Question

Deuteron is a bound state of a neutron and a proton with a binding energy B = 2.2 MeV. A γ -ray of energy E is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the n and p move in the direction of the incident γ-ray. If E = B, show that this cannot happen. Hence calculate how much bigger than B must E be for such a process to happen.

Answer 1

From conservation of energy

From conservation of momentum

If E = B, the first equation gives p_n = p_p = 0 and hence the second equation cannot be satisfied, and the process cannot take place.

For the process to take place, Let E = B + λ, where l would be <<B.

Then : substituting for p_n from Equation (2) into Equation (1),

Since the determinant must be positive for p_p to be real :