# Regularity of atomic nuclei with random interactions: *sd* bosons

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## Abstract

Atomic nuclei are complex systems with gigantic configuration spaces, therefore truncations of model spaces are indispensable. Due to the short-range nature of the nuclear interactions, one may resort to a truncation by using coherent nucleon-pairs which are conveniently further simplified as bosons, such as *sd* bosons. The discovery of the spin-zero ground state dominance with random two-body interactions led to a series of studies on regular structure for *sd* bosons in the presence of random interactions, and this review article summarizes studies along this line in last two decades. We concentrate on various patterns exhibited in *sd* boson systems, and demonstrate that many random samples which were thought to be noisy exhibit very regular patterns, some of which are interpreted in terms of the U(5), O(6), \(\overline {O\left( 6 \right)} \), SU(3), and \(\overline {SU\left( 3 \right)} \) dynamical symmetries of the *sd* interacting boson model.

## Keywords

regularity random interactions*sd*bosons

## Notes

### Acknowledgements

We thank Professor Arima Akito for his collaboration and constant encouragements in studies summarized in this paper, and many other works such as the nucleon-pair approximations, systematics of nuclear masses, and algebraic studies of angular momentum. He is one of the co-authors in most of these papers; without him many of these studies would not likely be performed. We thank the National Natural Science Foundation of China under Grant No. 11675101, Shanghai Key Laboratory (Grant No. 11DZ2260700), and the Program of Shanghai Academic/Technology Research Leader (Grant No. 16XD1401600) for financial support.

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