Nuclear physics

Atoms in nature generally are electrically neutral, as they have equal numbers of protons in the nucleus and orbiting electrons. However, within the nucleus there are other particles called neutrons, which are electrically neutral but have about the same mass as protons. There are two numbers used to characterize a nucleus:

Z, the atomic number, which equals the number of protons;

A, the mass number, which equals the number of nucleons (protons and neutrons).

An element X is defined by the atomic number Z , while A denotes the particular isotope of that element. The usual notation for an element X is AZ X – for example, there are four common isotopes of Carbon: 116 C , 126 C , 136 C , and 146 C , with 126 C being the most abundant ( > 98% ).

It is convenient in some circumstances to measure masses in terms of the unified mass unit, u, which is defined so that 12 C has a mass of 12 u exactly; in SI units,

1 u = 1.66 x 10- 27 kg . (1)

There is also another convenient unit of mass which arises from Einstein’s Special Theory of Relativity. We have not covered this in this course, so we simply quote the relevant (well-known) relation:

E = mc 2, (2)

which associates an energy E to a mass m , with c = 3.0 x 108 m/s being the speed of light. Thus, dimensionally, E/c 2 is a unit of mass. It is customary to express this unit in terms of MeV/c 2, where 1 MeV=10 6

eV= 1.6 x 10- 13 J – note that “c” here is considered part of the unit, and one does not substitute the numerical value of 3.0 x 108 m/s in it. This will be illustrated later in some examples. Through this relation one can find the energy equivalent of 1 u:

E = (1.67 x 10- 27 kg )(3.0 x 108 m/s )2

= 1.50 x 10- 10 J = 9.39 x 108 eV = 939 MeV , (3)

which is then written as

1 u = 939 MeV/c 2.

Nuclear physics deals with the properties of nuclei and how their properties may be understood in terms of the interactions between the constituents Thus the properties of nuclei have their origins in the basic interactions of elementary particles, quarks and gluons, while the macroscopic evolution of the universe is directly related to the interactions between nuclei.

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