The oscillating behaviour of backbending

Abstract

The anomaly of the moment of inertia usually called backbending varies in its strength regularly as a function of the neutron number for the rare earth nuclei. This oscillating behaviour of backbendina due to the rotational alignment of two i_13/2 neutrons is explained in a particle number and angular momentum conserving model. The neutrons in the i_13/2-shell are described by shell model wave functions and are weakly coupled to the rotation of the core. It is shown that the alignment is arranged by the nucleus by scattering two i_13/2 neutrons mainly from the $\Omega = \frac{1}{2}$ and $\Omega = \frac{3}{2}$ i_13/2 orbits into the core. The aligned band has therefore in average two neutrons less in the i_13/2-shell Interaction between the valence nucleon and the core is due to the pairing force. It is shown that this interaction has $j - \frac{3}{2}$ zeros. No interaction between the ground band and the aligned band means strong backbending while a strong interaction means no backbendina. In the second part of this talk we explain the behaviour of the second anomaly of the moment of inertia by the alignment of two h_11/2 protons corresponding to the same oscillating behaviour as discussed before. In this way we can explain that for the N=90 isotones ⁶⁶₁₅₆ Dy shows no backbending, ⁶⁸₁₅₈ Er shows upbending and ⁷⁰₁₇₀ Yb shows a strong second anomaly of the moment of inertia.

Part of Lectures given at the Chinese Winter School on Nuclear Physics in Peking, China, December 22, 1980 – January 9, 1981.