π̃h92⊗ν̃i132bands in doubly odd Tl isotopes including a proton-neutron residual interaction

The level staggering in $\tilde{\pi }{h}_{\frac{9}{2}}\otimes \tilde{\nu }{i}_{\frac{13}{2}}$ two-quasiparticle bands in doubly odd Tl isotopes, for $A\gtrsim 198$, is shown to be related to the signature dependence of the Coriolis interaction even in the presence of a proton-neutron residual interaction obtained from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Bi}$. The study of the neutron number dependence of this system suggests the existence of new isomeric states in very neutron deficient Tl isotopes and also reveals a possible inadequacy of the residual force or of the model itself.