  We derive expressions for the coupling coefficients for electromagnetic
four-wave mixing in the non-linear quantum vacuum. An experimental setup for
detection of elastic photon-photon scattering is suggested, where three
incoming laser pulses collide and generate a fourth wave with a new frequency
and direction of propagation. An expression for the number of scattered photons
is derived and, using beam parameters for the Astra Gemini system at the
Rutherford Appleton Laboratory, it is found that the signal can reach
detectable levels. Problems with shot-to-shot reproducibility are reviewed, and
the magnitude of the noise arising from competing scattering processes is
estimated. It is found that detection of elastic photon-photon scattering may
for the first time be achieved.
