How does the probability of pair production in the interacting medium vary?

The probability of pair production is influenced significantly by the atomic number (Z) of the interacting medium. The process of pair production, which occurs when a photon with sufficient energy interacts with the electromagnetic field of a nucleus, leads to the creation of a particle-antiparticle pair, typically an electron and its anti-particle, a positron.

The likelihood of this occurrence increases with higher atomic numbers due to the stronger electromagnetic fields present around heavier nuclei. This is where the relationship proportional to Z^2 comes into play, as it captures the greater probability of interaction in materials with higher atomic numbers. The Z^2 dependence arises from the fact that the cross-section for pair production is particularly sensitive to the electric charge of the nucleus, which is represented by Z.

Consequently, in environments with high-Z materials, there is a much higher chance of photon energies being converted into pairs since the availability of the nuclear field to facilitate this interaction is greater. This characteristic makes the response to Z^2 a key factor in understanding pair production dynamics in terms of material choice for various applications, like radiation shielding or in medical treatments using high-energy photons.