The nucleus-electron frequency wall hypothesis. Where particles with their own de Broglie clocks meet

Philippe Catillon, Nelson Cue, M. J. Gaillard +7 more

P. R. Silva

M. Gouanère, M. Spighel, Nelson Cue +7 more

The particle internal clock conjectured by L. de Broglie in 1924 was looked for in a channeling experiment with -80 MeV electrons traversing a 1-μm thick silicon crystal aligned along the 〈110〉 direction. Part of them undergo what is called the rosette motion, in which they interact with a single atomic row. When the electron energy is finely varied, the rate of electron transmission at 0° shows an 8% dip within 0.5% of the resonance energy, 80.874 MeV, for which the frequency of atomic collisions matches the internal clock frequency. Our observation is compatible with the de Broglie hypothesis.

Vinay Venugopal, Piyush S Bhagdikar

The undergraduate courses on modern physics generally consider the particle interpretation of Compton effect. Motivated by a student's solution in an undergraduate examination on modern physics here we consider the wave characteristics of recoiled electrons in the Compton effect. The de Broglie wavelength, wave and clock frequency of the scattered electrons are expressed in terms of the wavelength and the frequency of the incident and the scattered photons respectively using the familiar particle interpretation of the Compton effect, where initially the electron is at rest and its spin is ignored. Both non-relativistic and relativistic cases are considered. Numerical values of de Broglie wavelength, wave and clock frequency of the scattered electron are calculated for an incident photon energy that was used in the original experiment of Compton as a function of the scattering angle of the recoiled electron. Considering the relativistic effects which are however insignificant for the de Broglie wavelength of the recoiled electron under these conditions, the minimum value obtained is in the range of X-rays. The non-relativistic de Broglie wave frequency obtained by neglecting the rest mass of the electron leads to an underestimation of its value. The implications of de Broglie wavelength and clock frequency for Compton scattering experiments are briefly discussed and possible extensions of the obtained mathematical formulations are indicated. The results are useful for understanding the wave-particle duality of the recoiled electron in the context of the Compton effect.

J. R. Croca, Miguel Ferrero, Augusto Garuccio +1 more

M. Bauer

Electron channeling in silicon crystals has brought forward the possibility of having detected the particle's "de Broglie internal clock", as giving rise to the observed resonance peak at the center of the expected transmission probability dip. A classical multiple scattering calculation fails to represent the experimental results unless, surprisingly, the interaction frequency is twice the de Broglie's clock frequency, that is, the "Zitterbewegung" frequency. In the present paper, the observed characteristics of this process are shown to be consistent with a free particle quantum mechanical motion described by Dirac's Hamiltonian.