Heights of Nuclear Potential Barriers and Nuclear Structure

Abstract

I RECENTLY pointed out in these columns¹ that experimental evidence indicates that the heights of the potential barriers of the light nuclei are proportional to the atomic number. This simple relation can be shown to fit in with Heisenberg's suggestion² that nuclei are composed of protons and neutrons and that there is an attractive force J(r) between neutron and proton at close distances, and between neutron and neutron K(r), the former being the greater. An α-particle contains two neutrons and two protons, a nucleus contains n₁ neutrons and n₂ protons; there will therefore be an attractive force between nuclear neutrons and -particle protons and nuclear protons and -particle neutrons, superposed on the Coulomb repulsion between protons. Thus we have (neglecting the neutron-neutron force K(r), since it is less than J(r)): for the potential at a distance r. I have assumed a law of force of the form to represent J(r). This gives . It happens that for the light elements n₁ is very nearly equal to n₂, never differing by more than one unit. Thus we have approximately, This gives for Vc the maximum when dv/dr = 0 the value If p is constant, that is, if the law of force is the same from element to element, we have that Vc is a straight line function of n₂, which is what is found experimentally.