheme provides four quantum numbers plus a multiplicity label, thus giving rise to a non-orthogonal basis for which general analytic expressions are known. The overlap integrals of two functions are included as particular cases. The relevance of the mentioned integrals for the quantum mechanical study of three-body systems is pointed Out. In particular, it is shown that the transformation brackets between the different bases adapted to each pair of bodies are extremely simple, thereby facilitating very much the treatment of the various two-body interactions in systems where not all 3 particles are identical.