Transition sum rules in the shell model
Abstract
An important characterization of electromagnetic and weak transitions in atomic nuclei are sum rules. We focus on the non-energy-weighted sum rule (NEWSR), or total strength, and the energy- weighted sum rule (EWSR); the ratio of the EWSR to the NEWSR is the centroid or average energy of transition strengths from an nuclear initial state to all allowed final states. These sum rules can be expressed as expectation values of operators, in the case of the EWSR a double commutator. While most prior applications of the double-commutator have been to special cases, we derive general formulas for matrix elements of both operators in a shell model framework (occupation space), given the input matrix elements for the nuclear Hamiltonian and for the transition operator. With these new formulas, we easily evaluate centroids of transition strength functions, with no need to calculate daughter states. We then apply this simple tool to a number of nuclides, and demonstrate the sum rules follow smooth secular behavior as a function of initial energy, as well as compare the electric dipole (E1) sum rule against the famous Thomas-Reiche-Kuhn version. We also find surprising systematic behaviors for ground state electric quadrupole (E2) centroids in the $sd$-shell.
- Authors:
-
- Qufu Normal Univ., Shandong (China). College of Physics and Engineering; Shanghai Jiao Tong Univ., Shanghai (China). School of Physics and Astronomy; San Dieog State Univ., CA (United States). Dept. of Physics
- San Diego State Univ., CA (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- San Diego State Univ., CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); National Natural Science Foundation of China (NSFC)
- OSTI Identifier:
- 1430213
- Alternate Identifier(s):
- OSTI ID: 1430378
- Grant/Contract Number:
- FG02-03ER41272; FG02-96ER40985; 11225524; 11705100; SC0009971
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review C
- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 3; Journal ID: ISSN 2469-9985
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; nuclear shell model; electromagnetic transitions; sum rules; electroweak interactions in nuclear physics
Citation Formats
Lu, Yi, and Johnson, Calvin W. Transition sum rules in the shell model. United States: N. p., 2018.
Web. doi:10.1103/PhysRevC.97.034330.
Lu, Yi, & Johnson, Calvin W. Transition sum rules in the shell model. United States. https://doi.org/10.1103/PhysRevC.97.034330
Lu, Yi, and Johnson, Calvin W. Thu .
"Transition sum rules in the shell model". United States. https://doi.org/10.1103/PhysRevC.97.034330. https://www.osti.gov/servlets/purl/1430213.
@article{osti_1430213,
title = {Transition sum rules in the shell model},
author = {Lu, Yi and Johnson, Calvin W.},
abstractNote = {An important characterization of electromagnetic and weak transitions in atomic nuclei are sum rules. We focus on the non-energy-weighted sum rule (NEWSR), or total strength, and the energy- weighted sum rule (EWSR); the ratio of the EWSR to the NEWSR is the centroid or average energy of transition strengths from an nuclear initial state to all allowed final states. These sum rules can be expressed as expectation values of operators, in the case of the EWSR a double commutator. While most prior applications of the double-commutator have been to special cases, we derive general formulas for matrix elements of both operators in a shell model framework (occupation space), given the input matrix elements for the nuclear Hamiltonian and for the transition operator. With these new formulas, we easily evaluate centroids of transition strength functions, with no need to calculate daughter states. We then apply this simple tool to a number of nuclides, and demonstrate the sum rules follow smooth secular behavior as a function of initial energy, as well as compare the electric dipole (E1) sum rule against the famous Thomas-Reiche-Kuhn version. We also find surprising systematic behaviors for ground state electric quadrupole (E2) centroids in the $sd$-shell.},
doi = {10.1103/PhysRevC.97.034330},
journal = {Physical Review C},
number = 3,
volume = 97,
place = {United States},
year = {Thu Mar 29 00:00:00 EDT 2018},
month = {Thu Mar 29 00:00:00 EDT 2018}
}
Web of Science
Works referenced in this record:
Electric Dipole Ground-State Transition Width Strength Function and 7-Mev Photon Interactions
journal, April 1962
- Axel, Peter
- Physical Review, Vol. 126, Issue 2
Effective interactions for the 1p shell
journal, November 1965
- Cohen, S.; Kurath, D.
- Nuclear Physics, Vol. 73, Issue 1
Gamow-teller strength functions with the Lanczos algorithm
journal, January 1984
- Bloom, S. D.
- Progress in Particle and Nuclear Physics, Vol. 11
The Wick theorem for coupled fermion clusters
journal, September 1993
- Chen, Jin-Quan
- Nuclear Physics A, Vol. 562, Issue 2
Nuclear spin and isospin excitations
journal, April 1992
- Osterfeld, Franz
- Reviews of Modern Physics, Vol. 64, Issue 2
Nuclear level densities and γ-ray strength functions in
journal, October 2007
- Larsen, A. C.; Guttormsen, M.; Chankova, R.
- Physical Review C, Vol. 76, Issue 4
Level density of and low-energy enhancement of γ-strength function
journal, July 2006
- Voinov, A. V.; Grimes, S. M.; Agvaanluvsan, U.
- Physical Review C, Vol. 74, Issue 1
Impact of a low-energy enhancement in the -ray strength function on the neutron-capture cross section
journal, July 2010
- Larsen, A. C.; Goriely, S.
- Physical Review C, Vol. 82, Issue 1
Increase in Width of the Giant Dipole Resonance in Hot Nuclei: Shape Change or Collisional Damping?
journal, May 1995
- Bracco, A.; Camera, F.; Mattiuzzi, M.
- Physical Review Letters, Vol. 74, Issue 19
Neutrinoless double- decay matrix elements in large shell-model spaces with the generator-coordinate method
journal, November 2017
- Jiao, C. F.; Engel, J.; Holt, J. D.
- Physical Review C, Vol. 96, Issue 5
Modification of the Brink-Axel hypothesis for high-temperature nuclear weak interactions
journal, December 2014
- Misch, G. Wendell; Fuller, George M.; Brown, B. Alex
- Physical Review C, Vol. 90, Issue 6
Photonuclear Sum Rule for Light Nuclei
journal, November 1978
- Gari, M.; Hebach, H.; Sommer, B.
- Physical Review Letters, Vol. 41, Issue 19
The (p,n) reactions and beta decays
journal, February 1963
- Ikeda, K.; Fujii, S.; Fujita, J. I.
- Physics Letters, Vol. 3, Issue 6
Gamow-Teller Strength Distributions in by the and Reactions and Two-Neutrino Double- Decay Nuclear Matrix Elements
journal, July 2009
- Yako, K.; Sasano, M.; Miki, K.
- Physical Review Letters, Vol. 103, Issue 1
Level densities in and
journal, November 2003
- Schiller, A.; Algin, E.; Bernstein, L. A.
- Physical Review C, Vol. 68, Issue 5
Level density and -decay properties of closed shell Pb nuclei
journal, February 2009
- Syed, N. U. H.; Guttormsen, M.; Ingebretsen, F.
- Physical Review C, Vol. 79, Issue 2
Orbital M 1 versus E 2 strength in deformed nuclei: A new energy weighted sum rule
journal, June 1993
- Moya de Guerra, E.; Zamick, L.
- Physical Review C, Vol. 47, Issue 6
Low-Energy Enhancement of Magnetic Dipole Radiation
journal, December 2013
- Schwengner, R.; Frauendorf, S.; Larsen, A. C.
- Physical Review Letters, Vol. 111, Issue 23
New “USD” Hamiltonians for the shell
journal, September 2006
- Brown, B. Alex; Richter, W. A.
- Physical Review C, Vol. 74, Issue 3
Possible Unified Interpretation of Heavy Nuclei
journal, May 1985
- Casten, R. F.
- Physical Review Letters, Vol. 54, Issue 18
First observation of the Coulomb-excited double giant dipole resonance in via double-γ decay
journal, February 1993
- Ritman, J.; Berg, F. -D.; Kühn, W.
- Physical Review Letters, Vol. 70, Issue 5
Correlation between E 2 and M 1 transition strength in even-even vibrational, transitional, and deformed nuclei
journal, December 1991
- Heyde, K.; De Coster, C.
- Physical Review C, Vol. 44, Issue 6
Linearity of nuclear level energies with the P-factor
journal, October 1992
- Brenner, D. S.; Casten, R. F.; Chou, W. -T.
- Physics Letters B, Vol. 293, Issue 3-4
Validity of the Generalized Brink-Axel Hypothesis in
journal, January 2016
- Guttormsen, M.; Larsen, A. C.; Görgen, A.
- Physical Review Letters, Vol. 116, Issue 1
Program in C for studying characteristic properties of two-body interactions in the framework of spectral distribution theory
journal, January 2014
- Launey, K. D.; Sarbadhicary, S.; Dytrych, T.
- Computer Physics Communications, Vol. 185, Issue 1
Total nuclear photon absorption cross sections for some light elements
journal, October 1975
- Ahrens, J.; Borchert, H.; Czock, K. H.
- Nuclear Physics A, Vol. 251, Issue 3
Efficient method for evaluating energy-dependent sum rules
journal, June 2014
- Nevo Dinur, N.; Barnea, N.; Ji, C.
- Physical Review C, Vol. 89, Issue 6
Empirical strengths of spin operators in nuclei
journal, January 1984
- Wildenthal, B. H.
- Progress in Particle and Nuclear Physics, Vol. 11
Strong correlation and saturation of E 2 and M 1 transition strengths in even-even rare-earth nuclei
journal, March 1991
- Rangacharyulu, C.; Richter, A.; Wörtche, H. J.
- Physical Review C, Vol. 43, Issue 3
Systematics of strength function sum rules
journal, November 2015
- Johnson, Calvin W.
- Physics Letters B, Vol. 750
Pygmy resonances and radiative nucleon captures for stellar nucleosynthesis
journal, April 2015
- Tsoneva, N.; Goriely, S.; Lenske, H.
- Physical Review C, Vol. 91, Issue 4
Radiative neutron captures by neutron-rich nuclei and the r-process nucleosynthesis
journal, September 1998
- Goriely, S.
- Physics Letters B, Vol. 436, Issue 1-2
The particle-hole interaction and the beta decay of 14B
journal, December 1975
- Millener, D. J.; Kurath, D.
- Nuclear Physics A, Vol. 255, Issue 2
Factorization in large-scale many-body calculations
journal, December 2013
- Johnson, Calvin W.; Ormand, W. Erich; Krastev, Plamen G.
- Computer Physics Communications, Vol. 184, Issue 12
Factorization of commutators: The Wick theorem for coupled operators
journal, March 1993
- Jin-Quan, Chen; Bing-Qing, Chen; Klein, Abraham
- Nuclear Physics A, Vol. 554, Issue 1
Electric-dipole sum rule and two-body correlations in nuclei
journal, October 1973
- Weng, W. T.; Kuo, T. T. S.; Brown, G. E.
- Physics Letters B, Vol. 46, Issue 3
Proton-neutron pairing amplitude as a generator coordinate for double- decay
journal, September 2014
- Hinohara, Nobuo; Engel, Jonathan
- Physical Review C, Vol. 90, Issue 3
Evidence for radiative coupling of the pygmy dipole resonance to excited states
journal, November 2012
- Angell, C. T.; Hammond, S. L.; Karwowski, H. J.
- Physical Review C, Vol. 86, Issue 5
The shell model as a unified view of nuclear structure
journal, June 2005
- Caurier, E.; Martínez-Pinedo, G.; Nowacki, F.
- Reviews of Modern Physics, Vol. 77, Issue 2
Valence p - n interactions and the development of collectivity in heavy nuclei
journal, February 1987
- Casten, R. F.; Brenner, D. S.; Haustein, P. E.
- Physical Review Letters, Vol. 58, Issue 7
Magnetic dipole excitations in nuclei: Elementary modes of nucleonic motion
journal, September 2010
- Heyde, Kris; von Neumann-Cosel, Peter; Richter, Achim
- Reviews of Modern Physics, Vol. 82, Issue 3
Large Low-Energy Strength for within the Nuclear Shell Model
journal, December 2014
- Brown, B. Alex; Larsen, A. C.
- Physical Review Letters, Vol. 113, Issue 25
Relation between E 2 and orbital M 1 transition strengths using a Q ⋅ Q interaction: Further developments
journal, November 1992
- Zamick, L.; Zheng, D. C.
- Physical Review C, Vol. 46, Issue 5
First Principles Description of the Giant Dipole Resonance in
journal, September 2013
- Bacca, S.; Barnea, N.; Hagen, G.
- Physical Review Letters, Vol. 111, Issue 12
Effect of exchange currents on orbital g-factors and E1 sum rule for photoabsorption
journal, April 1973
- Arima, A.; Brown, G. E.; Hyuga, H.
- Nuclear Physics A, Vol. 205, Issue 1
Works referencing / citing this record:
Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons
journal, August 2019
- Oishi, Tomohiro; Paar, Nils
- Physical Review C, Vol. 100, Issue 2