## The Fundamental Forces of Nature and the Weak Force

Of the four fundamental forces (gravity, electromagnetism, strong nuclear force and weak nuclear force), the weak force is the most enigmatic. Whereas the other three forces act through attraction/repulsion mechanisms, the weak force is responsible for transmutations, i.e. changing one element into another, and incremental shifts between mass and energy at the nuclear level.

Most systems in nature tend to seek the lowest-energy state available to them because a lowest-energy state is more stable than a higher-energy state. This is called the principle of minimum energy. I.e., a restatement of the second law of thermodynamics for a closed system with fixed entropy: for a closed system with fixed entropy, the total energy is minimized at equilibrium.

The following diagram shows the nuclear binding energy for various atomic nuclei. Nuclear binding energy is the energy required to split a nucleus of an atom into its component parts. The component parts are neutrons and protons, which are collectively called nucleons. On the horizontal scale, we have the atomic mass or the total number of protons and neutrons (also called nucleons) inside the nucleus of an atom. On the vertical scale, we have the binding energy , increasing binding energy goes from top to bottom instead of the usual case because we want to show that in Nature, at fixed entropy, the total energy tries to find a minimum. The minimum is here the highest binding energy (it means that the higher the binding energy is, the higher is the energy required to inject into the atom’s nuclei to separate its nucleus into its constituents). Iron/Fe 56 is close to a maximum of binding energy and thus, for nuclei heavier than iron (going to the right side of the diagram), the trend reverses. The reason for that is the growing positive charge of the nuclei (i.e. the increasing number of protons). The electric force is less powerful than the nuclear force, but its range is greater: in an iron nucleus (with 26 protons), each proton repels the other 25 protons, while the nuclear force only binds close neighbors. So the isotope Iron/Fe 56 is one of the most efficiently bound nucleus, meaning that it has the lowest average mass/energy per nucleon.

To summarize, The net binding energy of a nucleus is that of the nuclear attraction or strong force between nucleons, minus the disruptive energy of the electric force. As nuclei get heavier than helium (He 4), their net binding energy per nucleon (deduced from the difference in mass between the nucleus and the sum of masses of component nucleons) grows more and more slowly, reaching its peak at iron/Fe 56. As nucleons are added, the total nuclear binding energy always increases, but the total disruptive energy of electric forces (positive protons repelling other protons) also increases, and past iron, the second increase outweighs the first.

But, what does that have to do with the weak force?

Simply put, the weak force is the way Nature seeks stability. Stability at the nuclear level permits elements to form, which make up all of the familiar stuff of our world. Without the stabilizing action of the weak force, the material world, including our physical bodies, would not exist. The weak force is responsible for the radioactive decay of heavy (radioactive) elements into their lighter, more stable forms (nuclear fission). But the weak force is also at work in the formation of the lightest of elements, hydrogen and helium, and all the elements in between (nuclear fusion).

To reduce the disruptive energy of the electric force, the weak interaction allows the number of neutrons to exceed that of protons, for instance, the main isotope of iron/Fe 56 has 26 protons and 30 neutrons. Isotopes also exist where the number of neutrons differs from the most stable number for that number of nucleons. If the ratio of protons to neutrons is too far from stability, nucleons may spontaneously change from proton to neutron, or neutron to proton. The two methods for this conversion are mediated by the weak force and are also called respectively negative beta decay (n into p) and positive beta decay (p into n).

The weak force, like the strong force, has a short range, but is much weaker than the strong force. The weak force tries to make the number of neutrons and protons into the most energetically stable configuration. For nuclei containing less than 40 particles (atomic mass/nb of nucleons under 40), these numbers are usually about equal, and the number of protons and neutrons in the nucleus are closely related. However, as the number of particles increases toward a maximum of about 209, the number of neutrons to maintain stability begins to outstrip the number of protons, until the ratio of neutrons to protons is about three to two.

A another way to understand the weak force is in comparison with the actions of the other forces at work in the center of the Sun. Our Sun, although extraordinarily hot (10 million degrees inside the core), is cool enough for the constituent parts of matter, quarks, to clump together to form protons. A proton is necessary to form an element, which occurs when it attracts an electron, i.e. the simplest case being hydrogen, which is composed of a single proton and a single electron. By the force of gravity, protons are pulled together until two of them touch, but because of the electrostatic repulsion of their two positive charges, their total energy becomes unstable and one of the protons undergoes a form of radioactive decay, turning it into a neutron and emitting a positron (the antiparticle of an electron) and a neutrino. This action forms a deuteron (nucleus of deuteron with one proton and one neutron), which is more stable than the two repelling protons. This transmutation of proton into neutron plus beta particles is a beta+ decay. As already discussed previously, beta decay occurs when, in a nucleus with too many protons or too many neutrons, one of the protons or neutrons is transformed into the other. Beta decay of protons into neutrons and more specifically, the low rate for this process, (meaning that it does not occur very often) guarantees a long life for stars like our Sun.

It is important to stress that a free proton(*) or a hydrogen atom(*) (bound with an electron and with no neutrons) or a hydrogen nucleus(*) without an electron or neutrons, does not beta decay. From the conservation of energy and momentum, a decay is only possible if the sum of the masses of the particles to which the initial object decays is less than the mass of the original object, and therefore, there is nothing these (*) can decay into. Another explanation for this is: the proton mass is not roughly equal to the sum of the masses of the objects that the proton contains, there is no way to break the proton into pieces and to get the proton to do anything interesting requires energies equal at least to the mass-energy of the proton itself! Molecules, atoms and nuclei are comparatively simple, the proton and the neutron are extremely complex.

NOTES:
(1) There are other types of decay, not all types involve the weak force. The weak force is responsible for beta decay, BUT the strong force together with the electromagnetic force for alpha decay (heavy radioactive elements decaying by producing alpha particles), and the electromagnetic force for gamma decay (producing gamma rays)

(2) Among the heaviest nuclei, starting with tellurium nuclei (element 52) containing 106 or more nucleons, electric forces may be so destabilizing that entire chunks of the nucleus may be ejected, usually as alpha particles, which consist of two protons and two neutrons (alpha particles are fast helium nuclei). (Beryllium-8 also decays, very quickly, into two alpha particles.) Alpha particles are extremely stable. This type of decay becomes more and more probable as elements rise in atomic weight past 106. (This is also called alpha decay)

(3) beta+ decay cannot occur in an isolated proton because it requires energy due to the mass of the neutron being greater than the mass of the proton. beta+ decay can only happen inside nuclei when the daughter nucleus has a greater binding energy (and therefore a lower total energy) than the mother nucleus. The difference between these energies goes into the reaction of converting a proton into a neutron, a positron and a neutrino and into the kinetic energy of these particles

(4) A free neutron is unstable and will decay with a half-life of 10.5 minutes

(5) A very good reference that explains things hidden between the lines of many nuclear physics textbooks: http://profmattstrassler.com/