dorsal/arxiv
View SchemaAlternative sets of hyperspherical harmonics: Satisfying cusp conditions through frame transformations
| Authors | T. A. Heim, D. Green |
|---|---|
| Categories | |
| ArXiv ID | physics/9905053 |
| URL | https://arxiv.org/abs/physics/9905053 |
| DOI | 10.1063/1.532857 |
| Journal | J. of Math. Phys. vol. 40 (1999) 2162-2180 |
Abstract
By extending the concept of Euler-angle rotations to more than three dimensions, we develop the systematics under rotations in higher-dimensional space for a novel set of hyperspherical harmonics. Applying this formalism, we determine all pairwise Coulomb interactions in a few-body system without recourse to multipole expansions. Our approach combines the advantages of relative coordinates with those of the hyperspherical description. In the present method, each Coulomb matrix element reduces to the ``1/r'' form familiar from the two-body problem. Consequently, our calculation accounts for all the cusps in the wave function whenever an interparticle separation vanishes. Unlike a truncated multipole expansion, the calculation presented here is exact. Following the systematic development of the procedure for an arbitrary number of particles, we demonstrate it explicitly with the simplest nontrivial example, the three-body system.
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"abstract": "By extending the concept of Euler-angle rotations to more than three\ndimensions, we develop the systematics under rotations in higher-dimensional\nspace for a novel set of hyperspherical harmonics. Applying this formalism, we\ndetermine all pairwise Coulomb interactions in a few-body system without\nrecourse to multipole expansions. Our approach combines the advantages of\nrelative coordinates with those of the hyperspherical description. In the\npresent method, each Coulomb matrix element reduces to the ``1/r\u0027\u0027 form\nfamiliar from the two-body problem. Consequently, our calculation accounts for\nall the cusps in the wave function whenever an interparticle separation\nvanishes. Unlike a truncated multipole expansion, the calculation presented\nhere is exact. Following the systematic development of the procedure for an\narbitrary number of particles, we demonstrate it explicitly with the simplest\nnontrivial example, the three-body system.",
"arxiv_id": "physics/9905053",
"authors": [
"T. A. Heim",
"D. Green"
],
"categories": [
"physics.atm-clus",
"nucl-th"
],
"doi": "10.1063/1.532857",
"journal_ref": "J. of Math. Phys. vol. 40 (1999) 2162-2180",
"title": "Alternative sets of hyperspherical harmonics: Satisfying cusp conditions through frame transformations",
"url": "https://arxiv.org/abs/physics/9905053"
},
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