On Saturday March 26, 1938 the director of the Institute of Physics at the University of Naples in Italy, Antonio Carrelli, received a mysterious telegram. It had been sent the previous day from the Sicilian capital Palermo, some 300 km across the Tyrrhenian Sea, and read: “Don't worry. A letter will follow. Majorana.” That same Saturday, Ettore Majorana – who had just been appointed as full professor of theoretical physics at the university at the age of 31 – had not turned up to give his three-weekly lecture on theoretical physics. By Sunday the promised letter had reached Carrelli. In it Majorana wrote that he had abandoned his suicidal intentions and would return to Naples, but it revealed no hint of where the illustrious physicist might be. The picture was quickly becoming clear: Majorana had disappeared.

Worried by these circumstances, Carrelli called his friend Enrico Fermi in Rome, who immediately realized the seriousness of the situation. Fermi was working in his laboratory with the young physicist Giuseppe Cocconi at the time. In order to give him an idea of the seriousness of the loss to the community of physicists caused by Majorana's disappearance, Fermi told Cocconi:

Fortunes and misfortunes of a genius

Physicists working in several areas of research know quite well the name of Ettore Majorana, since it is currently associated with fundamental concepts like Majorana neutrinos in particle physics and cosmology or Majorana fermions in condensed matter physics. For non-specialists, the name of Ettore Majorana is usually intimately related to the fact that he disappeared rather mysteriously in 1938 and was never seen again.

From January to March 1938 – as we have seen in Chapter 1 – Majorana delivered his only lectures on quantum mechanics at the University of Naples, where he obtained a position as a full professor of theoretical physics. He prepared a set of lecture notes [26] for his students (see Section 13.5), and, among the original manuscripts of these lectures, we find some additional spare papers that cannot be considered as notes for academic lectures, even for an advanced course such as that taught by Majorana. Instead, as suggested in Refs. [328, 329], they probably refer to a seminar or conference held at the University of Naples, whose main topic was likely the theoretical interpretation of the molecular bonding in the framework of quantum mechanics; the notes were prepared by Majorana for his own personal use.

Scientific interest in this dissertation, however, focuses not on its main topic, nor on the calculations (which are practically absent from the manuscript), but rather on the interpretation given by Majorana to key concepts of the quantum theory, i.e. the concept of quantum state and the direct application of the quantum theory to the particular case of molecular bonding. The manuscript indeed discloses a peculiar cleverness on the part of Majorana in referring to this pivotal argument of quantum mechanics, and also reveals the concept was at least ten years ahead of its time. This link had been already noted earlier by Nicola Cabibbo [330], who saw in the Majorana manuscript a vague and approximate anticipation of the idea underlying the Feynman interpretation of quantum mechanics in terms of path integrals. A more analytic study has revealed, however, some intriguing surprises, upon which we will focus here.

In addition to the historical interest of Majorana's manuscript, we stress also the particularly powerful didactic method used by him on the given subject: his original presentation of the quantum-mechanical problems is exceedingly useful in teaching now those or related topics. For this reason, in the Appendix we will report the entire text (translated from the Italian) as prepared by Majorana.

At the end of 1920s, the activities of the Fermi group in Rome focused almost exclusively on atomic physics and related subjects, as did the other major research centers throughout Europe. After having obtained several significant results in atomic and molecular spectroscopy, around 1930 some people in the group realized that such a field could no longer offer any great prospects, and Fermi himself predicted that the interest would shift from the study of the external parts of the atom to its nucleus. However, no general consensus was reached initially inside the group, and the spectroscopic activities continued, along with the acquisition of theoretical knowledge and experimental technologies required by nuclear physics, until 1934, when the Fermi group discovered the radioactivity induced by neutrons and the important properties of slow neutrons [231].

Majorana also actively participated in scientific discussions within the Rome group [10, 11], but, as we have seen in Section 2.6, we are left with only one published paper of his on nuclear physics topics (that is, paper(s) N.8), dealing with the Heisenberg–Majorana exchange forces in nuclei, while nothing was published of his previous works on these matters. Remarkably, Majorana was the first in Rome to study nuclear physics; in 1929 (on July 6) he defended his degree thesis on “The quantum theory of radioactive nuclei,” and his studies on such topics continued for several years, independent of the main line of research carried out by the Fermi group. In this chapter we will focus on these (unpublished) studies [232], performed around 1929–30, devoted mainly to nuclear reactions induced by α particles.

Probing the atomic nucleus with α particles

The first steps of nuclear physics were taken in the realm of radioactive phenomena, among which those involving α emission were readily recognized to induce a profound modification of the atomic nucleus by virtue of the large mass of the emitted particles.