Studies of high-spin states in rare-earth nuclei using the angular-momentum projection method: (III). Signature splitting in odd mass nuclei

Abstract

The problem of signature splitting in odd-mass rare-earth nuclei is investigated by using the angular-momentum projection method. According to the present theory, the inversion of signature dependence observed in odd-proton nuclei is due to the crossing between a single-proton band ( h 1 2 ) amd a band consisting of a single-proton state ( h 9 2 ) coupled to a neutron broken pair. In odd-neutron nuclei, in contrast, crossing between a single-neutron band ( i 13 2 ) and a band consisting of 3 single-neutron state ( i 13 2 ) coupled to a proton broken pair occurs at much higher spins, because the proton broken pair ( h 11 2 2 ) is less a aligned compared to that of the neutron ( i 13 2 2 ). This is the reason why two types of odd-mass nuclei show rather different characteristics (e.g. 165Lu and 165Yb). We point out that such a difference would not arise if it originated from the effect of γ-deformation (static) or γ-vibration (dynamical), because there would be no essential difference in the ways the γ degree of freedom affects the (last) odd proton and odd neutron. It is therefore important that a theory has to be tested on both types of nuclei for the sake of consistency. We compare our theory with experiments over a number of odd-mass nuclei. The results are quite satisfactory.