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4 General Properties of Nuclei - Pg. 98

4 General Properties of Nuclei 4.1 Introduction The basic properties of nucleons were presented in chapters 1, 2, and 3, together with the development of the deuteron theory. Our purpose in this and the following chapters is to study the physics of nuclei with any number A of nucleons, to establish the system- atics of their properties, and to present the theories that aim to explain them. However, the approach we have followed for the deuteron is not applicable here. The Schrödinger equation is already not exactly soluble for a three-nucleon system, and to establish the properties of a heavy nucleus starting from the interaction of all its constituents is not a feasible task. The reasonable approach is the use of idealized models that incorporate part of the physics involved and explain a limited set of experimental data. This chapter presents the general characteristics of nuclei and introduces some basic ideas that will be employed in the elaboration of nuclear models. The detailed presentation of these models will be done in chapter 5. 4.2 Nuclear Radii The radius of protons and neutrons that compose the nucleus is of the order of 1 fm. Suppose that a nucleus has A nucleons distributed inside a sphere of radius R. If the nucleons could be considered as small hard spheres of radius r in contact with each other, we could write A = 4 3 3 R 4 3 3 r or, in another way, R r 0 A 1/3 , = (4.1) where we put r 0 in place of r to take into account that, even in this model of "packed"