Isomeric states, shell model

The odd-neutron nuclei close to the N = 82 neutron-shell closure are shown to be well described by available shell-model neutron states. The N = 81 isotones below the shell closure exhibit 1 = 3/2 ground states in the elements up to samarium (Z = 62), where there is a change to I = 1/2 ground states. This behaviour is explained by the lowering of the Sj shell-mo l state with respect to dj with increasing proton number. The 1 = 11/2 isomeric states in the full range are due to h,. The measured moments also support the assignments above. 

Strutinsky developed an extension of the liquid drop model which satisfactorily explains the fission isomers and asymmetric fission. For such short half-lives the barrier must be only 2-3 MeV. Noting the manner in which the shell model levels vary with deformation ( 11.5, the "Nilsson levels"), Strutinsky added shell corrections to the basic liquid-drop model and obtained the "double-well" potential energy curve in Figure 14.14b. In the first well the nucleus is a spheroid with the major axis about 25 % larger than the minor. In the second well, the deformation is much larger, the axis ratio being about 1.8. A nucleus in the second well is metastable (i.e. in isomeric state) as it is unstable to y-decay to the first well or to fission. Fission from the second well is hindered by a 2 - 3 MeV barrier, while from the first well the barrier is 5 - 6 MeV, accounting for the difference in half-lives. 

When the fission isomeric states were discovered (Polikhanov et al. 1962), it became clear that the fission potential should have a second minimum as a function of the deformation and the observed fission isomers are shape isomers in such a second minimum. Strutinsky s proposal (see O Chap. 2 in this Volume) was to combine the virtues of both the LDM and shell models to describe such a second minimum of the fission potential. 

Figure 3 Fraaional population decay curves for a model of three-state molecular isomerization with all trajectories initially distributed uniformly on the constant-energy shell within a single isomer...

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