Possible Mechanism for the Formation of Yrast Traps at Very High Spins

Abstract

We discuss a possible mechanism, namely the maximization of the overlap of nucleonic wave functions by alignment, for the formation of isomers in the yrast band in the rare nuclei at very high spin states 0 Our results indicate that the possibility of existence of such yrast traps is restricted to a few nuclei with special irregularities in the singleparticle level s e With the advent of heavy-ion accelerators it has been made possible to transfer in a fusion experiment angular momenta as large 1 as ~ 60/z into compound nuclei. This makes feasible the experimental studies of very high-spin states of the nuclei. The information from these experiments, 1,2 however, is restricted to measurements of the continuum y rays 1 and y-ray multiplicities, 2 ' 3 since it is impossible to resolve single y lines above spin ~ 22/L The experimental situation would, therefore, be greatly improved, if an isomeric state at a very high angular momentum (yrast trap) could be found as discussed first by Bohr and Mottelson. 4 The purpose of this note is to suggest more in detail a mechanism for the formation of such yrast traps.The calculations of the deformation energy surfaces performed in the framework of the liquiddrop model 5 using a rigid-body moment of inertia in the rotational energy indicate that up to spin ~80# (rare-earth region) the nucleus is oblate (y = -60°) with the symmetry axis coinciding with the rotation axis. Calculations performed with the inclusion of the shell correction 6,7 and microscopic calculations, 8 however, do not yield such shapes for many nuclei. Even so in this note we want to restrict the quantitative considerations to rotation around the symmetry axis preferred by the liquid-drop model. In such a situation a collective rotation is forbidden out of general quantum-mechanical arguments. Any further increase of the total spin can be obtained only from the individual nucleonic excitations. Once such a stage is reached any irregularities on the yrast line may lead to isomeric states/ A possible mechanism for producing isomeric states is the maximization of overlap of nucleonic wave functions by alignment (MONA) of the single-particle angular momenta outside closed shells. This effect is clearly demonstrated for the 18 + state 9,10 of 212 Po 128 at 2.93 MeV with a half-life of 45 sec. This state is formed by aligning the (7r/z 9^) 2 (vz n/^) 2 configuration outside the doubly closed 208 Pb. Because of the short-range nature of the nucleon-nucleon interaction we have the largest overlap of the nucleonic wave functions for angular momentum J = 0. For intermediate angular momenta the overlap is reduced and increased again for the fully aligned configuration. Moreover, Schiffer 11 and Molinari et al. 12 found that a suitable normalized effective residual interaction depends only on the angle between the angular momenta: The residual interaction is almost symmetric around 90° and is strongly attractive for 0° and 180°. This property of the effective interaction lowers the J= 18 + state in 212 Po below the 16 ...

Review of metastable states in heavy nuclei

“…2.2, the basic case of two identical particles in a single-j shell interacting through a short-range attractive interaction, such as a δ force or a quadrupole-quadrupole force [146], leads naturally to isomers. The 0 + state in which the particle angular momenta are anti-aligned (or more generally, paired) is depressed in energy, and a gradual bunching of levels up to the maximum spin of 2j −1 occurs.…”

“…High-spin isomers are known to dominate the yrast structure of many nuclei in the region near 146 Gd, where spherical shape is stabilised by the N = 82 shell gap combined with the Z = 64 sub-shell closure. The properties of nuclei in this region were reviewed by de Voigt et al [36], but since then many new isomers have been observed in nuclei near N=81-85 and Z=60-71, in parallel with studies in the radon region.…”

Rotation of nuclei around a prolate symmetry axis at very high spin states

“…In general, one can therefore conclude that at the end of the shell the nucleus prefers to rotate around the prolate symmetry axis and at the beginning around an oblate symmetry axis at high spin states. Both results are due to the MONA effect [12]: The increased overlap near the equator due to alignment of the single particle (or hole) angular momenta produces for particles (beginning of shell) a rotation around an oblate symmetry axis while the same effect for holes (at the end of a shell) yields a rotation around a prolate symmetry axis.…”

“…The stabilisation of the rotation around the prolate symmetry axis at the end of the rare earth region up to 2~ seems to be mainly due to the MONA effect [12]: The high angular momentum is formed by alignment of the single hole angular momenta along the rotational axis. Since the holes are concentrated near the equator this favours rotation around a prolate symmetry axis at the end of a shell.…”

“…The calculation has been performed in a few nuclei which have the lowest minimum at the 7 = 120~ fi > 0 line for the angular momenta between 30 h and 50 h. The yrast states have been constructed using the theoretical approach developed in [11]. We shall see that the MONA effect [12] (Maximisation of the Overlap of Nucleonic wave functions by Alignment) plays an important role in favouring the rotation around the oblate symmetry axis at the beginning and around the prolate symmetry axis at the end of a shell at high spin states. The deformation energy surfaces and the trajectories of the lowest energy minimum in the fi-7 plane are presented in Section 2.…”