Question

Show that the γ-quantum can not form a pair outside the nucleus field, even if such process is energetically possible.

Answer 1

To form pair it is necessary that the γ-quantum energy is greater than 2mc², where m is the mass of each particle. Obviously, you can always go to a reference system where the γ-quantum energy is less than 2mc² and the pair creation would be impossible. But if this process is not possible in one reference system, it is not possible in any other.