Parity Doublet Levels at Superdeformation

Abstract

Recently many yrare superdeformed bands and subsequently the quantization of alignments¹ are observed in the superdeformed region of A ~ 190 (Hg, Os)² and A ~ 150 (Dy, Tb, Gd)³, but they are not found in the A ~ 130 region (Ce, Nd)⁴. It is our motivation to start this work to find the origin to produce this difference. When we look at the simple Nilsson diagramm^5,6, we find the degeneracy of $\left[ {880} \right]\frac{1}{2}$and $\left[ {761} \right]\frac{1}{2}$ in v shell and $\left[ {770} \right]\frac{1}{2}$and $\left[ {651} \right]\frac{1}{2}$ in π shell around β ~ 0.6 and just over the fermi surface of N = 112 and Z = 80. This kind of degeneracy is always observed among the two levels with asymptotic quantum numbers $\left[ {N\;,\;{n_z}\; = \;N\;,\; \wedge \; = \;0} \right]\frac{1}{2}$and $\left[ {N\; - \;1,{n_z} = N - 2,\; \wedge = 1} \right]\frac{1}{2}$at large deformation. The former level belongs to the unique parity levels with $\Omega = \frac{1}{2}$, and the latter level to the pseudo-spin family as $\left[ {\tilde N - 2,\tilde N - 2.\tilde 0} \right]\tfrac{1}{2}$in the pseudo-spin representation^7,8, which has no pseudo-spin partner. We will name this different parity-pair levels as parity-doublet (P-D) levels from now on. The P-D levels become nearly degenerate around the fermi surface in superdeformed shape for A ~150 and A ~ 190 regions, but not for A ~ 130 region. We propose the idea that these P-D levels are responsible for the quantization of alignment.