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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.

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From conservation of energy

From conservation of momentum

If E = B, the first equation gives pn = pp = 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 pn from Equation (2) into Equation (1),

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

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