SU(3) Symmetry in Atomic Nuclei

This book provides an understandable review of SU(3) representations, SU(3) WignerRacah algebra and the SU(3) SO(3) integrity basis operators, which are often considered to be difficult and are avoided by most nuclear physicists. Explaining group algebras that apply to specific physical systems and discussing their physical applications, the book is a useful resource for researchers in nuclear physics. At the same time it helps experimentalists to interpret data on rotational nuclei by using SU(3) symmetry that appears in a variety of nuclear models, such as the shell model, pseudo-SU(3) model, proxy-SU(3) model, symplectic Sp(6, R) model, various interacting boson models, various interacting bosonfermion models, and cluster models. In addition to presenting the results from all these models, the book also describes a variety of statistical results that follow from the SU(3) symmetry.

Discusses the technical aspects of SU(3) algebra in an easily understandable form Describes a large number of nuclear models that admit SU(3) Highlights the importance of group theoretical models in nuclei Helps researchers in nuclear physics to interpret data on rotational nuclei using SU(3) symmetry

Auteur
V. K. B. Kota is an honorary faculty member at the Theoretical Physics Division, Physical Research Laboratory, Ahmedabad, India, which he joined in 1980. He completed his Ph.D. in Physics at Andhra University, Visakhapatnam, India. From 2007-2015, he was an Adjunct Professor at the Department of Physics and Astronomy, Laurentian University, Sudbury, Canada.

During his last 40 years of research, he made three major contributions to theoretical physics. Firstly, he identified and developed more than 10 new bosonic, fermionic and boson-fermion Lie algebraic group symmetries for collective states in atomic nuclei. In particular, he worked extensively on hexadecapole degree of freedom in nuclei and published the first review article on this topic with one of his former students. His work on group theoretical models and on nuclear spectroscopy resulted in the book Structure of Medium Mass Nuclei: Deformed Shell Model and Spin-Isospin Interacting Boson Model (CRC Press, 2017),co-authored with Professor R. Sahu. Secondly, he derived several new statistical laws using unitary group decompositions, quantum chaos and random matrices, for the spectral distributions of observables (part of statistical nuclear spectroscopy), with applications in nuclear astrophysics and neutrino physics. This work led to a number of review articles and the book Spectral Distributions in Nuclei and Statistical Spectroscopy (World Scientific, 2010) , co-authored with Prof. R.U. Haq. Thirdly, he introduced and analyzed random matrix ensembles, generically called "embedded random matrix ensembles," generated by random interactions with Lie algebraic symmetries. These were proved to be applicable to isolated finite interacting quantum systems, ranging from complex nuclei to mesoscopic devices of condensed matter to black holes. Dr. Kota wrote the first review article on this topic in 2001 and later a book, Embedded Random Matrix Ensembles in Quantum Physics (Springer, 2014).

Résumé
"The book is an exhaustive and detailed presentation of such a symmetry and its applications in nuclear structure ... . Each chapter ends with rich bibliography. ... The textbook is interesting for Ph.D students and researchers in theoretical nuclear physics particularly who are working with SM and collective models like for example IBM and Bohr-Mottelson Models." (Mustapha Oulne, zbMATH 1476.81002, 2022)

Contenu
Introduction.- SU(3) Algebra in Nuclei: Preliminaries.- SU(3) Wigner-Racah Algebra Details.- SU(3) Wigner-Racah Algebra Details II.- SU(3) SO(3) Integrity Basis Operators.- SU(3) in Shell Model Descriptions of Nuclei.- SU(3) in Interacting Boson Model for Even-Even Nuclei.- SU(3) in Interacting Boson-Fermion Models.- Other Aspects of SU(3) Symmetry in Nuclei.- Multiple SU(3) Algebras in SM and IBM.- Statistical Results with SU(3).- Appendixes.