Colloquium: Ettore Majorana and the birth of autoionization

In some of the first applications of modern quantum mechanics to the spectroscopy of many-electron atoms, Ettore Majorana in 1931 solved several outstanding problems by developing the theory of autoionization. Later literature makes only sporadic references to this accomplishment. After reviewing his work in its contemporary context, we describe subsequent developments in understanding the spectra treated by Majorana and extensions of his theory to other areas of physics. Several puzzles are found concerning the treatment of Majorana’s work in the subsequent literature and the way in which the modern theory of autoionization was developed.

Figure 1

Ettore Majorana, date unknown. (Photo reproduced with permission of E. Recami and F. Majorana.)

Figure 2

Grotrian diagram for the $\mathrm{Cd}\mathrm{I}$ $5s5p$ ${}^{3}P–5p^2$ ${}^{3}P$ transitions. The doubly excited $4p^2$ ${}^{3}P$ levels in $\mathrm{Zn}\mathrm{I}$ and the $6p^2$ ${}^{3}P$ levels in $\mathrm{Hg}\mathrm{I}$ are also above the ${}^{2}S$ principal ionization energy. The dashed lines indicate $n{p}^2$ ${}^{3}P_2$ transitions not observed or not classified in the original interpretations of these multiplets.

Figure 3

The plate of the $\mathrm{Cd}\mathrm{I}$ $5s5p$ ${}^{3}P^{\circ }–5p^2$ ${}^{3}P$ multiplet observed in absorption by Foote and co-workers, whose study led Majorana to identify the role of “spontaneous ionization.” The correspondences between modern and early atomic notation are $5s5p$ ${}^{3}P_{2,1,0}=2p_{1,2,3}$ and $5p^2$ ${}^{3}P_{2,1,0}=2p_{1,2,3}^{\prime }$. Wavelengths, in air and in angstrom units, are given above the lines, with $1\mathrm{\AA }=0.1\mathrm{nm}$. From 32.

Figure 4

The $\mathrm{Zn}\mathrm{I}$ multiplet $4s4p$ ${}^{3}P^{\circ }–4p^2$ ${}^{3}P$ as photographed in 1970 with a $10.7\mathrm{m}$ spectrograph at the National Bureau of Standards (now NIST). Each line of the multiplet is identified by the $J$ values of the lower and upper levels, respectively. The lines without an indicated multiplet classification belong to the $\mathrm{Zn}\mathrm{II}$ spectrum. The source for this emission spectrum was a high-pressure arc discharge in helium between zinc electrodes (59). The lines are strongest at a point near the center of their length that received light from a region of high electron density near one of the electrodes; this effect is much enhanced for the two broad “lines” from the autoionizing $4p^2$ ${}^{3}P_2$ level.

Figure 5

Optogalvanic spectra of $\mathrm{Cd}\mathrm{I}$ autoionizing resonances: (a) $5s5p$ ${}^{3}P_2–5p^2$ ${}^{3}P_1$ at $232.9\mathrm{nm}$; (b) $5s5p$ ${}^{3}P_1–5p^2$ ${}^{3}P_1$ at $226.7\mathrm{nm}$; (c) $5s5p$ ${}^{3}P_0–5p^2$ ${}^{3}P_1$ at $224.0\mathrm{nm}$; and (d) $5s5p$ ${}^{3}P_1–5p^2$ ${}^{3}P_0$ at $230.7\mathrm{nm}$. Wave number scale on the horizontal axis is shown in mK units $(1\mathrm{mK}=0.001{\mathrm{cm}}^{-1})$. From 7.

Figure 6

Absorption spectra of helium, neon, and argon atoms in the extreme ultraviolet spectral region from 49. These are images of photographic plates exposed to radiation from the electron synchrotron at the National Bureau of Standards (now the SURF Synchrotron Ultraviolet Radiation Facility). The synchrotron radiation was passed through a gas cell and then dispersed by a diffraction grating to show the dependence of absorption upon wavelength in angstrom units. Increased blackness indicates increased absorption by the gas. From 19.

Figure 7

Absorption coefficient vs wavelength for excitation to the $2s2p$ ${}^{1}P^{\circ }$ state of the helium atom, corresponding to the strongest absorption feature of Fig. 6, around $206\mathrm{\AA }$, as reported by 50. Note that the wavelength increases to the right here, opposite to the display of Fig. 6. The points are experimental data; the solid line is a fit to the Fano profile formula, with the values $q$ and $\Gamma$ as indicated. From 19.

Figure 8

Schematic level diagrams for the quantum dot experiment of 45. Upper left, He autoionization scheme leading to the Fano profile; upper right, analogous level scheme and relaxation processes appropriate for the photoexcitation of the quantum dots; lower frames, energy-level diagrams of two different samples. For the lower right, the increased capping layer thickness leads to the appearance of two-dimensional continuum states, coupled via tunneling with the valence dot level. CB, conduction band; VB, valence band; and $E_F$, Fermi energy. From 45.

Figure 9

Normalized absorption profiles for single quantum dot spectroscopy (45), with increasing laser power, from $0.33\mathrm{nW}$ on the far left up to $22\mathrm{nW}$ on the far right vs the laser detuning, in $\mu \mathrm{eV}$. The symbols represent the experimental data and the solid lines are a guide to the eye based on the Fano line shape. From 45.

Figure 10

(Color online) Scattering spectra from a high quality-factor planar photonic nanocavity for two different excitation conditions. The dots represent experimental results and the lines are best fits to the Fano line shape of Eq. (4). (a) A tightly focused laser beam produced a $d_1\approx 2\mu \mathrm{m}$ spot diameter on the nanocavity and a strong coupling to the cavity modes corresponding to $q_1=-0.348$. (b) A slightly defocused laser beam produced a $d_2\approx 10\mu \mathrm{m}$ spot diameter and a small coupling described by $q_2=-0.016$. Quality factors $Q$ are also reported. From 36.