135Ba - A First Test of the E(5/4) Bose-Fermi Symmetry

Very recently, the first case of a critical point Bose-Fermi symmetry for odd-mass nuclei, E(5/4) was developed. It describes analytically a gamma-soft critical point E(5) core coupled to a j = 3/2 particle, where E(5) represents a second order phase transition from a vibrator U(5) to a gamma-soft rotor O(6). Since 134Ba has been found to be an empirical manifestation of E(5), 135Ba - in which the last neutron can occupy the 2d3/2 orbit, is the natural initial test of E(5/4). To complement this test and provide a perspective, we performed shell model and interacting boson-fermion approximation calculations. We will present the work and discuss the results. We will show that E(5/4) can account for some of the observables in 135Ba but that it does not provide a fully satisfactory description. Specifically, many of the collective and forbidden B(E2) values of E(5/4) agree well with the data.