The Role of the Pauli Exclusion Principle in Nuclear Physics Models
Abstract
:1. Introduction
2. Nuclear Cluster Physics and Algebraic Models
2.1. The Nuclear Vibron Model
2.2. The Semimicroscopic Algebraic Cluster Model
2.3. The Algebraic Cluster Model
2.4. Applications to Multi- Cluster Systems
2.4.1. C
- Each -cluster is assumed to be in a (0,0) irrep of the shell model.
- Between the first two ’s the Wildermuth condition requires a minimal number of four oscillation quanta. (Be has 4 oscillation quanta within the shell model and each contributes zero, thus, 4 oscillation quanta have to be in the relative motion). The same is the case for the relative motion of the third particle with respect to the first two. C has 8 oscillation quanta and the 2- subsystem already 4, thus, 4 more oscillation quanta have to be added in the relative motion of the second Jacobi-coordinate.
- The symmetric states of the three -system is obtained using the procedure as exposes in [30].
- The obtained list of possible irreps is compared to the shell model space (programs are available for that), resulting in the final model space.
- At low energy there is only one state in the SACM, while in the ACM there are 2, a consequence of ignoring the PEP.
- The spectrum in the ACM is denser at low energy than in the SACM. For example, several predicted parity doublets vanish when the PEP is taken into account.
- Within the ACM, the maximal number of bosons was used as a parameter, which is not allowed. The number N is a cut-off and convergence should be checked with increasing N. This is also a problem in the SACM: we used finite N, otherwise the space becomes too large. One conforms with a renormalization of the parameters when N increases.
2.4.2. O
3. Algebraic Models in Nuclear Structure Physics
The Interacting Boson Model
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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0 | (0,4) |
1 | (3,3) |
2 | (2,4), (6,2) |
3 | (3,4), (5,3), (9,1) |
4 | (0,6), (4,4), (6,3), (8,2), (12,0) |
5 | (3,5), (5,4), (7,3), (9,2), (11,1) |
6 | (2,6), (6,4), (8,3), (10,2), (12,1), (14,0) |
EXP.[WU] | [WU] | SACM [WU] | ACM | |
---|---|---|---|---|
4.65 | 5.37 | 5.15 | ||
0.0 | 7.73 | 0.8 | ||
6.32 | 24.28 | 5.14 |
Kato | SACM | |
---|---|---|
0 | ||
1 | ||
2 | ||
3 | ||
4 | ||
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Berriel-Aguayo, J.R.M.; Hess, P.O. The Role of the Pauli Exclusion Principle in Nuclear Physics Models. Symmetry 2020, 12, 738. https://doi.org/10.3390/sym12050738
Berriel-Aguayo JRM, Hess PO. The Role of the Pauli Exclusion Principle in Nuclear Physics Models. Symmetry. 2020; 12(5):738. https://doi.org/10.3390/sym12050738
Chicago/Turabian StyleBerriel-Aguayo, Josué R. M., and Peter O. Hess. 2020. "The Role of the Pauli Exclusion Principle in Nuclear Physics Models" Symmetry 12, no. 5: 738. https://doi.org/10.3390/sym12050738