The scattering $\gamma \gamma \rightarrow \gamma \gamma$ is a loop induced process. Which means it does not occur at tree level pertubation order. Therefore it is not that likely to occur, but it can e.g. by processes including a box of charged leptons running around.

Some calculation of the cross section for the process is given in this paper by Böhm and Schuster (Scattering of light by light in the electroweak Standard Model), which should answer the question in which energy scales light by light scattering occurs.

More recently light by light scattering was observed at heavy ion collisions at CERN, where they collide Pb-ions with which, caused by there high charge, photon photon scattering is detectable. You can take a look at this paper.

The process is kind of interesting because it could be sensible for beyond standard model extensions including e.g. charged higgs bosons.

The scattering $\gamma \gamma \rightarrow \gamma \gamma$ is a loop induced process. Which means it does not occur at tree level pertubation order. Therefore it is not that likely to occur, but it can e.g. by processes including a box of charged leptons running around.

Some calculation of the cross section for the process is given in this paper by Böhm and Schuster (Scattering of light by light in the electroweak Standard Model), which should answer the question in which energy scales light by light scattering occurs. This paper should be interesting to you since they calculate the mean free path (due to scattering on the cosmic microwave background) for low energy photons.

More recently light by light scattering was observed at heavy ion collisions at CERN, where they collide Pb-ions with which, caused by there high charge, photon photon scattering is detectable. You can take a look at this paper.

The process is kind of interesting because it could be sensible for beyond standard model extensions including e.g. charged higgs bosons.