Systematics of strength function sum rules
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink–Axel hypothesis is unsurprising: one expectssum rules to evolve with excitation energy. Moreover, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).
- Publication Date:
- Grant/Contract Number:
- FG02-96ER40985
- Type:
- Accepted Manuscript
- Journal Name:
- Physics Letters. Section B
- Additional Journal Information:
- Journal Volume: 750; Journal Issue: C; Journal ID: ISSN 0370-2693
- Publisher:
- Elsevier
- Research Org:
- Louisiana State Univ., Baton Rouge, LA (United States); San Diego State Univ., San Diego, CA (United States)
- Sponsoring Org:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; strength functions; sum rules; Brink–Axel hypothesis; spectral distribution theory; shell model; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
- OSTI Identifier:
- 1241246
- Alternate Identifier(s):
- OSTI ID: 1438019
Johnson, Calvin W. Systematics of strength function sum rules. United States: N. p.,
Web. doi:10.1016/j.physletb.2015.08.054.
Johnson, Calvin W. Systematics of strength function sum rules. United States. doi:10.1016/j.physletb.2015.08.054.
Johnson, Calvin W. 2015.
"Systematics of strength function sum rules". United States.
doi:10.1016/j.physletb.2015.08.054. https://www.osti.gov/servlets/purl/1241246.
@article{osti_1241246,
title = {Systematics of strength function sum rules},
author = {Johnson, Calvin W.},
abstractNote = {Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink–Axel hypothesis is unsurprising: one expectssum rules to evolve with excitation energy. Moreover, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).},
doi = {10.1016/j.physletb.2015.08.054},
journal = {Physics Letters. Section B},
number = C,
volume = 750,
place = {United States},
year = {2015},
month = {8}
}