Among the astonishing facts about the nuclear realm that make possible the world in which we live is the stabilization of the neutron. If a neutron were not stabilized in the presence of one or more protons, the world would have not 92 elements occurring naturally but just one, hydrogen. A neutron alone undergoes the beta decay process, transforming to proton, electron, and antineutrino after an average time of 15 minutes. Joined to a proton, it can acquire an infinite lifetime, making possible the building of all the elements heavier than hydrogen.
What stabilizes the neutron is a rather peculiar “chance,” that the force between a neutron and a proton happens to be just a little bit stronger than the same force acting between two protons (or between two neutrons). The nucleus of deuterium, or heavy hydrogen, consists of one proton and one neutron. The mass of this combination (the deuteron) is not simply the mass of a proton plus the mass of a neutron, but somewhat less than this sum. Here are the figures, expressed in atomic mass units1 (the subscripts p, n, and d refer to the proton, neutron, and deuteron):
| mp = 1.00728 amu |
| mn = 1.00866 amu |
| ___________________ |
| mp + mn = 2.01594 amu |
| md = 2.01355 amu |
The attractive force that pulled neutron and proton together has released energy, and this lost energy, the binding energy, is reflected in a decreased mass of the deuteron. The mass decrease of 0.00239 amu is equivalent to about 2.2 MeV. The neutron in the deuteron has a natural “inclination” to undergo beta decay. This is normally a “downhill” process, for the neutron transforms to a lighter combination of proton, electron, and antineutrino.2 As the following numbers make clear, the free neutron is “barely” unstable.
| Before | After |
| mn = 1.00866 amu | mp = 1.00728 amu |
| me = 0.00055 amu | |
| mν ≅ 0 | |
| ____________________ | |
| mtotal = 1.00783 amu | |
| —— Allowed Decay ——→ | |
If the deuteron’s neutron decides to follow its inclination for beta decay, the deuteron becomes suddenly a pair of protons (plus an electron and antineutrino). But the nuclear force attracts these protons somewhat less strongly than it attracts a neutron-proton pair; in fact, the force is not quite strong enough to bind the proton pair together. In this hypothetical beta decay process, therefore, the deuteron would transform itself into a pair of free protons. The masses before and after compare as follows:
| Before | After |
| md = 2.01355 amu | mp = 1.00728 amu |
| mp = 1.00728 amu | |
| me = 0.00055 amu | |
| mν ≅ 0 | |
| mtotal = 2.01511 amu | |
| —— Forbidden Decay ——→ | |
The gain in going from heavier neutron to lighter proton is more than offset by the loss of binding energy. The law of energy conservation therefore prevents the neutron within the deuteron from decaying. The neutron is stabilized by the energy binding it to the proton. (In heavier stable nuclei, the neutron beta decay would merely reduce, not eliminate, the binding energy.) This is all a very delicate balance, the stabilization of the neutron amounting to less than one part in a thousand of the neutron mass. Yet we have reason to be grateful for this rather strange combination of circumstances—that the neutron happens to be only slightly heavier than the proton and that the nuclear force between a neutron and proton happens to be a little stronger than between two protons. Viewed in terms of our present knowledge of fundamental-particle interactions, it is a remarkable miracle that nature has some 90 atomic building blocks available instead of just one.
1 One atomic mass unit (amu) is defined as one twelfth of the mass of an atom of carbon 12 (its nucleus plus its six electrons). The energy equivalent of 1 amu is 931 MeV.
2 The mass of the antineutrino emitted in beta decay is not known, but is very likely less than 0.0000001 amu, or effectively zero on the scale considered here.