Semiclassical quantization of the electron-dipole system

Abstract

A recent note by Fox called attention to a semiclassical treatment by Fermi in 1925 of the motion of an electron in the field of two stationary positive charges. The similarity of this problem to that of an electron moving in a dipole field prompted the author to investigate the latter system under semiclassical quantization. It is shown that Bohr quantization leads to the value Dmin = (3√3/4) ea0=1.30ea0 for the minimum dipole moment required to bind an electron. The implied separation of unit dipole charges is identical with a special value for unit positive-charge separation given by Fermi. Furthermore, this semiclassical value of Dmin is more than twice the quantum-mechanical value Dmin=0.639ea0.