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03. THE FORMIDABLE THEORY OF BETA RAYS

THE FORMIDABLE THEORY OF BETA RAYS

In December 1933, Fermi formulated his revolutionary theory of beta decay.

The nucleus, made up of only protons and neutrons, undergoes beta decay when a neutron transforms into a proton, simultaneously emitting an electron, called a “beta ray”, and a neutrino, both created during the decay process and previously not existing in the nucleus. Fermi thus introduced a new type of fundamental interaction: the weak interaction. Fermi’s explanation of beta decay constitutes his major contribution to theoretical physics: Both the possibility that a particle changes its identity, and the assertion that, in addition to gravity and electromagnetism, there is a third force, will be central to the development of nuclear physics.

In natural radioactivity, the phenomenon of beta decay consists of a nuclear transition from an initial energy state Ei to a final energy state Ef with the emission of an electron that is detected. Of course, the final nucleus has a charge of Z + 1 compared to that of the initial nucleus Z. The energy of the emitted electron varies continuously up to the maximum possible Ei -Ef. There is a precise probabilistic distribution for the energy of the emitted electron.

 

Understanding the physical modalities of beta emission gives very important information about the structure of nuclei. Until December 1933, this understanding was difficult to attain due to two apparently insurmountable conceptual problems …

These difficulties concern two peculiar problems of beta decay. The electron, which is certainly emitted, must assume a difficult possible location in the nucleus that existed before the beta decay. The emitted electron apparently takes away only part of the available energy, creating a serious problem with the principle of energy conservation.

The electron is emitted but cannot pre-exist in the nucleus.

There are serious difficulties in imagining a mechanism that can allow an electron, which is a light particle, to remain confined within a nucleus that has dimensions on the order of only 10–13 cm. According to Heisenberg’s uncertainty principle, a particle as light as an electron confined to a very small area of ​​space such as a nucleus should acquire a very high energy. Furthermore, it is difficult to imagine a type of force that could produce this confinement.

However, in 1932–1933, the theory of the Heisenberg–Majorana nucleus predicted that the nucleus is made up of only protons and neutrons, held together by special attractive exchange forces, which are opposed by the repulsive Coulomb interactions between protons.

Is energy conserved?

Since the electron emitted in beta decay generally takes only part of the available energy, there is a serious problem with the principle of energy conservation. At the time, the idea was even raised by authoritative scholars, such as Niels Bohr, that energy conservation was valid on average, but not necessarily in a single event. We will see how Fermi managed to brilliantly solve this problem too, adopting the neutrino hypothesis, advanced a few years earlier by Wolfgang Pauli.

To build his theory of beta decay, Fermi developed two ingenious ideas that allowed him to brilliantly overcome all the difficulties offered by the physical understanding of the modalities of beta decay.

First of all, it advanced beyond the scheme of ordinary quantum mechanics and adopted the point of view of quantum field theory, in which particles can be created and destroyed.

It also adopted a hypothesis put forward by Wolfgang Pauli according to which the beta decay actually involves a new hypothetical particle, not yet observed experimentally at the time, which takes care of energy conservation and explains the continuous energy spectrum of the emitted electron.

The electron created at the time of decay

Fermi fully adopted the scheme of the nucleus consisting of only protons and neutrons, developed by Heisenberg and Majorana, and assumed that beta decay occurs through the transformation of a neutron into a proton, with the consequent creation of an electron and a neutrino, to the full satisfaction of the principle of conservation of energy. It is therefore the neutrino, then not experimentally revealed, that takes away the apparent energy lost in the process.

Furthermore, Fermi’s theory is based on precise quantitative bases, and allows to explain how the available energy is divided in probabilistic terms between the electron and the neutrino, providing the energy distribution curve of the observed electron, and also a connection between the maximum energy and the decay period.

Fermi’s theory is based on an effective analogy with the phenomena present in quantum electrodynamics. With his interpretation of beta decay, Fermi discovered a new fundamental force of nature, the weak nuclear force.

It is called weak because, at the characteristic energies of beta decay, which are low for elementary particles, it is much less intense than the strong nuclear force and the electromagnetic force. We know today that this is due to the high value of the mass of the boson which averages the weak interaction, in round numbers equal to 100 times the mass of the proton, while the photon, which is the boson that mediates the electromagnetic interaction, has zero mass.

Already in the 1933 article, Fermi evaluated, by comparison with experimental data, the value of the constant g that characterizes the intensity of the weak interaction and regulates the beta decay, known as the Fermi constant. In the units of measurement used by Fermi in his original article

the constant corresponds to

a very small value.

Under the current Standard Model of elementary particles, weak interactions and electromagnetic interactions are unified in a single electroweak interaction. The value of the universal Fermi constant is now known with great precision (up to seven significant digits).

The neutrino allows the conservation of energy

In order to allow the conservation of energy in beta decay, Wolfgang Pauli in 1930 had introduced the hypothesis that a further very light particle, not experimentally observed, of zero charge, was involved in the decay and took the apparently missing energy.

Fermi adopted this hypothesis, but in a completely new context, in which at the time of decay, both the electron and the neutrino, not pre-existing in the nucleus, are created in accordance with a quantum field theory scheme.

The Pauli neutrino hypothesis would have produced great difficulties if the neutrino had been admitted as a constituent of nuclei, even higher than those resulting from admitting electrons as nuclear constituents.

Instead, in the scheme developed by Fermi, there is no need to understand how the neutrino can be confined to nuclei because this particle is also created at the time of decay, together with the electron.

Fermi’s theory of beta decay shows a marked analogy with electromagnetic emission (and absorption) phenomena, as pointed out by Fermi himself.

In electromagnetic emission, the electronic cloud of the atom undergoes a rearrangement passing from a certain initial energy level to a final one. Electromagnetic energy is emitted in the form of a photon, which certainly does not pre-exist in the atom, but is created at the time of emission, according to the laws of quantum electrodynamics. Of course, the reverse phenomenon of absorption is also possible.

Fermi’s theory, expressed in the language of quantum field theory, is perfectly analogous to electromagnetic emission. At the moment of beta decay, an electron and a neutrino, not existing in the nucleus, are created and emitted by the nucleus. The phenomenon occurs in full compliance with quantum mechanics and relativity. The reverse phenomenon is also possible.

Of course, at the time, only the emitted electron could be observed.

It would take a few decades before we could have experimental confirmation of the existence of the neutrino.

It should be noted that today we know that there are three types of neutrinos associated with the electron and two other similar heavier particles called μ and τ. They are denoted by νe, νμ, and ντ, respectively, and there is an antiparticle for each. Of these, the neutrino introduced by Fermi is the electronic antineutrino. The decay is therefore

The electronic antineutrino can induce the reverse process

through with which it would be revealed in 1956.

Intense sources of antineutrinos are provided by nuclear reactors, wherein fission products undergo beta decay and produce antineutrinos.

Instead, in the course of solar activity and other similar stars, phenomena of nuclear fusion occur, in which four protons, through a chain of nuclear reactions, can fuse, producing an alpha particle (i.e., a nucleus of helium) and releasing energy. The alpha particle is made up of two protons and two neutrons, and therefore in the fusion process two of the protons must lose their charge by transforming into neutrons with the consequent emission of two positrons (e+) and two neutrinos (Ve).

The weak interaction discovered by Fermi therefore explains why the Sun slowly burns hydrogen (whose core is made up of a single proton) without exploding like a bomb.

The detection of “neutrinos” will have to follow other experimental paths, depending on whether they are reactor antineutrinos or solar neutrinos.

Reactor neutrinos

In 1956, Clyde L. Cowan and Frederick Reines were able to detect reactor antineutrinos. Cowan died in 1974, and Reines received the 1995 Nobel Prize for his work on neutrino physics.

The detection method is based on the reaction:

Near a reactor, there is an intense flow of electronic antineutrinos from beta decays in fission processes.

In nuclear fission, it happens that nuclei of heavy material absorb neutrons, dividing themselves so as to each produce two or more lighter nuclei (fission fragments) and other neutrons, and releasing energy. These fragments are unstable because they are rich in neutrons and give rise to a chain of beta decays up to a stable configuration.

In the Cowan and Reines experiment, the antineutrinos coming from the reactor hit a target consisting of 200 l of water, a substance rich in protons, divided into two containers. The detector, consisting of 1,400 l of liquid scintillator, was divided into three containers alternating with the two containers of water.

The scintillator supplies a light signal to the passage of charged particles: In this specific case, it is the electrons present in the scintillator itself that are hit by photons. The detection of the positron and the neutron was given by a pair of signals: one immediate, that due to the two gamma photons produced in the annihilation of the positron with an electron of the medium, and the other delayed, due to the gamma photons emitted in the de-excitation of a nucleus of cadmium (dissolved in water) that captures the neutron.

Solar neutrinos

Solar neutrinos were discovered experimentally by Raymond Davis Jr. in 1967, who was awarded the Nobel Prize in Physics in 2002. The method used is that using radio-chemical chloro-argon, originally proposed by Bruno Pontecorvo in 1946.

Using a large amount of a chlorine compound (perchlorethylene), one tries to observe the following reaction, corresponding to an inverse beta decay:

where a neutrino hitting a nucleus of the isotope 37Cl, corresponding to about 24% of natural chlorine, produces an argon nucleus (37Ar), with the emission of an electron.

The difficulty of the Davis experiment can be realized by thinking that an argon nucleus was peroduced only every two days or so. After a few weeks of exposure, the few nuclei of argon had to be “extracted” from the 380 m3 of perchlorethylene in which they were produced. In fact, argon-37 is one of the few isotopes for which such a separation is achievable.

It is a radioactive beta species, with a half-life of 34 days, which again decays into 37Cl with an electron reaction of the type

where the argon nucleus captures an electron of its own atom from a K orbital level (closer to the nucleus) and transforms into chlorine by re-emitting a neutrino.

Due to the loss of the captured electron K, the electron cloud of the argon atom is rearranged, allowing even the expulsion of an orbital electron (according to a particular process studied and described by the physicist Pierre Victor Auger, the so-called ” Auger issue”). This electron can be conveniently detected by means of proportional counters.