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 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).
- Research Organization:
- Louisiana State Univ., Baton Rouge, LA (United States); San Diego State Univ., CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- Grant/Contract Number:
- FG02-96ER40985
- OSTI ID:
- 1556185
- Alternate ID(s):
- OSTI ID: 1241246; OSTI ID: 1438019
- Journal Information:
- Physics Letters B, Journal Name: Physics Letters B Vol. 750 Journal Issue: C; ISSN 0370-2693
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- Netherlands
- Language:
- English
Web of Science
Electric and magnetic dipole modes in high-resolution inelastic proton scattering at 0°
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journal | July 2019 |
Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons
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journal | August 2019 |
Validity of the Generalized Brink-Axel Hypothesis in
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journal | January 2016 |
Test of the Brink-Axel Hypothesis for the Pygmy Dipole Resonance
|
journal | November 2017 |
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