dorsal/arxiv
View SchemaThe Nuclear Scissors Mode from Various Aspects
| Authors | E. B. Balbutsev, P. Schuck |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0602031 |
| URL | https://arxiv.org/abs/nucl-th/0602031 |
| DOI | 10.1016/j.aop.2006.04.014 |
| Journal | Annals Phys. 322 (2007) 489-529 |
Abstract
Three methods to describe collective motion, Random Phase Approximation (RPA), Wigner Function Moments (WFM) and the Green's Function (GF) method are compared in detail and their physical content analyzed on an example of a simple model, the harmonic oscillator with quadrupole--quadrupole residual interaction. It is shown that they give identical formulae for eigenfrequencies and transition probabilities of all collective excitations of the model, including the scissors mode, which is the subject of our special attention. The exact relation between the RPA and WFM variables and the respective dynamical equations is established. The transformation of the RPA spectrum into the one of WFM is explained. The very close connection of the WFM method with the GF one is demonstrated. The normalization factor of the ``synthetic'' scissors state and its overlap with physical states are calculated analytically. The orthogonality of the spurious state to all physical states is proved rigorously. A differential equation describing the current lines of RPA modes is established and the current lines of the scissors mode analyzed as a superposition of rotational and irrotational components.
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"abstract": "Three methods to describe collective motion, Random Phase Approximation\n(RPA), Wigner Function Moments (WFM) and the Green\u0027s Function (GF) method are\ncompared in detail and their physical content analyzed on an example of a\nsimple model, the harmonic oscillator with quadrupole--quadrupole residual\ninteraction. It is shown that they give identical formulae for eigenfrequencies\nand transition probabilities of all collective excitations of the model,\nincluding the scissors mode, which is the subject of our special attention. The\nexact relation between the RPA and WFM variables and the respective dynamical\nequations is established. The transformation of the RPA spectrum into the one\nof WFM is explained. The very close connection of the WFM method with the GF\none is demonstrated. The normalization factor of the ``synthetic\u0027\u0027 scissors\nstate and its overlap with physical states are calculated analytically. The\northogonality of the spurious state to all physical states is proved\nrigorously. A differential equation describing the current lines of RPA modes\nis established and the current lines of the scissors mode analyzed as a\nsuperposition of rotational and irrotational components.",
"arxiv_id": "nucl-th/0602031",
"authors": [
"E. B. Balbutsev",
"P. Schuck"
],
"categories": [
"nucl-th"
],
"doi": "10.1016/j.aop.2006.04.014",
"journal_ref": "Annals Phys. 322 (2007) 489-529",
"title": "The Nuclear Scissors Mode from Various Aspects",
"url": "https://arxiv.org/abs/nucl-th/0602031"
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