text: When a photoemission event takes place, the following energy conservation rule holds:
  where  is the photon energy,  is the electron BE (binding energy with respect to the vacuum level) prior to ionization, and  is the kinetic energy of the photoelectron. If reference is taken with respect to the Fermi level (as it is typically done in photoelectron spectroscopy)  must be replaced by the sum of the binding energy (BE) relative to the Fermi level, , and the sample work function,  .
  From the theoretical point of view, the photoemission process from a solid can be described with a semiclassical approach, where the electromagnetic field is still treated classically, while a quantum-mechanical description is used for matter.
  The one—particle Hamiltonian for an electron subjected to an electromagnetic field is given by:
  where  is the electron wave function,  is the vector potential of the electromagnetic field and  is the unperturbed potential of the solid.
  In the Coulomb gauge (), the vector potential commutes with the momentum operator 
  (), so that the expression in brackets in the Hamiltonian simplifies to:
  Actually, neglecting the  term in the Hamiltonian, we are disregarding possible photocurrent contributions. Such effects are generally negligible in the bulk, but may become important at the surface.
  The quadratic term in  can be instead safely neglected, since its contribution in a typical photoemission experiment is about one order of magnitude smaller than that of the first term .
  In first-order perturbation approach, the one-electron Hamiltonian can be split into two terms, an unperturbed Hamiltonian , plus an interaction Hamiltonian , which describes the effects of the electromagnetic field:
  In time-dependent perturbation theory, for an harmonic or constant perturbation, the transition rate between the initial state  and the final state  is expressed by Fermi's Golden Rule:
  where  and  are the eigenvalues of the unperturbed Hamiltonian in the initial and final state, respectively, and  is the photon energy. Fermi's Golden Rule uses the approximation that the perturbation acts on the system for an infinite time. This approximation is valid when the time that the perturbation acts on the system is much larger than the time needed for the transition. It should be understood that this equation needs to be integrated with the density of states  which gives:
  In a real photoemission experiment  the ground state core electron BE cannot be directly probed, because the measured BE 
  incorporates both initial state and final state effects, and the spectral linewidth is broadened owing to the finite core-hole lifetime ().
  Assuming an exponential decay probability for the core hole in the time domain (), the spectral function will have a Lorentzian shape, with a FWHM (Full Width at Half Maximum)  given by:
  From the theory of Fourier transforms,  and  are linked by the indeterminacy relation:
  The photoemission event leaves the atom in a highly excited core ionized  state, from which it can decay radiatively (fluorescence) or non-radiatively (typically by Auger decay).
  Besides  Lorentzian broadening, photoemission spectra are also affected by a Gaussian broadening, whose contribution can be expressed by
  Three main factors enter the Gaussian broadening of the spectra: the experimental energy resolution,  vibrational and inhomogeneous broadening.
  The first effect is caused  by the non perfect monochromaticity of the photon beam -which results in a finite bandwidth- and by the limited resolving power of the analyzer. The vibrational component is produced by the excitation of low energy vibrational modes both in the initial and in the final state. Finally, inhomogeneous broadening can originate from the presence of unresolved core level components in the spectrum.