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Beta decay

A new force of nature

 In the years immedialy after the discovery of radiation Rutherford noticed that the radiation emitted was of at least two distinct types: one, easily absorbed by matter. He called alpha radiation and another, much more penetrating, he called beta radiation. To these was soon added a third type, even more penetrating, called gamma radiation. These three types of radiation were later indentified respectively with “helium nuclei” (alpha rays), “electrons” (beta rays) and “X-ray type high frequency electromagnetic radiation” (gamma rays). Given their diverse nature, their behavior in magnetic fields was alaso different: alpha and beta rays deviate in opposite directions and with different curvatures (much more accentuated in the case of beta rays), while gamma rays don’t deviate.

Hence the suggestive design representing radioactivity used by Marie Curie in her 1903 doctoral thesis, draawing a vase of flowers (Radium) out of which sprout three branches, one straight and two bent in different directions. The discovery of the processes occurring inside the nucleus that give rise to these emissions (later called respectively alpha decay, beta decay and gamma decay) required much research.  A brilliant theoretical explanation was found for alpha decay but for beta decay, one of the main theoretical difficulties was how to justify the fact that the emitted electrons had energy that could assume any value between zero and a certain maximum instead of having specific values such as how light emitted by atoms would be expected to behave based on the progress of quantum mechanics.

Niels Bohr, who in those years was truly a scientific authority, thought that to explain this phenomenon it might be necessary to give up on the law of conservation of energy, a fundamental pillar of Physics. Wolfgang Pauli was firmly against this idea and as a “last desperate attempt” theorized the existence of a new neutral particcle called the “neutron”. It was Fermi who then coined the term “neutrino” after “neutron” was used for the particle observed in 1932 and heavy as a proton but with no charge.  In December of 1933 Fermi wrote the article “A possible theory for the emission of beta rays”, published in the Italian magazine Nuovo Cimento: with the neutrino theory, Fermi built upon the idea that a neutron could transform into a proton with the subsequent creation of an electron and a neutrino. During the beta emission process a neutrino would be emitted along with an electron and the two particles would have shared the available energy. What’s more, according to the conservation of mass, the neutrino would be a very light neutral particle and because of its minimum interaction with matter would be difficult to observe.

In Fermi’s theory, the transformation of a neutron into a proton would activate a new kind of current called “weak current” that causes the creation of these coupled particles. Fermi created the basis for a new kind of fundamental force, weak interaction, that only 30 years later acquired a more detailed theoretical aspect: successive studies on weak interactions were awarded about ten Nobel prizes. A second important result of Fermi’s was his estimate, through the energetic distribution of emitted electrons, of neutrino mass which turned out to be very, very small. In his article, there appeared an unknown parameter, today known as Fermi’s Constant, that determines the intensity of this new force; the name “weak interactions” was given to the very small value of this constant. Fermi founded his theory of the neutrino well ahead of his time: it was only eventually discovered through a fission reactor 22 years later, in 1956.

The Sun

Energy of the stars

 The beta decay discovered by Fermi plays an important role in determining the speed of nuclear reactions in stars. These give off radiation thanks to nuclear fusion that transforms the lightest and most abundant element in the universe—hydrogen, composed of a single proton—into heavier elements. This process can be compared to a continuous thermonuclear explosion and is what powers all active stars. Great quantities of energy are released through fusion: inside the Sun, 600 million tons of hydrogen are burned each second and of these, 4 million tons are converted into energy, according to Einstein’s famous equation, E=mc², energy is equal to mass times the square of the speed of light.

Nuclear fusion is a reaction in which two or more atomic nuclei combine to form one or more different atomic nuclei. The difference of mass between the nuclei before and after the reaction is visible as a release of energy and is derived from the difference in energy of the atomic bonds between the nuclei before and after the reaction. Protons are positively charged and repulse each other according to the force of Coulomb. Besides the force of Coulomb there’s another force that comes into play, the strong nuclear force, that holds protons together inside the atomic nucleus.  So, the release of energy from the fusion of light elements is due to the interaction of two opposite forces: the nuclear force that combines protons and neutrons and the force of Coulomb that makes protons repulse each other. A lot of energy is needed to override this repellent force and that happens only at temperatures above 10 million degrees kelvin.

Two transformations are necessary for fusion. In the first, two protons merge to form a nucleus of deuterium (composed of a proton and a neutron), releasing a positively charged electron or positron, and a neutrino. The second transformation is called beta decay and its function was predicted by Enrico Fermi. This is the bottleneck of the whole process because the proton has to wait around 10 billion years before it can combine into deuteriumAfter its production, deuterium can fuse with another hydrogen nucleus to form helium.

Stars pass about 90% of their existence in a stable phase during which they melt the hydrogen in their nucleus into helium at very high temperatures and pressure; this phase is called the principal sequence and in it, the interior of the star is in a steady state in which the two predominant forces—gravity (that pulls towards the center of the star) and thermal energy of the mass of plasma generated by fusion which pushes in the opposite direction—counterbalance each other perfectly. The duration of the principal sequence phase depends mainly on the quantity of nuclear fuel available, as well as the speed at which it melts; in other words on the initial mass and luminosity of the star. The length of the principal sequence of our Sun is estimated to be around 10 billion years. Larger stars consume their “fuel” rather quickly and have a decidedly shorter lifespan (tens to hundreds of millions of years); smaller stars burn the hydrogen in their nucleus more slowly and have a much longer existence (tens to hundreds of billions of years).