Quantum Theory Improvement of the Photoelectric Effect on Metals

Abstract

This paper concerns the full interaction of a flux of photons onto any metal whose extraction potential is known. The photons are described with a full wavefunction, including all states of polarization, and the ejected electrons are considered with their two spin states. The purpose is to give a full theoretical description of the interaction of the photoelectric effect, known since a long time, it verifies that the electron of any peculiar metal can escape if a threshold is met. These wavelengths are accessible for many metals, the photoelectrons exist if the condition: . U0 is the extraction potential given in eV, these are tabulated. The system wavefunction (electron + photon) a product of the electron free wave and of the photon, taken as , is defined, and the total Ψ(t) is truncated as required by the condition . It is possible to use any combination of polarization states for the photon, with at maximum a mixture of all possible polarizations, which is linear and right and left circular. The method applied takes into account the basic electron photon interaction, the free electron, which is the ejected electron, is described by a free wave, restricted to the first momenta. The quantum theory of the interaction needs to evaluate the integrals: , where rmax is a cut-off parameter to insert to enable finite values of these integrals. The I is calculated on the variables r, θ, φ, and the r3 concerns the radial volume multiplied by the r coming from the dipolar interaction. It follows that using the Fermi golden rule leads to an estimate of the probability of escape of an electron Pij, assuming that the normalisation factor of the A the electomagnetic vector is . The results for copper metal are given, the probabilty of escape, Pij has the correct dimension .