Nuclear Sizes and Shapes

One can parameterize this distribution by saying that the nuclear radius R can be written as 

A somewhat more sophisticated approach to the problem of defining the nuclear size and density is to assume the nuclear density distribution, p(r), assumes the form of a Fermi distribution, that is, 

the lighter nuclei are mostly skin and the heaviest nuclei still have substantial skin regions. These approximate models for the nuclear size and density distribution compare favorably to the measured distributions for typical nuclei (Fig. 2.11). 

Up to this point, we have assumed that all nuclei are spherical in shape. That is not true. There are regions of large stable nuclear deformation in the chart of nuclides, that is, the rare earths (150 A 180) and the actinides (220 A 260). We shall discuss these cases in more detail later in this chapter when we discuss the electric moments of nuclei. 

Another question we might pose to ourselves is whether the neutron and proton distributions in nuclei are the same Modern models for the nuclear potential predict the nuclear skin region to be neutron-rich. The neutron potential is predicted to extend out to larger radii than the proton potential. Extreme examples of this behavior are the halo nuclei. A halo nucleus is a very n-rich (or p-rich) nucleus (generally with low A) where the outermost nucleons are very weakly bound. The density distribution of these weakly bound outermost nucleons extends beyond the radius expected from the R °c A1 /3 rule. Examples of these nuclei are nBe, nLi, and 19C. The most well-studied case of halo nuclei is 1 Li. Here the two outermost nucleons are so weakly bound (a few hundred keV each) as to make the size of 11 Li equal to the size of a 208Pb nucleus (see Fig. 2.12). 

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Bigeleisen, J. Nuclear size and shape effects in chemical reactions. Isotope chemistry of the heavy elements, J. Am. Chem. Soc., 118, 3676 (1996). 

Stringent limitation to this value is the incomplete knowledge of nuclear size and shape, as will be discussed below. 

Table 7.3 Nuclear size and shape effects on the 1s orbital of...

Nuclear Applications. Powder metallurgy is used in the fabrication of fuel elements as well as control, shielding, moderator, and other components of nuclear-power reactors (63) (see Nuclearreactors). The materials for fuel, moderator, and control parts of a reactor are thermodynamically unstable if heated to melting temperatures. These same materials are stable under P/M process conditions. It is possible, for example, to incorporate uranium or ceramic compounds in a metallic matrix, or to produce parts that are similar in the size and shape desired without effecting drastic changes in either the stmcture or surface conditions. OnlyHttle post-sintering treatment is necessary. 

Uranium and mixed uranium—plutonium nitrides have a potential use as nuclear fuels for lead cooled fast reactors (136—139). Reactors of this type have been proposed for use ia deep-sea research vehicles (136). However, similar to the oxides, ia order for these materials to be useful as fuels, the nitrides must have an appropriate size and shape, ie, spheres. Microspheres of uranium nitrides have been fabricated by internal gelation and carbothermic reduction (140,141). Another use for uranium nitrides is as a catalyst for the cracking of NH at 550°C, which results ia high yields of H2 (142). 

The influence of nuclear substituents on the properties of a homopolymer depends on the nature, size and shape of the substituent, the number of the substituents and the position of entry into the benzene ring. 

W. Brown, R. Johnsen, P. Stilbs, B. Lindman. Size and shape of nonionic amphiphile (Ci2Eg) micelles in dilute aqueous solutions as derived from quasielastic and intensity of light scattering, sedimentation and pulsed-field-gradient nuclear magnetic resonance self-diffusion data. J Phys Chem 87 4548-4553, 1983. 

In a sample of bulk Pt metal, all of the nuclei have the same interaction with the conduction electrons and thus see the same local field. The resulting NMR line is quite narrow. However, in our samples of small Pt particles, many of the nuclei are near a surface where the state of the conduction electron is disturbed. This tends to reduce the Knight shift for these nuclei. Since the Pt particles in our samples are of many different sizes and shapes, this reduction in the Knight shift is not the same for every nuclear spin near a surface. Thus, we obtain a broad "smear" of Knight shifts resulting in the lineshapes of Figure 5. 

Today nuclear weapons are built in many sizes and shapes not available in the 1940s and 1950s, and are de-... 

These are unique to scintillation cameras, known as Auger cameras, used in nuclear medicine studies. Approximately 19-91 PMTs are mounted on a Na(Tl) crystal used in the camera. These crystals are typically-thick. The number of PMTs, which are optically coupled to the back of the crystal, is determined by the size and shape of the crystal. A maximum amount of light will be received by the PMT nearest to the point of interaction compared with the other PMTs, which are positioned differently. The amount of light received in these PMTs is proportional to the solid angle subtended by the PMT. Therefore, X-Y-posi-tioning of the camera has to be controlled and known so that X-Y-coordinate of the y-Ray interaction can be assessed accurately. These data are stored in a computer and then processed or recorded on Polaroid or X-Ray films. 

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