In the case of atomic and molecular electronic structure problems, it is well known that the self-consistent field (SCF) approximation is relevant at least as a starting point of more elaborate methods.
[11] It has been experimentally observed in the anionic yields from photofragmentation of small molecules to provide details of internal structure.
In fact the shape resonance occurs where the integral number of wavelengths of the particle sit within the potential of the nucleus of radius R. Therefore, the measure of the energies of the shape resonances in the neutron-nucleus scattering have been used in the years from 1947 to 1954 to measure the radii R of the nuclei with the precision of ±1×10−13 cm as it can be seen in the chapter "Elastic Cross Sections" of A Textbook in Nuclear Physics by R. D.
[14] The "shape resonances" are discussed in general introductory academic courses of quantum mechanics in the frame of potential scattering phenomena.
This quantum interference in many body system has been described using quantum mechanics by Gregor Wentzel, for the interpretation of the Auger effect, by Ettore Majorana for the dissociation processes and quasi bound states, by Ugo Fano for the atomic auto-ionization states in the continuum of helium atomic spectrum and by Victor Frederick Weisskopf.