dorsal/arxiv
View SchemaSolutions of the Bohr hamiltonian, a compendium
| Authors | Lorenzo Fortunato |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0411087 |
| URL | https://arxiv.org/abs/nucl-th/0411087 |
| DOI | 10.1140/epjad/i2005-07-115-8 |
| Journal | Eur.Phys.J. A26S1 (2005) 1-30 |
Abstract
The Bohr hamiltonian, also called collective hamiltonian, is one of the cornerstone of nuclear physics and a wealth of solutions (analytic or approximated) of the associated eigenvalue equation have been proposed over more than half a century (confining ourselves to the quadrupole degree of freedom). Each particular solution is associated with a peculiar form for the $V(\beta,\gamma)$ potential. The large number and the different details of the mathematical derivation of these solutions, as well as their increased and renewed importance for nuclear structure and spectroscopy, demand a thorough discussion. It is the aim of the present monograph to present in detail all the known solutions in $\gamma-$unstable and $\gamma-$stable cases, in a taxonomic and didactical way. In pursuing this task we especially stressed the mathematical side leaving the discussion of the physics to already published comprehensive material. The paper contains also a new approximate solution for the linear potential, and a new solution for prolate and oblate soft axial rotors, as well as some new formulae and comments, and an appendix on the analysis of a few interesting numerical sequences appearing in this context. The quasi-dynamical SO(2) symmetry is proposed in connection with the labeling of bands in triaxial nuclei.
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"abstract": "The Bohr hamiltonian, also called collective hamiltonian, is one of the\ncornerstone of nuclear physics and a wealth of solutions (analytic or\napproximated) of the associated eigenvalue equation have been proposed over\nmore than half a century (confining ourselves to the quadrupole degree of\nfreedom). Each particular solution is associated with a peculiar form for the\n$V(\\beta,\\gamma)$ potential. The large number and the different details of the\nmathematical derivation of these solutions, as well as their increased and\nrenewed importance for nuclear structure and spectroscopy, demand a thorough\ndiscussion. It is the aim of the present monograph to present in detail all the\nknown solutions in $\\gamma-$unstable and $\\gamma-$stable cases, in a taxonomic\nand didactical way. In pursuing this task we especially stressed the\nmathematical side leaving the discussion of the physics to already published\ncomprehensive material. The paper contains also a new approximate solution for\nthe linear potential, and a new solution for prolate and oblate soft axial\nrotors, as well as some new formulae and comments, and an appendix on the\nanalysis of a few interesting numerical sequences appearing in this context.\nThe quasi-dynamical SO(2) symmetry is proposed in connection with the labeling\nof bands in triaxial nuclei.",
"arxiv_id": "nucl-th/0411087",
"authors": [
"Lorenzo Fortunato"
],
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],
"doi": "10.1140/epjad/i2005-07-115-8",
"journal_ref": "Eur.Phys.J. A26S1 (2005) 1-30",
"title": "Solutions of the Bohr hamiltonian, a compendium",
"url": "https://arxiv.org/abs/nucl-th/0411087"
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