

(1) 
In the typical vacuum ultraviolet (VUV) energy regime this ratio is of the order of 10^{5} which demonstrates the experimental difficulties inherent in an inverse photoemission process.
Following the Green function approach, the photocurrent within the sudden approximation ^{1} is simply given by the spectral representation of the oneparticle Green function:

(2) 
where the summation runs over all initial states Y_{i} and final states Y_{f} with energy e_{i} and e_{f}, respectively and denotes the energy of the incident photons. The perturbation to the system caused by the incident radiation is given by

(3) 
where and Φ are the vector and scalar potentials of the incident light field. Several approximations for M reduce the problem to a managable size. By neglecting multiphoton processes the term in (3) vanishes. If localfield corrections considering the inhomogeneity of the electron system are neglected, one has ∇ = 0 (taking the commutation relation of operators into account) and in the Coulomb gauge Φ vanishes. Since in the UV spectral range wavelengths are large compared to typical atomic distances, can be regarded as independent of (dipole approximation). Within this approximations M becomes

(4) 
In the noninteracting limit, the photocurrent becomes simply

(5) 
with oneparticle matrix elements
Photoemission data are usually analyzed on the basis of the more simple ''threestepmodel''[8,9] consisting of bulk optical excitation followed by subsequent electron transport to, and escape through the surface. This model dates back to at least 1945 [10]. It was shown [11] that in the limit of sufficiently weak electron damping, the transition matrix elements for photoemission become the usual crystalmomentum conserving matrix elements. Thus, besides the energy conservation in (5) the crystal momentum is conserved within a reciprocal lattice vector :

(6) 
The momentum of the photon can be neglected for energies in the VUV and thus, only vertical transitions are allowed. If the final state energy is large enough, and in the absence of inelastic scattering, the electron can be emitted into the vacuum. By passing through the surface, the components parallel to the surface of the final state electron momenta inside and outside the solid are related by

(7) 
where is a reciprocal lattice vector of the surface and

(6) 
with E_{kin}, kinetic energy of the outcoming electron and emission polar angle J and azimuth j. Therefore, a Bloch wave of crystal momentum can be transmitted into the vacuum in any of a number of beams. The value of k_{⊥} thereby remains undetermined because of the broken translational symmetry perpendicular to the surface. However, suitable assumptions on that part of the band structure complementary to that under investigation (e.g. freeelectron like final states) allow, in principle, the determination of the vertical component of wave vector k_{⊥} within the direct transition model. Nevertheless,improved methods of exploitation such as electrontransition plots (ETplots [12]) where initial state energies of spectral features are displayed as a function of the corresponding final state energies avoid the problem of determining k_{⊥} and experimental results can be directly compared with theory.