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Title: Systematics of strength function sum rules

Abstract

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 expects sum rules to evolve with excitation energy. Furthermore, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).

Authors:
Publication Date:
Research Org.:
Louisiana State Univ., Baton Rouge, LA (United States); San Diego State Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1556185
Alternate Identifier(s):
OSTI ID: 1241246; OSTI ID: 1438019
Grant/Contract Number:  
FG02-96ER40985
Resource Type:
Published Article
Journal Name:
Physics Letters B
Additional Journal Information:
Journal Name: Physics Letters B Journal Volume: 750 Journal Issue: C; Journal ID: ISSN 0370-2693
Publisher:
Elsevier
Country of Publication:
Netherlands
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

Citation Formats

Johnson, Calvin W. Systematics of strength function sum rules. Netherlands: N. p., 2015. Web. doi:10.1016/j.physletb.2015.08.054.
Johnson, Calvin W. Systematics of strength function sum rules. Netherlands. https://doi.org/10.1016/j.physletb.2015.08.054
Johnson, Calvin W. Sun . "Systematics of strength function sum rules". Netherlands. https://doi.org/10.1016/j.physletb.2015.08.054.
@article{osti_1556185,
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 expects sum rules to evolve with excitation energy. Furthermore, 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 B},
number = C,
volume = 750,
place = {Netherlands},
year = {Sun Nov 01 00:00:00 EDT 2015},
month = {Sun Nov 01 00:00:00 EDT 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.physletb.2015.08.054

Citation Metrics:
Cited by: 22 works
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Works referencing / citing this record:

Electric and magnetic dipole modes in high-resolution inelastic proton scattering at 0°
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Electric and magnetic dipole modes in high-resolution inelastic proton scattering at 0°
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Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons
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Validity of the Generalized Brink-Axel Hypothesis in Np 238
journal, January 2016


Test of the Brink-Axel Hypothesis for the Pygmy Dipole Resonance
journal, November 2017