Deformable shell

The effects of a rather distinct deformed shell at = 152 were clearly seen as early as 1954 in the alpha-decay energies of isotopes of californium, einsteinium, and fermium. In fact, a number of authors have suggested that the entire transuranium region is stabilized by shell effects with an influence that increases markedly with atomic number. Thus the effects of shell substmcture lead to an increase in spontaneous fission half-Hves of up to about 15 orders of magnitude for the heavy transuranium elements, the heaviest of which would otherwise have half-Hves of the order of those for a compound nucleus (lO " s or less) and not of milliseconds or longer, as found experimentally. This gives hope for the synthesis and identification of several elements beyond the present heaviest (element 109) and suggest that the peninsula of nuclei with measurable half-Hves may extend up to the island of stabiHty at Z = 114 andA = 184. 

In this picture, the excitation of nucleons into shell-model intruder states leads to the coexistence of states with different deformations. Shell-model intruder states for the odd-mass Au isotopes, for example, are presented in fig. 2. Note that the h9 2 and i13y2 intruders drop rapidly as one goes more neutron deficient [ZGA80]. 

A theoretical calculation was carried out to see if all the observed features of the Tl isotopes will emerge from the deformed shell model. First the equilibrium shape of the intrinsic mean field was determined by the... 

Keywords Polyelectrolytes Multilayers Mechanical properties Deformation Shells Capsules... 

The assumption of spherical symmetry is only reasonable for closed-shell systems, to which our discussion will apply. For open-shell systems, departures from sphericity occur due to the Jahn-Teller effect, and can be described by analogy with the deformed-shell model of nuclear physics [687], but lie beyond the scope of the simple theory described here. 

Wetherill GW (1975) diometiic chronology of the early solar system. Ann Rev Nud Sci 25 283 Wilczynski J, Volkov W, Decowski P (1967) Some features of the mechanism of many-neutron-transfer reactions. Sov J Nud Phys 5 672 Yad Fiz 5 942 Wilkins BD, Steinberg EP, Chasman RR (1976) Scission-point model of nuclear fission based on deformed-shell effects. Phys Rev G 14 1832 Wilkinson DH, Wapstra AH, Ulehla I et al (1993) Discovery of the transfermium dements, Report of the Transfermium Working Group of lUPAC and lUPAP II, Introduction to discovery profiles. III, Discovery profiles of the transfermium elements. Pure Appl Chem 65 1757, 1764 Willard JE (1953) Chemical effects of nuclear transformations. Ann Rev Nud Sci 3 193... 

A deformed shell model has been elaborated also with the Saxon-Woods potential (see, e.g., Soloviev 1981). In the advanced versions of the theory, pairing correlations, octupole and hexadecapole deformations, and Coriolis mixing have also been included. 

Taking into account the success of the spherical and deformed shell models, it is tempting to calculate the total energy of nucleus by summation of single-particle proton and neutron energies up to the Fermi level. Then... 

Introducing the conditions at c and // (Fig. 8.2) w here Ih deformed shell is WTpendicular to lh axes, we find that... 

The main focus on shell gaps in the study of superheavy elements has always been the next spherical shell closure for protons and neutrons. However, since the majority of heavy and superheavy nuclei are well deformed, it is also important to understand the effects of deformed shell closures in lighter systems. Here too doubly magic systems can be found, albeit with a different understanding of the magic character. 

Figure 26. Schematic representation of a deformed shell, S, of matrix stress,o. Partial dewetting occurs with a debonding angle...

An interesting extension of the shell model is the deformable shell model or breathing shell model introduced by SCHRODER [4.16]. This model allows for radial deformations of the shells in the course of lattice vibrations which leads to three-body interactions and, correspondingly, the model does not predict the Cauchy relations [4.46]. 

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