Abstract We evaluate the allowed $\beta^-$-decay properties of nuclei with $Z = 8$–$15$ systematically under the framework of the nuclear shell model using the valence space Hamiltonians derived from modern ab initio methods, such as in-medium similarity renormalization group and coupled-cluster theory. For comparison we also show results obtained with fitted interaction derived from chiral effective field theory and phenomenological universal $sd$-shell Hamiltonian version B interaction. We have performed calculations for O $\rightarrow$ F, F $\rightarrow$ Ne, Ne $\rightarrow$ Na, Na $\rightarrow$ Mg, Mg $\rightarrow$ Al, Al $\rightarrow$ Si, Si $\rightarrow$ P, and P $\rightarrow$ S transitions. Theoretical results for $B(GT)$, $\log ft$ values, and half-lives are discussed and compared with the available experimental data.
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Nonempirical Interactions for the Nuclear Shell Model: An Update
The nuclear shell model has perhaps been the most important conceptual and computational paradigm for the understanding of the structure of atomic nuclei. While the shell model has been used predominantly in a phenomenological context, there have been efforts stretching back more than half a century to derive shell model parameters based on a realistic interaction between nucleons. More recently, several ab initio many-body methods—in particular, many-body perturbation theory, the no-core shell model, the in-medium similarity renormalization group, and coupled-cluster theory—have developed the capability to provide effective shell model Hamiltonians. We provide an update on the status of these methods and investigate the connections between them and their potential strengths and weaknesses, with a particular focus on the in-medium similarity renormalization group approach. Three-body forces are demonstrated to be important for understanding the modifications needed in phenomenological treatments. We then review some applications of these methods to comparisons with recent experimental measurements, and conclude with some remaining challenges in ab initio shell model theory.
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- Award ID(s):
- 1713901
- NSF-PAR ID:
- 10179961
- Date Published:
- Journal Name:
- Annual Review of Nuclear and Particle Science
- Volume:
- 69
- Issue:
- 1
- ISSN:
- 0163-8998
- Page Range / eLocation ID:
- 307 to 362
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1146/annurev-nucl-101917-021120
