Shell model structure of proxy-SU(3) pairs of orbitals
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Shell model structure of proxy-SU(3) pairs of orbitals Dennis Bonatsos1,a
, Hadi Sobhani2 , Hassan Hassanabadi2
1 Institute of Nuclear and Particle Physics, National Centre for Scientific Research “Demokritos”, 15310
Aghia Paraskevi, Attiki, Greece
2 Faculty of Physics, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran
Received: 1 July 2020 / Accepted: 3 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The Nilsson orbitals used in the substitutions occurring in the proxy-SU(3) scheme, which are the orbitals bearing the maximum value of total angular momentum in each shell, have an extremely simple structure in the shell model basis |Nl j, with each Nilsson orbital corresponding to a single-shell model eigenvector. This simple structure is valid at all deformations for these orbitals, while in other orbitals it is valid only at small deformations. Nilsson 0[110] pairs are found to correspond to |1110 pairs in the spherical shell model basis, paving the way for using the proxy-SU(3) approximation within the shell model.
1 Introduction SU(3) symmetry has been playing an important role in nuclear physics for a long time [1]. After its discovery by Elliott [2–4] in the nuclear sd shell, it has been used in the framework of several algebraic models using bosons, like the Interacting Boson Model [5–7] and the Vector Boson Model [8–10], or fermions, like the symplectic model [11,12] and the Fermion Dynamic Symmetry Model [13]. Furthermore, approximate SU(3) symmetries have been introduced in heavier shells, including the pseudo-SU(3) [14,15], quasi-SU(3) [16,17], and proxy-SU(3) [18,19] schemes. SU(3) techniques are also used within large-scale no-core shell model calculations [20,21] in order to reduce their size. In the present work, we are going to focus attention on the recently introduced proxySU(3) scheme [18], which has provided successful parameter-free predictions [19] for the collective variables β and γ , expressing the deviation of atomic nuclei from the spherical shape and from axial symmetry, respectively [22]. In addition, proxy-SU(3) has provided [19,23] a solution to the long-standing puzzle [24] of the dominance of prolate over oblate shapes in the ground state bands of even–even nuclei, as well as a prediction for the prolate to oblate shape phase transition in the heavy rare earths, in agreement to experimental evidence [25]. Shell-like quarteting in heavy nuclei [26] has also been considered recently within the proxy-SU(3) approach. Nuclear shells are known to be derived in the nuclear shell model [27,28] from threedimensional harmonic oscillator (3D-HO) shells bearing U(N) symmetries possessing SU(3) subalgebras [29–32]. These symmetries are broken beyond the sd shell by the strong spin– orbit interaction, which influences maximally within each shell the orbitals bearing the highest
a e-mail: [email protected] (corresponding author)
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