From the Majorana theory of "Incomplete P' triplets" to Feshbach resonances

Abstract

The Ettore Majorana paper "Theory of incomplete P' triplets", published in 1931, focuses on the role of selection rules for the non-radiative decay of two electron excitations in atomic spectra, involving the configuration interaction between discrete and continuum channels. This work is a key step for understanding the 1935 work of Ugo Fano on the asymmetric lineshape of two electron excitations and the 1958 Herman Feshbach paper on the shape resonances in nuclear scattering arising from configuration interaction between many different scattering channels. The Feshbach resonances and shape resonances are today of high scientific interest in many different fields and in particular for ultracold gases and high T c superconductivity. Ettore Majorana's legacy and the Physics of the XXI century

Far from Equilibrium Percolation, Stochastic and Shape Resonances in the Physics of Life

“…Majorana has used these ideas in one paper on the atomic auto-ionization processes i.e ., the two electrons photo-absorption lines above the ionization potential in atomic spectra [ 61 ]. Majorana was also attracted by the nuclear physics problem of α decay: the artificial disintegration of nuclei by bombardment with alpha-particles as a quantum phenomenon, but he did not publish his works [ 62 – 64 ]. Fano in 1935 developed the theory of the “shape resonance” due to interference effects between a closed and an open scattering channel for the two electron excitations above the ionization potential in Helium [ 65 , 66 ].…”

Fermi-Bose Mixtures and BCS-BEC Crossover in High-Tc Superconductors

“…The Bose fermion or Fermi-Bose model for high temperature superconductors is therefore described as the case of Feshbach resonance driven by Majorana exchange interaction between bosonic pairs making a BEC condensate with cooper pairs making a BCS condensate [142][143][144] which is described in the right panel of figure 6.…”