Shell-model states

Given the following shell model state, /ci7/2, show qualitatively how it might split as a function of increasing prolate deformation. Label each... 

Shown in Fig 2 is a schematic representation of the shell model states for the region near 1 8Gd. There has been a great deal of interest in this mass region since it was proposed [0GA78] that a shell closure occurs for Z-64. 

The N = 83, 85 and 87 isotones above the neutron-shell closure at N = 82 are described essentially by the f7 shell-model state. Calculations withing the particle-rotor model of Larsson et al. [77], assuming small nuclear deformations of the core, account qualitatively for the measured nuclear moments (cf. Fig. 3). The variation in the spectroscopic quadrupole moments reflects the successive filling of the f j neutron shell. This is realized from the formula [78] ... 

The doubly-odd europium isotopes in the range Eu are well described by the dj proton state coupled to the different neutron-shell model states, discussed above in connection ivith the odd-neution nuclei d in Eu, h Q in Eu and in i4 -i5ogjj gy usjug g-factors of the neighbouring odd-A nuclei and the additivity theorem, tiie magnetic moments of these doubly-odd europium isotopes are weU reproduced. The strongly deformed Eu and Eu are shown to be due to the configurations 3 (p[413 5/2] n[505 11/2]) and 0 (p[413 5 ] n[642 5/2]), respectively. 

Fig. 7 Nilsson diagram for odd protons, including sublevels of the shell model states gy,2, d 2 and The Fermi levels of jl, Cs andgfii, g Fr are shown to be located at the lower parts of the gj,2, dg and h sublevels, respectively. The theoretical results on the spectroscopic quadrupole moments as a function of d ormation are given to the right. The potential parameters used are k=0.066, p = 0575for I and Cs, and k = 0.060, p = 0.630for Bi and Fr.

Furthermore, the spin I = S/2,7/2 and 9/2 states discussed here are built up mainly of sublevels from dj/j, Z n and h, j, respectively. One may therefore conclude that the nuclear structure of mesc we y deformed nuclei are described by relatively pure shell-model states, as evidence also by the measured spins and magnetic moments, and that the variations in occupation of the corresponding sublevels with increasing deformation account for the observed changes in the spectroscopic quadrupole moments. 

Zeh and Mang (1962) have calculated the a-decay probabilities in the Po-Bi region in the vicinity of the double magic ° Pb. The calculations have shown that it is very important to take into account the residual interaction between the valence nucleons. The consideration of the pairing force leads to a substantial increase of the absolute values of the reduced widths (by a factor of 30 or even more), and to a smoothing of the local fluctuations caused by different subshells. The results are sensitive to the shell-model states included in the calculations. The agreement between experimental and theoretical data for the relative values was especially good for even-even nuclei. 

Table 1 Shell model states for each oscillator shell, their occupancies and the resulting shell...

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