How do I calculate the average energy of a particle leaving a nuclear reaction?

[cajunjacket]

I feel like a fraud. I learned neutron kinematics many years ago, yet I don't even know how to determine the Average energy of each particle being emitted from a basic nuclear reactions such as the one in the subject line.

What am I trying to calculate?

The average energy of a particle leaving a reaction such as the one above, i.e. not an elastic or inelastic reaction. A reaction involving a Q-value.

In particular, I want to calculate the average energy for a given incoming neutron energy. The test case I am using as a sanity check is a 20 MeV neutron striking ¹⁴N, producing a proton and ¹⁴C. The Q-value for this reaction is 625.8706 keV. The average energy of the exiting proton is supposed to be 3.974 MeV.

I have attempted to calculate the average energy, but I keep getting 17.9874 MeV using the methods presented in: http://www.wepapers.com/Papers/3834/16-_Neutron_Interactions_Q-Equation,_Elastic_Scattering, yet I did not consider relativistic effects. Regardless the relativistic effects shouldn't be a factor 4 difference in this case because of the relatively low kinetic energy compared with the rest mass of a neutron.

Any help would be greatly appreciated.

Thanks

 

[mfb]

It must be somewhat close to the 20 MeV, assuming we produce ¹⁴C in the ground state. Some of the energy will go to the nucleus and some of the energy is lost to binding energy, but overall most of the energy will go to the proton.