To analyse the masses even better we use the atomic mass unit (amu), which is 1/12th of the mass of the neutral carbon atom,
(4.1) |
This can easily be converted to SI units by some chemistry. One mole of C weighs , and contains Avogadro’s number particles, thus
(4.2) |
The quantity of most interest in understanding the mass is the binding energy, defined for a neutral atom as the difference between the mass of a nucleus and the mass of its constituents,
(4.3) |
With this choice a system is bound when , when the mass of the nucleus is lower than the mass of its constituents. Let us first look at this quantity per nucleon as a function of , see Fig. 4.1
This seems to show that to a reasonable degree of approximation the mass is a function of alone, and furthermore, that it approaches a constant. This is called nuclear saturation. This agrees with experiment, which suggests that the radius of a nucleus scales with the 1/3rd power of ,
(4.4) |
This is consistent with the saturation hypothesis made by Gamov in the 30’s:
As increases the volume per nucleon remains constant.
For a spherical nucleus of radius we get the condition
(4.5) |
or
(4.6) |
From which we conclude that
(4.7) |