dorsal/arxiv
View SchemaUltracold collisions in tight harmonic traps: Quantum defect model and application to metastable helium atoms
| Authors | Gillian Peach, Ian B Whittingham, Timothy J Beams |
|---|---|
| Categories | |
| ArXiv ID | physics/0212003 |
| URL | https://arxiv.org/abs/physics/0212003 |
| DOI | 10.1103/PhysRevA.70.032713 |
Abstract
We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two highly efficient computational methods for determining the bound state energies and eigenfunctions of such systems. The perturbed harmonic oscillator problem is characterized by a long asymptotic region beyond the effective range of the interatomic potential. The first method, which is based on quantum defect theory and is an adaptation of a technique developed by one of the authors (GP) for highly excited states in a modified Coulomb potential, is very efficient for integrating through this outer region. The second method is a direct numerical solution of the radial Schr\"{o}dinger equation using a discrete variable representation of the kinetic energy operator and a scaled radial coordinate grid. The methods are applied to the case of trapped spin-polarized metastable helium atoms. The calculated eigenvalues agree very closely for the two methods, and with those computed self-consistently using the generalized self-consistent method.
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"abstract": "We analyze a system of two colliding ultracold atoms under strong harmonic\nconfinement from the viewpoint of quantum defect theory and formulate a\ngeneralized self-consistent method for determining the allowed energies. We\nalso present two highly efficient computational methods for determining the\nbound state energies and eigenfunctions of such systems. The perturbed harmonic\noscillator problem is characterized by a long asymptotic region beyond the\neffective range of the interatomic potential. The first method, which is based\non quantum defect theory and is an adaptation of a technique developed by one\nof the authors (GP) for highly excited states in a modified Coulomb potential,\nis very efficient for integrating through this outer region. The second method\nis a direct numerical solution of the radial Schr\\\"{o}dinger equation using a\ndiscrete variable representation of the kinetic energy operator and a scaled\nradial coordinate grid. The methods are applied to the case of trapped\nspin-polarized metastable helium atoms. The calculated eigenvalues agree very\nclosely for the two methods, and with those computed self-consistently using\nthe generalized self-consistent method.",
"arxiv_id": "physics/0212003",
"authors": [
"Gillian Peach",
"Ian B Whittingham",
"Timothy J Beams"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1103/PhysRevA.70.032713",
"title": "Ultracold collisions in tight harmonic traps: Quantum defect model and application to metastable helium atoms",
"url": "https://arxiv.org/abs/physics/0212003"
},
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