Sargent plot , weak interactions , and the geometry of the flat space - time

Sargent plot, summarizes part of one of the pioneers experiments on nuclear beta decay. Here it is proposed to be used as a motivation, to teach undergraduate students some basic features of the weak interactions. This is done by considering only elementary aspects of special relativity and quantum theories. 1 – Introduction It has been elapsed a time interval of eighty years, since B. W. Sargent [1,2] published in the prestigious periodic: “Proceedings of the Royal Society of London”, a study of the beta-decay from Uranium and other radioactive nuclei. In figure 2 of his paper, Sargent makes a plot of the logarithms of the disintegration constant, λ, versus logarithms of the maximum energies, Em, of the beta-particles (electrons or positrons). These plots could be approximately interpolated by two straight lines of different inclinations. If each disintegration curve (not the interpolations) is represented by a power law in the maximum energy, the exponent lies between 3 and 7. In this note we intend to use this remarkable discovery as a means to motivate undergraduate students in the learning of the weak interactions. 2. Statement of the problem It is well known from the study of particle physics that the great majority of elementary particles are short-lived, exceptions being done to the proton and the electron for instance. If there is not a conservation law which forbids a given decaying mode, this process will occur. With respect to the fundamental interactions participating in the game, we have by order of intensity, the strong force associated to quarks and gluons, the electromagnetic force between electric charges and intermediated by the photons, and the weak force intermediated by the massive W and Z bosons [3,4]. If the two first forces are prohibited to work, due to some conservation law, may be the weak force plays its role. This is just what happens in the nuclear transmutation (the alchemist dream?), which was investigated by Sargent.