dorsal/arxiv
View SchemaLevinson's Theorem for Dirac Particles
| Authors | J. Piekarewicz |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9306011 |
| URL | https://arxiv.org/abs/nucl-th/9306011 |
| DOI | 10.1103/PhysRevC.48.2174 |
| Journal | Phys.Rev.C48:2174-2181,1993 |
Abstract
Levinson's theorem for Dirac particles constraints the sum of the phase shifts at threshold by the total number of bound states of the Dirac equation. Recently, a stronger version of Levinson's theorem has been proven in which the value of the positive- and negative-energy phase shifts are separately constrained by the number of bound states of an appropriate set of Schr\"odinger-like equations. In this work we elaborate on these ideas and show that the stronger form of Levinson's theorem relates the individual phase shifts directly to the number of bound states of the Dirac equation having an even or odd number of nodes. We use a mean-field approximation to Walecka's scalar-vector model to illustrate this stronger form of Levinson's theorem. We show that the assignment of bound states to a particular phase shift should be done, not on the basis of the sign of the bound-state energy, but rather, in terms of the nodal structure (even/odd number of nodes) of the bound state.
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"abstract": "Levinson\u0027s theorem for Dirac particles constraints the sum of the phase\nshifts at threshold by the total number of bound states of the Dirac equation.\nRecently, a stronger version of Levinson\u0027s theorem has been proven in which the\nvalue of the positive- and negative-energy phase shifts are separately\nconstrained by the number of bound states of an appropriate set of\nSchr\\\"odinger-like equations. In this work we elaborate on these ideas and show\nthat the stronger form of Levinson\u0027s theorem relates the individual phase\nshifts directly to the number of bound states of the Dirac equation having an\neven or odd number of nodes. We use a mean-field approximation to Walecka\u0027s\nscalar-vector model to illustrate this stronger form of Levinson\u0027s theorem. We\nshow that the assignment of bound states to a particular phase shift should be\ndone, not on the basis of the sign of the bound-state energy, but rather, in\nterms of the nodal structure (even/odd number of nodes) of the bound state.",
"arxiv_id": "nucl-th/9306011",
"authors": [
"J. Piekarewicz"
],
"categories": [
"nucl-th",
"hep-th"
],
"doi": "10.1103/PhysRevC.48.2174",
"journal_ref": "Phys.Rev.C48:2174-2181,1993",
"title": "Levinson\u0027s Theorem for Dirac Particles",
"url": "https://arxiv.org/abs/nucl-th/9306011"
},
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