SU(3) model description of Be isotopes

Abstract

Experimental data on light nuclei close to dripline suggests that as the nucleon number asymmetry increases, the shell structure from stability line is not preserved. In contrast with spherical shell model, Elliott's SU(3) model, uses a deformed multi-nucleon basis to describe nuclear states. The SU(3) symmetry is a strong feature of 1p shell nuclei, where symmetry breaking spin-orbit force is rather weak. We have calculated the binding energies and low-lying energy spectra of Be isotopes (A=6 to A=14), within the framework of Elliott's SU(3) model, with special emphasis on effects due to the presence of intruder orbit 1S 1/2 in the region. The model space includes SU(3) basis states that maximize the quadrupole-quadrupole interaction (−χQ.Q). An extended model space includes, in addition, a set of 2p-2h excitations, with excited nucleons occupying lowest energy SU(3) states in harmonic oscillator shell N=2. Group theoretical methods have been used to classify the states and calculate the nuclear interaction matrix elements. Good angular momentum states are projected out from intrinsic deformed SU(3) states by using standard angular momentum projection techniques. The interaction used contains the monopole-monopole, quadrupole-quadrupole and isospin dependent terms. Interaction parameters are fixed so as to reproduce the binding of 4 nucleons in N=1 orbit for the N=Z isotope-

Time Evolution Operators for Periodic SU(3)

“…For a historical overview of the development of the SU(3) model in nuclear physics, consult [8] for an overview of the development of the nuclear quadrupole interaction model. [10] c. 2004 contains a good reference for physical implementation of SU(3) states, and discussion of the topic from the angle of nuclear quadrupole moments. Much work has been done from the continuous wavefunction perspective using the original results of Elliot (1958Elliot ( -1963 [11], who developed an SU(3) formalism to deal with quadrupole-quadrupole coupling elements in a Hamiltonian schemata.…”

“…Doing so has interesting consequences, as we shall see. In [10], the authors use an expansion of the angular momentum state to model the quadrupole-quadrupole interactions in Be isotopes. It is a good reference for some heavy nuclei calculations that may be compared with experiment.…”

Time Optimal Quantum Control of Spinor States

“…As we shall have some use in passing for SU(3), a descriptor of SU(3) symmetry states and their implementation in beryllium isotopes is contained in [1] where an SU(3) form of quadrupolar-quadrupolar interaction is used to model a set of excitations. This may provide us with a mechanism to move to continuous systems via orthogonal polynomials.…”