Search for Transverse Wobbling in $^{135}$Pr

Nuclear wobbling has previously been observed in $^{161,163,165,167}$Lu and in $^{167}$Ta. In these cases the inter-band transitions display the expected $\Delta$I=1, E2 nature, but the wobbling frequency, ($\Delta E=\hbar\omega_{w}I=E(I,\alpha=\frac{1}{2})-(E(I-1,\alpha=-\frac{1}{2}) +E(I+1,\alpha=-\frac{1}{2}))/2 $), decreases with increasing spin. This remains an open theoretical problem as the Hamiltonian suggests increasing frequency with spin. Here the concept of a ``transverse wobbler'' provides an explanation. In this the angular momentum wobbles about the short axis and at a critical frequency this motion becomes unstable and the frequency becomes zero. A previous level scheme of $^{135}$Pr showed two h$_{\frac{11}{2}}$ bands whose properties seemed to exhibit the traits expected of a transverse wobbler. Results from investigations of $^{135}$Pr at both Gammasphere and INGA will be presented.