Speaker
Description
Despite long-term research, the origin of spin cutoff parameter of angular-momentum distribution in nuclear level density (NLD) remains incompletely elucidated. The lack of spin information in the NLD severely impacts many applications, including nuclear astrophysics, fragment study in nuclear fission, and nuclear data evaluation. To classify the NLD based on total angular momentum J, it was hypothesized that a complex nucleus is analogous to a rigid rotor with effective moment of inertia, possessing 2 J + 1 K quantum numbers to define the orientation of J. Following this line of thought, exploring the relationship between spin cutoff and moment of inertia has been a major research direction; however, the research has achieved limited success.
We find that the existence of the spin cutoff problem can be traced back to Bethe’s initial assumption that nucleons are independent random variables. By constructing a statistical ensemble that enforces rotational invariance through angular-momentum coupling [1], we obtain an analytical expression for the spin cutoff parameter, which includes a previously undiscovered finite population correction (FPC). The FPC term fully incorporates the shell effect, and its correction to the spin distribution varies with the temperature-dependent occupancy of single particles. At the high temperature limit, the degeneracy is much greater than the occupation number, the FPC term can be ignored [2].
Our finding does not change the general Gaussian form provided by Ericson’s formula, but rather explores the physical origin and inevitability of the spin distribution. It shows that even in the absence of interaction, nuclear many-body states exhibit correlations arising from fermionic antisymmetry and angular-momentum coupling. From this perspective, we propose that spin cutoff may be interpreted as a quantitative measure of the geometric correlation imposed by symmetry in nuclear level statistics, to distinguish the dynamic correlation caused by the usual residual interactions [3].
[1] J.-C. Guo and Y. Sun, New angular momentum coupling method based on Wigner rotation theory, Phys. Rev. C 112, 064307 (2025).
[2] J.-C. Guo, A novel method for studying nuclear level density based on fundamental principles of quantum mechanics, Doctoral dissertation, Shanghai Jiaotong University, (2025).
[3] J.-C. Guo and Y. Sun, Symmetry-imposed correlation in nuclear level statistics: The spin distribution, to be published.
| Contribution category | Theory |
|---|---|
| Presenter status | Faculty/Staff |