I was recently studying Pair Production and Annihilation. The author mentions that a nearby nucleus is required when the photon materialises into a particle and an anti-particle. The explanation given is that the momentum and the energy must be conserved. However, there is no calculation given that shows the violation of energy. The reason is just blankly stated. Is there more to this concept. Please explain? As far as I know that from the knowledge of Particle Physics, virtual photons can violate the conservation laws if the time scales are very small due to the Heisenberg Uncertainty Principle. Then why can't we apply the same idea here?