# Nuclear reaction: creation of deuterium

A proton p collides with a neutron(at rest) n at relatively low-energies and creates a 'deuterium-core' d:

$$p+n->d+\gamma$$

Find the wavelength for the photon as a function of the proton's momentum and the angle that the photon creates with the proton.Do this relativistic.

So seems I'm supposed to set up two equations: energy- and momentum-balance. I tried to set up the relativistic energy equation as function of momentum, but became messy to solve. Any hint on what this energy equation could look like?

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"So seems im supposed to set up two equations: energy- and momentum-balance." Yep. Except that you have three equation: one for energy, one for momentum along the protons initial momentum and one for transverse momentum. The problem is highly constrained: there is only one free parameter which can be the angle they've asked about. Do it using $E^2 = m^2 + p^2$ (in $c = 1$ units or the expanded version if you prefer) and do not muck about with factors of $\gamma$: just momentum, energy and mass. –  dmckee Mar 16 '13 at 1:19
So the two form from decomposition of the momentum-equation? –  rakkararaka Mar 16 '13 at 1:36
Yep. For myself I would usual say one equation but it is one for equality of four-vectors. Or you are welcome to think of it as one for energy and one for the vector momentum. Or you can rip them apart and count them individually. In this case there is a rotational symmetry, but pick one plane (say, x--z) and work it that way. –  dmckee Mar 16 '13 at 1:46
So is this correct? E neutron at rest: mc^2 E incoming proton: (mc^2)/sqrt(1-v^2/c^2) E photon: hc/lambda E deuterium: (mc^2)/sqrt(1-v^2/c^2) –  user22104 Mar 17 '13 at 19:22