In order for a photon to interact with other photons to produce an electron-positron pair (also known as photon-photon pair production), the total energy of the colliding photons must exceed the rest mass energy of an electron-positron pair, which is approximately 1.02 MeV (mega-electron volts).
The minimum energy required for each individual photon involved in the interaction depends on the specific conditions and the angle at which the photons collide. However, if we consider head-on collisions, the minimum energy of each photon can be calculated by dividing the rest mass energy of an electron-positron pair by two (since two photons are involved):
Minimum energy of each photon = (Rest mass energy of electron-positron pair) / 2
Minimum energy of each photon ≈ 0.51 MeV
It is important to note that this is a simplified calculation and assumes idealized conditions. In reality, the process of photon-photon pair production involves various factors, including conservation laws, quantum field theory calculations, and the effects of the background electromagnetic field. The probability of pair production also depends on factors such as photon polarization and the intensity of the photon beams involved.