GALAXY

PAIR PRODUCTION

DEFINITION

When a photon strikes a heavy nucleus, it disintegrates and produces a pair of an electron and a positron. Electron and positron always move in opposite directions so that the momentum is conserved. This phenomenon is called pair production or materialization of energy.

ROLE OF NUCLEUS

The role of the nucleus is just to share some energy and momentum in order to conserve the two quantities.

COLLISION GEOMETRY

ENERGY EXPRESSION FOR PAIR PRODUCTION

Let us suppose that the energy of incident photon is E = hu (where u = frequency of photon)
Now we suppose that the rest mass energies of electron and positron are respectively,

Ee^- = m_oc²
Ee⁺ = m_oc²

Where m_o= rest mass of electron/positron
c = velocity of light
e^- = symbol for electron
e⁺ =symbol for positron

The energy of photon also provides additional energy to the pair of electron and positron so that they can move in their paths in opposite direction.

Their respective kinetic energies are:

(K.E)e^- = (K)e^-
(K.E)e⁺ = (K)e⁺

Since the process of pair production obeys the rules of elastic collision, therefore, in this process energy is also conserved, thus, total energy of striking photon is given by,

E = Ee^- + Ee⁺ + (K.E)e^- + (K.E)e⁺

hu = m_oc² + m_oc² + (K)e^- + (K)e⁺

hu = 2m_oc² + (K)e^- + (K)e⁺

But the value of m_oc² is equal to 0.51 Mev

hu = 2(0.51 Mev) + (K)e^- + (K)e⁺

hu = 1.02 Mev + (K)e^- + (K)e⁺

This expression clearly indicates that no pair production will takes place if energy of incident photon is less than 1.02 MeV. It means that to observe pair product, a photon must have 1.02 MeV of energy.