Speakers
Description
In a number of works, starting with [1], the term $k\hat{I}\hat{I}/(1+f\hat{I}\hat{I})$ was introduced into the IBM boson Hamiltonian to describe the compression of the energies of collective states, where $\hat{I}$ is the angular momentum operator. Using this additional term, collective states of the bands were considered, including in $^{164}$Er. In this nucleus, the states of the collective band are the states of the yrast band up to the spin $14^+_1$, and for large spins these will be the following excitations, namely $18^+_2$ , $20^+_2$, $22^+_2$. States $16^+_1$ and $16^+_2$ must be strongly mixed both with each other and experience strong fusion of other states containing quasiparticle pairs. The introduction of an additional term into the Hamiltonian is motivated by the experimental fact of compression of the spectrum of states with increasing spin. However, this also occurs due to the growth of the influence of non-collective states on collective states with increasing spin, ultimately leading to the bands crossing. For $^{164}$Er, the longest yrast band of all even Er isotopes is observed. The effective (kinematic) moment of inertia for it, as can be seen from the figure before the spin of the $14^+_1$, gives a practically linear dependence on the square of the rotation frequency. Then, from spin $18^+_1$, there is a smooth decrease in the moment of inertia down to the state with spin $36^+_1$. We analyzed this situation through the dual use of IBM. Namely, the parameters of the IBM Hamiltonian with the maximum number of bosons $\Omega=14$ were determined from the energies of the $2^+_1$, $4^+_1$, $6^+_1$, $8^+_1$, $10^+_1$, $12^+_1$, $14^+_1$, $18^+_2$, $20^+_2$, $22^+_2$, states. It was further assumed that a quasiparticle strip is constructed from the very beginning on a two-quasiparticle state with spin $J_q=10^+$ and energy $E_q$. The energies of this band are determined by the energies of states with spins from $18^+_1$ to $36^+_1$, and for IBM, minus $J_q=10^+$, these states have spins from $8^+_1$, to $26^+_1$ at $\Omega=13$. The quasiparticle energy $E_q=2.7$ MeV was determined in such a way that the energy match was the best. The results of the calculations, displayed through the moments of inertia, are given in the figure and, as we can see, are quite consistent with the experimental data, including the decrease in the moments of inertia after the state with spin $18^+_1$. The reason for this lies in the spin dependence of the moment of inertia. Thus, here we have the longest band of collective states that appears after the bands crossing. Moreover, the energies of the states of the strip formed after the crossing of the stripes are extremely close to the $SU$(3) IBM limit. This is manifested in the fact that the ratio of the energies of the band states to the energies of the purely rotational band are respectively equal to 1, 0.993, 0.985, 0.974, 0.96, 0.945, 0.928, 0.91, 0.891, 0.87, 0.85, 0.829, 0.806 for spins from $2^+_1$ to $26^+_1$.
- N. Yoshida et al., Physics Letters B 256, 129 (1991)
