dorsal/arxiv
View SchemaFitting theories of nuclear binding energies
| Authors | G. F. Bertsch, B. Sabbey, M. Uusnakki |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0412091 |
| URL | https://arxiv.org/abs/nucl-th/0412091 |
| DOI | 10.1103/PhysRevC.71.054311 |
| Journal | Phys.Rev. C71 (2005) 054311 |
Abstract
In developing theories of nuclear binding energy such as density-functional theory, the effort required to make a fit can be daunting due to the large number of parameters that may be in the theory and the large number of nuclei in the mass table. For theories based on the Skyrme interaction, the effort can be reduced considerably by using the singular value decomposition to reduce the size of the parameter space. We find that the sensitive parameters define a space of dimension four or so, and within this space a linear refit is adequate for a number of Skyrme parameters sets from the literature. We do not find marked differences in the quality of the fit between the SLy4, the Bky4 and SkP parameter sets. The r.m.s. residual error in even-even nuclei is about 1.5 MeV, half the value of the liquid drop model. We also discuss an alternative norm for evaluating mass fits, the Chebyshev norm. It focuses attention on the cases with the largest discrepancies between theory and experiment. We show how it works with the liquid drop model and make some applications to models based on Skyrme energy functionals. The Chebyshev norm seems to be more sensitive to new experimental data than the root-mean-square norm. The method also has the advantage that candidate improvements to the theories can be assessed with computations on smaller sets of nuclei.
{
"annotation_id": "1c15a8b0-596c-45ab-995f-9cef863085e7",
"date_created": "2026-03-02T18:00:04.206000Z",
"date_modified": "2026-03-02T18:00:04.206000Z",
"file_hash": "a49a0ddadb8f0ec2cfc9bb104797e520f24394811ffe88814fefa6e620c6dba7",
"private": false,
"record": {
"abstract": "In developing theories of nuclear binding energy such as density-functional\ntheory, the effort required to make a fit can be daunting due to the large\nnumber of parameters that may be in the theory and the large number of nuclei\nin the mass table. For theories based on the Skyrme interaction, the effort can\nbe reduced considerably by using the singular value decomposition to reduce the\nsize of the parameter space. We find that the sensitive parameters define a\nspace of dimension four or so, and within this space a linear refit is adequate\nfor a number of Skyrme parameters sets from the literature. We do not find\nmarked differences in the quality of the fit between the SLy4, the Bky4 and SkP\nparameter sets. The r.m.s. residual error in even-even nuclei is about 1.5 MeV,\nhalf the value of the liquid drop model. We also discuss an alternative norm\nfor evaluating mass fits, the Chebyshev norm. It focuses attention on the cases\nwith the largest discrepancies between theory and experiment. We show how it\nworks with the liquid drop model and make some applications to models based on\nSkyrme energy functionals. The Chebyshev norm seems to be more sensitive to new\nexperimental data than the root-mean-square norm. The method also has the\nadvantage that candidate improvements to the theories can be assessed with\ncomputations on smaller sets of nuclei.",
"arxiv_id": "nucl-th/0412091",
"authors": [
"G. F. Bertsch",
"B. Sabbey",
"M. Uusnakki"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.71.054311",
"journal_ref": "Phys.Rev. C71 (2005) 054311",
"title": "Fitting theories of nuclear binding energies",
"url": "https://arxiv.org/abs/nucl-th/0412091"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "1e029a33-c401-46d5-93a8-85fb35e4533e",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}