The Helion-Triton Model

Another useful model of nuclear structure, called the alpha-particle model or the helion-triton model, is based on the assumption that the nucleons in a nucleus can be considered to be grouped together into helions or tritons, occupying localized 1 j orbitals. For O, for example, the 8 protons and the 8 neutrons could be described as forming four helions, which are arranged at the corners of a tetrahedron. In the shell model the protons and the neutrons would be described as occupying the 1j orbital and the three p orbitals. These four orbitals can be hybridized, as described in Chapter 5, to form four localized tetrahedral orbitals, each of which is concentrated about one of the four corners of a tetrahedron. 

Sequence of energy levels for spin-orbit coupling, y = / + 4 orJ=l — i, for protons and neutrons, as given by the Mayer-Jensen shell model of nuclear structure. 

Nuclei with a larger number of helions and tritons might be expected to have a structure in which one helion or triton is at the center of the nucleus, and the others are arranged in a layer about it. This structure would. 

The sequence of nucleon energy levels (overlapping ranges), with assignment to successive layers (inner core, outer core, mantle) on the basis of the principal quantum number. 

The observed properties of many of the heavier nuclei have been interpreted as showing that the nuclei are not spherical but are permanently deformed. The principal ranges of deformation are from neutron number 90 to 116 and from 140 on. Most of the deformed nuclei are described as prolate ellipsoids of revolution, with major radii 20% to 40% larger than the minor radii. 

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An ellipsoidal nucleus with two spherons in the inner core has major radius greater than the minor radii by the radius of a spheron. about 1.5 f, which is about 25 percent of the mean radius. The amount of deformation given by this model is accordingly in rough agreement with that observed (18). In a detailed treatment it would be necessary to take into account the effect of electrostatic repulsion in causing the helions to tend to occupy the poles of the prolate mantle, with tritons tending to the equator. 

The shell-model diagrams for the magic numbers, with shells and subsubshells assigned to the different layers of the nucleus, are shown in Figure 20-16. The numbers of helions and tritons in these successive layers approximate the numbers for close-packed aggregates of spheres. 

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