dorsal/arxiv
View SchemaUnified algebraic treatment of resonance
| Authors | A. D. Alhaidari |
|---|---|
| Categories | |
| ArXiv ID | physics/0405017 |
| URL | https://arxiv.org/abs/physics/0405017 |
| DOI | 10.1142/S0217751X05021154 |
| Journal | Int. J. Mod. Phys. A 20, 2657 (2005) |
Abstract
Energy resonance in scattering is usually investigated either directly in the complex energy plane (E-plane) or indirectly in the complex angular momentum plane (L-plane). Another formulation complementing these two approaches was introduced recently. It is an indirect algebraic method that studies resonances in a complex charge plane (Z-plane). This latter approach will be generalized to provide a unified algebraic treatment of resonances in the complex E-, L-, and Z-planes. The complex scaling (rotation) method will be used in the development of this approach. The resolvent operators (Green's functions) are formally defined in these three spaces. Bound states spectrum and resonance energies in the E-plane are mapped onto a discrete set of poles of the respective resolvent operator on the real line of the L- and Z-planes. These poles move along trajectories as the energy is varied. A finite square integrable basis is used in the numerical implementation of this approach. Stability of poles and trajectories against variation in all computational parameters is demonstrated. Resonance energies for a given potential are calculated and compared with those obtained by other studies.
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"abstract": "Energy resonance in scattering is usually investigated either directly in the\ncomplex energy plane (E-plane) or indirectly in the complex angular momentum\nplane (L-plane). Another formulation complementing these two approaches was\nintroduced recently. It is an indirect algebraic method that studies resonances\nin a complex charge plane (Z-plane). This latter approach will be generalized\nto provide a unified algebraic treatment of resonances in the complex E-, L-,\nand Z-planes. The complex scaling (rotation) method will be used in the\ndevelopment of this approach. The resolvent operators (Green\u0027s functions) are\nformally defined in these three spaces. Bound states spectrum and resonance\nenergies in the E-plane are mapped onto a discrete set of poles of the\nrespective resolvent operator on the real line of the L- and Z-planes. These\npoles move along trajectories as the energy is varied. A finite square\nintegrable basis is used in the numerical implementation of this approach.\nStability of poles and trajectories against variation in all computational\nparameters is demonstrated. Resonance energies for a given potential are\ncalculated and compared with those obtained by other studies.",
"arxiv_id": "physics/0405017",
"authors": [
"A. D. Alhaidari"
],
"categories": [
"physics.atom-ph",
"physics.gen-ph"
],
"doi": "10.1142/S0217751X05021154",
"journal_ref": "Int. J. Mod. Phys. A 20, 2657 (2005)",
"title": "Unified algebraic treatment of resonance",
"url": "https://arxiv.org/abs/physics/0405017"
},
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