dorsal/arxiv
View SchemaBeyond mean-field study of excited states: Analysis within the Lipkin model
| Authors | A. P. Severyukhin, M. Bender, P. -H. Heenen |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0603069 |
| URL | https://arxiv.org/abs/nucl-th/0603069 |
| DOI | 10.1103/PhysRevC.74.024311 |
| Journal | Phys.Rev. C74 (2006) 024311 |
Abstract
Beyond mean-field methods based on restoration of symmetries and configuration mixing by the generator coordinate method (GCM) enable to calculate on the same footing correlations in the ground state and the properties of excited states. Excitation energies are often largely overestimated, especially in nuclei close to magicity, even when transition probabilities are well-described. We analyse here the origin of this failure. The first part of the paper compares realistic projected GCM and QRPA calculations for selected Sn isotopes performed with the same effective Skyrme interaction. Although it is difficult to perform RPA and GCM calculations under exactly the same conditions, this comparison shows that the projected GCM overestimates the RPA results. In the second part of this paper, we compare GCM and RPA in the framework of the exactly solvable Lipkin-Meshkov-Glick model. We show that the discretized GCM works quite well and permits to obtain nearly exact results with a small number of discretization points. This analysis indicates also that to break more symmetries of the nuclear Hamiltonian in the construction of the GCM basis is probably the best way to improve the description of excited states by the GCM.
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"abstract": "Beyond mean-field methods based on restoration of symmetries and\nconfiguration mixing by the generator coordinate method (GCM) enable to\ncalculate on the same footing correlations in the ground state and the\nproperties of excited states. Excitation energies are often largely\noverestimated, especially in nuclei close to magicity, even when transition\nprobabilities are well-described. We analyse here the origin of this failure.\nThe first part of the paper compares realistic projected GCM and QRPA\ncalculations for selected Sn isotopes performed with the same effective Skyrme\ninteraction. Although it is difficult to perform RPA and GCM calculations under\nexactly the same conditions, this comparison shows that the projected GCM\noverestimates the RPA results. In the second part of this paper, we compare GCM\nand RPA in the framework of the exactly solvable Lipkin-Meshkov-Glick model. We\nshow that the discretized GCM works quite well and permits to obtain nearly\nexact results with a small number of discretization points. This analysis\nindicates also that to break more symmetries of the nuclear Hamiltonian in the\nconstruction of the GCM basis is probably the best way to improve the\ndescription of excited states by the GCM.",
"arxiv_id": "nucl-th/0603069",
"authors": [
"A. P. Severyukhin",
"M. Bender",
"P. -H. Heenen"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.74.024311",
"journal_ref": "Phys.Rev. C74 (2006) 024311",
"title": "Beyond mean-field study of excited states: Analysis within the Lipkin model",
"url": "https://arxiv.org/abs/nucl-th/0603069"
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