First test of the E(5/4) Bose-Fermi symmetry: The structure of Ba-135

The first case of a Bose-Fermi critical point symmetry, E(5/4), representing the coupling of a $j=3/2$ fermion to an E(5) core, was recently proposed. Since $^{134}\mathrm{Ba}$ has been found to be an empirical manifestation of E(5), we carried out a \ensuremath{\beta}-decay experiment to study levels in $^{135}\mathrm{Ba}$, where the last neutron can occupy the $2{d}_{3/2}$ orbit, as the first test of E(5/4). The comparison shows significant areas of agreement as well as significant discrepancies. Comparison of interacting boson-fermion approximation and shell model calculations with the data are also presented.