# Majorana, Ettore

# MAJORANA, ETTORE

(*b*. Catania, Sicily, 5 August 1906; *d*. at sea, near Naples, 25/26 March 1938)

*physics*.

Majorana was the fourth of the five children of Fabio Massimo Majorana, an engineer and inspector general of the Italian ministry of communications, and Dorina Corso. At the age of four he revealed the first signs of a gift for arithmetic. After schooling at home he entered the Jesuit Istituto Massimo in Rome and completed his secondary school education at the Liceo Torquato Tasso, passing his *maturità classica* in the summer of 1923. That fall he entered the School of Engineering of the University of Rome, where his fellow students included his older brother Luciano, Emilio Segrè, and Enrico Volterra, later professor of civil engineering at the University of Houston. Majorana was persuaded by Segré to take up physics at the beginning of 1928. His lively mind, insight, and the range of his interests immediately impressed the new circle of physicists that had formed around Fermi. He was nicknamed “the Grand Inquisitor” for his exceptionally penetrating and inexorable capacity for scientific criticism, even of his own person and work. He received the doctorate in physics on 6 July 1929 with a thesis on the mechanics of radioactive nuclei sponsored by Fermi.

Fermi convinced Majorana to go abroad financed by a grant from the Consiglio Nazionale delle Ricerche; and Majorana began his journey at the end of January 1933, traveling first to Leipzig and then to Copenhagen. In Leipzig, Heisenberg persuaded Majorana to publish his paper on nuclear forces. He returned to Rome in the autumn of 1933 in poor health aggravated by gastritis, which he had developed in Germany and which was attributed by some to nervous exhaustion. He attended the Istituto di Fisica at intervals but stopped after a few months, despite his friends’ attempts to lead him back to a normal life.

Appointed professor of theoretical physics at Naples in November 1937, Majorana soon discovered that his course was too advanced for the majority of students. On 25 March 1938 he wrote from Palermo to his colleague and friend Antonio Carrelli that he found life in general, and his own in particular, useless and had decided to commit suicide. A few hourse later he sent a telegram to Carrelli asking him to disregard the letter and boarded a steamer for Naples that evening. Although he was seen at daybreak as the ship entered the Bay of Naples, no trace was ever found of him, despite an inquiry continued for several months and repeated appeals of his family published in the Italian press.

Majorana’s total scientific production consists of nine papers, which can be divided into two parts: six papers on problems of atomic and molecular physics, and three on nuclear physics or the properties of elementary particles. The first group of papers deals with the splitting of Roentgen terms of heavy elements induced by electron spin, the interpretation of recently observed spectral lines in terms of atomic states with two excited electrons, the formation of the molecular ion of helium, the binding of molecular hydrogen through a mechanism different from that of Walter Heitler and Heinz London, and the probability of reversing the magnetic moment of the atoms in a beam of polarized vapor moving through a rapidly varying magnetic field. The last paper remains a classic on nonadiabatic moment-inversion processes. Often quoted, it provides the basis for interpreting the experimental method of flipping neutron spin with a radio-frequency field. The other papers of this period (1928–1932) reveal a thorough knowledge of experimental data and an ease—particularly unusual at the time—in using the symmetry properties of the states to simplify problems or to choose the most suitable approximation for solving each problem quantitatively. The latter ability was at least partly due to Majorana’s exceptional gift for calculation.

Majorana’s major scientific contribution, however, is found in the last three papers. “Sulla teoria dei neclie” (1932) concerns the theory of light nuclie under the assumption that they consist solely of protons and neutrons that interact through exchange forces acting only on the space coordinates (and not on the spin), so that the alpha particle—rather than the deuteron—is shown to be, as it is, the system with greatest binding energy per nucleon. The essential work on this paper was completed in the spring of 1932, only two months after the appearance of J. Chadwick’s letter to the editor of *Nature* announcing the discovery of the neutron. Fermi and his friends tried in vain to persuade Majorana to publish, but he did not consider his work good enough and even forbade Fermi to mention his results at an international conference that was to take place in July 1932 in Paris. The July 1932 issue of *Zeitschrift für Physik* contains the first of Heisenberg’s three famous papers on the same subject. They are based on Heisenberg’s exchange forces, which differ from Majorana’s forces in that not only the space coordinates but also the spin of the two particles are exchanged.

“Teoria relativistica di particelle con momento intrinseco arbitrario” (1932), the first paper of Majoranan’s second phase, concerns the relativistic theory of particles with arbitrary intrinsic angular momentum. Although in some ways outside the mainstream of the development of elementary particle physics, it represents the first attempt to construct a relativistically invariant theory of arbitrary half-integer or integer-spin particles. Majorana’s mathematically correct theory contains the first recognition, and the simplest development and application, of the infinite dimensional unitary representations of the Lorentz group. This theory lies outside the mainstream of successive development primarily because, from the outset, Majorana set himself the task of constructing a relativistically invariant linear theory of which the eigenvalues of the mass were all positive. This viewpoint was justified at the time the paper was written (summer 1932), since news of C. D. Anderson’s discovery of the positron had not yet reached Rome.

Majorana’s last paper was written in 1937 on Fermi’s urging, after four years of not publishing because of poor health. It contains a symmetrical theory of the electron and the positron based on the Dirac equation but in which the states of negative energy are avoided and a neutral particle is identical to its antiparticle. The most characteristic point is the discovery of a representation of the Dirac matrices γ_{k} (*k* = 1, 2, 3, 4), in which the first three components are real, the fourth imaginary, like the vector
(Majorana representation).

At the present no neutral particle of the type suggested by Majorana is known, since it has been experimentally established that the neutron, lambda particle, and neutrino differ from their corresponding antiparticles. Neverthless, Majorana’s neutrino, *v _{M}* characterized by the equality

*ν*

_{M}=

*ν̄*

_{M}(the bar indicated the antiparticle), has played an important part in the physics of weak interactions, especially since the discovery by T. D. Lee and C. N. Yang of the nonconservation of parity and the development of the two-component theory, of the neutrino. This theory is related to that of Majorana, to which, in certain aspects, it is equivalent. Contrary to the two-component theory, Majorana’s does not require the neutrino to have a mass exactly equal to zero, and a small neutrino mass cannot at present be excluded on the basis of available experimental data.

Majorana had an extraordinary gift for mathematics, an exceptionally keen analytic mind, and an acute critical sense. It was perhaps the latter, together with a certain lack of balance on the human side, that interfered with his capacity for creative synthesis and prevented him from reaching a level of scientific productivity comparable to that attained at the same age by major contemporary physicists. Yet his choice of problems and his way—especially his mathematical methods—of attacking them showed that he was naturally in advance of his times and, in some cases, almost prophetic.

## BIBLIOGRAPHY

**I.** Original Works. Majorana’s papers on atomic and molecular physics are “Sullo sdoppiamento dei termini Roentgen e ottici a causa dell’elettrone rotante…” in *Atti dell’ Accademia nazionale dei Lincei. Rendiconti*, 6th ser., **8** (1928), 229–233, written with G. Gentile; “Sulla formazione dello ione molecolare di Elio,” in *Nuovo cimento* 8th ser., **8** (1931), 22–28; “I presunti termini anomali dell’Elio,” *ibid*., 78–83; “Reazione pseudopolare fra atomi di idrogeno,” in *Atti dell’Accademia nazionale dei Lincei. Rendiconti*, **13** (1931), 58–61; “Teoria dei tripletti P’ incompleti,” in *Nuovo cimento***8** (1931), 107–113; and “Atomi orientati in campo magnetico variabile,” *ibid*., **9** (1932), 43–50.

His papers on elementary particles are “Teoria relativistica di particelle con momento intrinseco arbitrario,” *ibid*., 335–344; “Sulla teoria dei nuclie,” in *Ricerca scientifica*, **4** (1933), 559–565; and “Teoria simmetrica dell’ elettrone e del positrone,” in *Nuovo cimento*, **14** (1937), 171–184. See also the posthumously published “II valore delle leggi statistiche nella fisica e nelle scienze sociali,” in *Scientia*(Bologna), **71** (1942, 58–66.

**II.** Secondary Literature. On Majorana’s life and work, see E. Amaldi, *La vita e lľopera di Ettore Majorana* (Rome, 1966); an English trans. of the biographical note in this work is A. Zichichi, ed., *Strong and Weak Interactions—Present Problems* (New York, 1966), 10–77, which also contains a list of Majorana’s **MSS at** the Domus Galileiana, Pisa.

Edoardo Amaldi

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**Majorana, Ettore**