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2-7: Nuclear Deformation, Summary

[Nuclear Deformation]
In the liquid drop model and the shell model which we have learned so far, nuclei are assumed to be spherical.
However, we have considered that nuclei must be soft and flexible in the liquid drop model, so that they may deviate from a spherical shape. Certainly, some nuclei whose charge distributions are largely deviated from a spherical shape are experimentally found in special regions of mass number. Namely, there exist remarkably deformed nuclei.
J. Rainwater (USA, 1919 - 86) pointed out that the nucleus is able to deform in an ellipsoidal or a spheroidal shape and he investigated the reason of the deformation (1950). Rough sketches of the nuclear spheroidal deformations are shown in the following figure.

If the nucleus is deformed in a ellipsoidal shape, we have to revise the nuclear shell model which is based on a spherical shape. This means that we have to combine the "flexible" liquid drop model with an average potential of a "rigid" shape.
A. Bohr (N. Bohr's son; Denmark, 1922 - ) and B. Mottelson (USA, Denmark, 1926 - ) proposed an advanced model called the Unified Model or the Collective Model in which the ordinary shell model and the liquid drop model are unified. Using this new model, they analysed a lot of experimental data on the so-called nuclear collective phenomena. Their analyses were very much successful. However, the details of them are somewhat hard to explain, so that let us omit here.

[Summary of Part 2]
Let us summarize what we have learned in Part 2.
(1) The existences of about 3000 nuclides have so far been confirmed. Each of them is specified by the proton number Z and the neutron number N.
(2) The size of nuclei or the nuclear radius is roughly given by

The nuclear density is approximately constant. This property is called the saturation of density.
(3) The nuclear binding energy per nucleon is approximately constant (= about 8 MeV). This property is called the saturation of binding energy.
(4) The nuclear structure is considered to be something like a drop of water. This is just the liquid drop model.
(5) Similarly to the case of atoms, the periodic law holds also for atomic nuclei. It can be interpreted by the nuclear shell model.
(6) Some nuclei are deformed to be of spheroidal shape. The new model ((liquid drop model + shell model) called the unified model) is very much successful.
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