Abstract
In this chapter, first introduced is SU(3) in an oscillator shell and then presented are various basic results of SU(3) algebra along with some preliminary applications to shell model (SM) and interacting boson model (IBM). Although the physics of SU(3) in nuclei is different from the one in particle physics, the algebraic results of SU(3) apply to both. In emphasizing this, in the end presented are the quantum numbers for elementary particles using some simple results derived for SU(3) in nuclei.
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References
J.P. Elliott, Collective motion in the nuclear shell model I. Classification schemes for states of mixed configurations. Proc. R. Soc. (Lond.) A 245, 128–145 (1958)
B.G. Wybourne, Symmetry Principles and Atomic Spectroscopy (Wiley, New York, 1970)
M. Hamermesh, Group Theory and Its Applications to Physical Problems (Addison-Wesley, Reading, 1964)
D.E. Littlewood, The Theory of Group Characters and Matrix Representations of Groups, 2nd edn. (AMS Chelsea Publishing, AMS, Providence, 2006)
B.G. Wybourne, Classical Groups for Physicists (Wiley, New York, 1974)
F. Iachello, Lie Algebras and Applications, 2nd edn. (Springer, Heidelberg, 2015)
V.K.B. Kota, Single particle SU(3) parentage coefficients. Pramana-J. Phys. 9, 129–140 (1977)
M. Vyas, V.K.B. Kota, Spectral properties of embedded Gaussian unitary ensemble of random matrices with Wigner’s \(SU(4)\) symmetry. Ann. Phys. (N.Y.) 325, 2451–2485 (2010)
P. Van Isacker, D.D. Warner, D.S. Brenner, Wigner’s spin-isospin symmetry from double binding energy differences. Phys. Rev. Lett. 74, 4607–4610 (1995)
V.K.B. Kota, R. Sahu, Structure of Medium Mass Nuclei: Deformed Shell Model and Spin-Isospin Interacting Boson Model (CRC Press, Taylor & Francis Group, Boca Raton, 2017)
J.P. Draayer, G. Rosensteel, \(U(3) \rightarrow R(3)\) integrity-basis spectroscopy. Nucl. Phys. A 439, 61–85 (1985)
K.T. Hecht, Collective models, in Selected Topics in Nuclear Spectroscopy, ed. by B.J. Verhaar (North Holland, Amsterdam, 1964), pp. 51–105
J.P. Elliott, Collective motion in the nuclear shell model II. The introduction of intrinsic wave-functions. Proc. R. Soc. (Lond.) A 245, 562–581 (1958)
K.T. Hecht, \(SU_3\) recoupling and fractional parentage in the \(2s-1d\) shell. Nucl. Phys. 62, 1–36 (1965)
E.P. Wigner, On the consequences of the symmetry of the nuclear Hamiltonian on the spectroscopy of nuclei. Phys. Rev. 51, 106–119 (1937)
J.C. Parikh, Group Symmetries in Nuclear Structure (Plenum, New York, 1978)
M. Harvey, The nuclear \(SU(3)\) model. Adv. Nucl. Phys. 1, 67–182 (1968)
Y. Akiyama, A. Arima, T. Sebe, The structure of the sd shell nuclei: (IV). \(^{20}\)Ne, \(^{21}\)Ne, \(^{22}\)Ne, \(^{22}\)Na and \(^{24}\)Mg. Nucl. Phys. A 138, 273–304 (1969)
V.K.B. Kota, R.U. Haq, Spectral Distributions in Nuclei and Statistical Spectroscopy (World Scientific, Singapore, 2010)
M. Chakraborty, V.K.B. Kota, J.C. Parikh, Unitary decomposition of Hamiltonian operators: SU(4) irreducible tensors, norms and their energy variation and symmetry breaking. Ann. Phys. (N.Y.) 127, 413–435 (1980)
P. Vogel, W.E. Ormand, Spin-isospin SU(4) symmetry in sd- and fp-shell nuclei. Phys. Rev. C 47, 623–628 (1993)
G. Rosensteel, J.P. Draayer, K.J. Weeks, Sympletic shell-model calculations for \(^{24}\)Mg. Nucl. Phys. A 419, 1–12 (1984)
D. Branford, A.C. McGough, I.F. Wright, Lifetime and branching measurements on the \(K^\pi = 0^+\) and \(K^\pi = 2^+\)\(^{24}\)Mg rotational levels. Nucl. Phys. A 241, 349–364 (1975)
F. Iachello, A. Arima, The Interacting Boson Model (Cambridge University Press, Cambridge, 1987)
A. Arima, F. Iachello, Interacting boson model of collective nuclear states II: the rotational limit. Ann. Phys. (N.Y.) 111, 201–238 (1978)
O. Scholten, The Program Package PHINT Manual Book (National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, 1982)
R.J. Casperson, Interacting boson model calculations for large system sizes. Comput. Phys. Commun. 183, 1029–1035 (2012)
R.F. Casten, D.D. Warner, The interacting boson approximation. Rev. Mod. Phys. 60, 389–469 (1988)
F. Iachello, I. Talmi, Shell-model foundations of the interacting boson model. Rev. Mod. Phys. 59, 339–362 (1987)
D. Griffiths, Introduction to Elementary Particles, 2nd edn. (Wiley-VCH, Weinheim, 2008)
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Kota, V.K.B. (2020). SU(3) Algebra in Nuclei: Preliminaries. In: SU(3) Symmetry in Atomic Nuclei. Springer, Singapore. https://doi.org/10.1007/978-981-15-3603-8_2
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DOI: https://doi.org/10.1007/978-981-15-3603-8_2
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