dorsal/arxiv
View SchemaEffective theories of scattering with an attractive inverse-square potential and the three-body problem
| Authors | Thomas Barford, Michael C. Birse |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0406008 |
| URL | https://arxiv.org/abs/nucl-th/0406008 |
| DOI | 10.1088/0305-4470/38/3/009 |
| Journal | J.Phys. A38 (2005) 697-720 |
Abstract
A distorted-wave version of the renormalisation group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wave function satisfies a Schroedinger equation with an attractive inverse-square potential, as shown by Efimov. The resulting oscillatory behaviour controls the renormalisation of the three-body interactions, with the renormalisation-group flow tending to a limit cycle as the cut-off is lowered. The approach used here leads to single-valued potentials with discontinuities as the bound states are cut off. The perturbations around the cycle start with a marginal term whose effect is simply to change the phase of the short-distance oscillations, or the self-adjoint extension of the singular Hamiltonian. The full power counting in terms of the energy and two-body scattering length is constructed for short-range three-body forces.
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"abstract": "A distorted-wave version of the renormalisation group is applied to\nscattering by an inverse-square potential and to three-body systems. In\nattractive three-body systems, the short-distance wave function satisfies a\nSchroedinger equation with an attractive inverse-square potential, as shown by\nEfimov. The resulting oscillatory behaviour controls the renormalisation of the\nthree-body interactions, with the renormalisation-group flow tending to a limit\ncycle as the cut-off is lowered. The approach used here leads to single-valued\npotentials with discontinuities as the bound states are cut off. The\nperturbations around the cycle start with a marginal term whose effect is\nsimply to change the phase of the short-distance oscillations, or the\nself-adjoint extension of the singular Hamiltonian. The full power counting in\nterms of the energy and two-body scattering length is constructed for\nshort-range three-body forces.",
"arxiv_id": "nucl-th/0406008",
"authors": [
"Thomas Barford",
"Michael C. Birse"
],
"categories": [
"nucl-th",
"hep-ph",
"quant-ph"
],
"doi": "10.1088/0305-4470/38/3/009",
"journal_ref": "J.Phys. A38 (2005) 697-720",
"title": "Effective theories of scattering with an attractive inverse-square potential and the three-body problem",
"url": "https://arxiv.org/abs/nucl-th/0406008"
},
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