Proxy-SU(4) symmetry in A = 60–90 region

Abstract

Applications of the proxy-SU(3) model of Bonatsos and collaborators to nuclei in A=60-90 region introduces proxy-SU(4) symmetry. Shell model spaces with single particle (sp) orbits 1p3⁄2, 1p1⁄2, 0f5⁄2 and 0g9⁄2 are essential for these nuclei and also protons and neutrons in this region occupy the same sp orbits. With this and applying the ”proxy scheme”, the 0g9⁄2 changes to 0f7⁄2 giving the SGA U(40)have the proxy-⊃ [U(10)SU⊃ G(3) model. It is easy to see that proxy-⊃ SO(3)] ⊗ [SU(4) ⊃ SUS(2) ⊗ SUT(2)]. With G = SU(3), weSU(3) symmetry implies goodness of the SU(4) symmetry appearing above, i.e. proxy-SU(4) symmetry. Shell model calculations pointing out the need for 0g9⁄2 orbit, ground state masses, shape changes and shape co-existence in A=60-90 region and GT distributions clearly show the importance of proxy-SU(4) in this mass region. Besides presenting this evidence, new proxy schemes with G = SU(5), SO(6) and SO(10) that are generated by good proxy-SU(4) symmetry are described in some detail. An important feature is that the four proxy symmetries SU(3), SO(6), SU(5) and SO(10) appear twice.