Shell effects in strong Coulomb fields

Recent experimental discoveries and searches for new superheavy elements, see recent reviews in Refs. [115,116], have triggered a substantial increase in the theoretical efforts to describe the structure and production of such systems, see recent Refs. [117,118,119,120,121,122] and [123,124,125,126,127], respectively. Although many nuclides in the uncharted region of Z>112-114 are predicted to have substantial barriers against fission, they can be experimentally produced only with extremely low cross-sections. Stability and existence of superheavy nuclei are entirely due to the shell effects, and hence a delicate balance between extremely strong Coulomb field and nuclear mean-field potential must be self-consistently taken into account [128].

  

Figure 9: Shell corrections calculated from spherical self-consistent single-particle spectra for even-even nuclei around Z=120 and N=180. (From Ref. [121]. Reprinted from Physics Letters B, Vol 515, 2001, Page 42, M. Bender et al, ``Shell stabilization of super- and hyperheavy nuclei without magic gaps'', Copyright (2001), with permission from Elsevier Science.)

Due to the large numbers of protons and neutrons, densities of single-particle states in superheavy and hyperheavy nuclei are much larger than those in usual stable nuclei [121]. Hence, the magic shell gaps are significantly smaller, and the corresponding shell corrections shown in Fig. 9 are not-so-well localized around the doubly-magic nuclei. This observation [121] decreases the importance of predicting which is the next proton magic number after Z=82 [119]. Indeed, we may expect a fairly wide island of superheavy nuclei with tangible life times, and not a single or several long-living superheavy nuclides. However, precise estimates of life times require a better determination of nuclear effective forces and reaction mechanisms, when they are used for extrapolations to very exotic systems.