  In this paper we analyse the mechanisms responsible for the bonding of
electrons to metal surfaces. We present and validate a method to measure the
energy distribution of dense electron ensembles at ambient conditions. We have
found sharp structures in the energy distribution of charge confined at metal
surfaces. These structures correspond to the onset of space charge i.e.
electron emission. The threshold energy for emission increases linear with the
free electron density. We conclude that the work function is a direct measure
of the Hartree-Fock exchange energy. Remarkably, the emissions that have been
observed do not obey the Einstein-Millikan threshold relation for the photo
electric effect. By discrimination between requirements for energy and momentum
we deduce that electron emissions are trigged by photon momentum. We claim that
the photo electric effect is the result of a phase transition in an electron
gas that connects a surface bound, condensed state to a free continuum state.
The assignment of a phase transition to the effect under consideration is
justified by analyzing the behaviour of the Fermi-Dirac energy distribution
upon raising the Fermi level. We predict an abrupt increment in the number of
electrons in the continuum that exceeds 70 orders of magnitude. Both the
observed threshold energy and the line shape of the transition are in good
agreement with theoretical predictions.
