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 orbits 1 p 3/2 , 1 p 1/2 , 0 f 5/2 and 0 g 9/2 are essential for these nuclei and also protons and neutrons in this region occupy the same single particle orbits. With this and applying the ‘proxy scheme’, the 0 g 9/2 changes to 0 f 7/2 giving the spectrum generating algebra U (40) ⊃ U (10) ⊃ G ⊃ SO (3) ⨂ SU ST (4) ⊃ SU S (2) ⨂ SU T (2). With G = SU (3), we have the proxy- SU (3) model. It is easy to see that proxy- SU (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 0 g 9/2 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.