Deformed subshell

Probing superheavy element space by " Ca-induced hot-fusion reactions is characterized by advancing beyond the = 162 deformed subshell closure toward nuclei that are spherical and tightly bound. The macroscopic-microscopic model characterizes the ground-states of nuclei with > 175 as having a prolate deformation parameter 62 < 0.1, making them nearly spherical [8, 58, 60]. At neutron numbers below N — 175, any cross section benefit of the " Ca-induced hot-fusion approach to the Island of Stability is expected to decrease, as the shell stabilization of the ground state of the compound nucleus decreases. If a coldfusion path to a particular superheavy nuclide is available, it is expected to be the better one however, very little experimental evidence of this is available. As an example, the attempt to produce Cn (Z — 112) in the UC Ca,4n) reaction was unsuccessful (cross section limit <0.6 pb) [8, 316], in contrast to its production in the ° Pb( °Zn,n) reaction (cross section 0.5 pb) [263, 271]. 

The trigger for this attempt was the observation of strong variations in the shape of Sg of neutron-rich odd-mass Rb isotopes [KRA81,83,84] which could be related to the spherical N=56 subshell closure and to the sudden onset of strong deformation at the deformed N=60 shell gap (see Fig.l). In... 

A special situation occurs at Zr (Z=40), where the neutron subshell closure (N=56) gives this nucleus a double subshell closure. Thus, particle-hole pair excitations across both subshell gaps are possible. This could produce situations much like those in doubly closed shell 0, in which the lowest-lying intruder deformed band has been shown to arise due to such excitations [BR064]. 

The first excited state of 9 Zr is a 0+ state, as in doubly closed shell 1 0 or closed shell/subshell 9 Zr. Support for the identification of the 0 state in 9 Zr as an intruder deformed state comes from particle transfer... 

It is important to understand what gives rise to the established coexisting intruder band in doubly closed subshell 9(>Zr. The slight predominance of the intruder deformed configuration in the ground state wavefunction of lO Mo shown in Fig. 1(b) cannot explain the tremendous difference between the alpha-pickup strengths to the two 0+ states of 9 >Zr clearly demonstrated by Fig. 1(a). This is not unexpected, since the simultaneous occurrence of proton and neutron subshell closures should produce a marked difference with respect to other nuclei near the middle of the 50 to 82 neutron shell where two-proton, two-hole excitations can account entirely for the observed shape coexistence phenomena. 

The information on nuclear deformation from the IS-data indicates that the steep increase, observed between N = 88 and 90, is restricted to a few elements around gadolinium (Z = 64). The effect becomes less pronounced in the lighter as well as heavier elements. In barium (Z 56) and ytterbium (Z = 70) the step vanishes completely and there is a smooth transition from spherical to strongly deformed shapes above N = 82. This behaviour indicates that the Z = 64 proton subshell closure, with its stbilizing effect for spherical shapes, plays an important role. 

The A=100 region is similar to the A=150 region. The onset of deformation is observed here in Sr, Zr, Mo and Ru isotopes, when the number of neutrons increases beyond N=5R. Also, the Z=40 subshell is eliminated for 11 60. 

We also include for comparison results obtained by KS-LDA calculations [77] for deformed Na v clusters restricted to spheroidal (axial) symmetry (Figure 4.4, top panel). As expected, except for very small clusters (N < 9), these results do not exhibit odd-even oscillations. In addition, significant discrepancies between the calculated and experimental results are evident, particularly pertaining to the amplitude of oscillations at shell and subshell closures. 

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