dorsal/arxiv
View SchemaAnalytical Expressions for a Hyperspherical Adiabatic Basis Three Particles in 2 Dimensions
| Authors | Anthony D. Klemm, Sigurd Yves Larsen |
|---|---|
| Categories | |
| ArXiv ID | physics/0105041 |
| URL | https://arxiv.org/abs/physics/0105041 |
Abstract
For a particular case of three-body scattering in 2 dimensions, we demonstrate analytically that the behaviour of the adiabatic potential is different from that of the hyperspherical coupling matrix elements, thereby leading to a phase shift that tends to zero, as the energy goes to zero, instead of to a constant. We consider two particles interacting with binary repulsive step potentials, one acting as a spectator, and solve analytically for the adiabatic eigenvalues and eigenvectors, for all values of rho. We are thereby able to obtain the leading terms in the long range behaviour of the effective potentials, and confirm its inverse logarithmic nature, suggested from a previous numerical study.
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"abstract": "For a particular case of three-body scattering in 2 dimensions, we\ndemonstrate analytically that the behaviour of the adiabatic potential is\ndifferent from that of the hyperspherical coupling matrix elements, thereby\nleading to a phase shift that tends to zero, as the energy goes to zero,\ninstead of to a constant. We consider two particles interacting with binary\nrepulsive step potentials, one acting as a spectator, and solve analytically\nfor the adiabatic eigenvalues and eigenvectors, for all values of rho. We are\nthereby able to obtain the leading terms in the long range behaviour of the\neffective potentials, and confirm its inverse logarithmic nature, suggested\nfrom a previous numerical study.",
"arxiv_id": "physics/0105041",
"authors": [
"Anthony D. Klemm",
"Sigurd Yves Larsen"
],
"categories": [
"physics.chem-ph",
"physics.atm-clus",
"physics.gen-ph"
],
"title": "Analytical Expressions for a Hyperspherical Adiabatic Basis Three Particles in 2 Dimensions",
"url": "https://arxiv.org/abs/physics/0105041"
},
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