Elliott's SU(3) model is at the basis of the shell-model description of rotational motion in atomic nuclei. Here we demonstrate that SU(3) symmetry can be realized in a truncated shell-model space if constructed in terms of a sufficient number of collective S, D, G,...pairs (i.e., with angular momentum zero, two, four,...) and if the structure of the pairs is optimally determined either by a conjugate-gradient minimization method or from a Hartree-Fock intrinsic state. We illustrate the procedure for six protons and six neutrons in the pf (sdg) shell and exactly reproduce the level energies and electric quadrupole properties of the ground-state rotational band with SDG (SDGI) pairs. The SD-pair approximation without significant renormalization, on the other hand, cannot describe the full SU(3) collectivity. A mapping from Elliott's fermionic SU(3) model to systems with s, d, g,... bosons provides insight into the existence of a decoupled collective subspace in terms of S, D, G,... pairs.
Fu, G. J., Johnson, Calvin W., Van Isacker, P., et al., "Nucleon-pair coupling scheme in Elliott's SU(3) model," Physical Review. C 103, no. 2 (2021), https://doi.org/10.1103/physrevc.103.l021302
@article{osti_1849463,
author = {Fu, G. J. and Johnson, Calvin W. and Van Isacker, P. and Ren, Zhongzhou},
title = {Nucleon-pair coupling scheme in Elliott's SU(3) model},
annote = {Elliott's SU(3) model is at the basis of the shell-model description of rotational motion in atomic nuclei. Here we demonstrate that SU(3) symmetry can be realized in a truncated shell-model space if constructed in terms of a sufficient number of collective S, D, G,...pairs (i.e., with angular momentum zero, two, four,...) and if the structure of the pairs is optimally determined either by a conjugate-gradient minimization method or from a Hartree-Fock intrinsic state. We illustrate the procedure for six protons and six neutrons in the pf (sdg) shell and exactly reproduce the level energies and electric quadrupole properties of the ground-state rotational band with SDG (SDGI) pairs. The SD-pair approximation without significant renormalization, on the other hand, cannot describe the full SU(3) collectivity. A mapping from Elliott's fermionic SU(3) model to systems with s, d, g,... bosons provides insight into the existence of a decoupled collective subspace in terms of S, D, G,... pairs.},
doi = {10.1103/physrevc.103.l021302},
url = {https://www.osti.gov/biblio/1849463},
journal = {Physical Review. C},
issn = {ISSN 2469-9985},
number = {2},
volume = {103},
place = {United States},
publisher = {American Physical Society (APS)},
year = {2021},
month = {02}}
San Diego State Univ., CA (United States); Texas A & M Univ., Commerce, TX (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Nuclear Physics (NP); National Key Research and Development Program of China; National Natural Science Foundation of China (NSFC); China-U.S. Theory Institute for Physics with Exotic Nuclei (CUSTIPEN)
BEAUTY IN PHYSICS: THEORY AND EXPERIMENT: In honor of Francesco Iachello on the occasion of his 70th birthday, AIP Conference Proceedingshttps://doi.org/10.1063/1.4759411
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 245, Issue 1240, p. 128-145https://doi.org/10.1098/rspa.1958.0072
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 245, Issue 1243, p. 562-581https://doi.org/10.1098/rspa.1958.0101