14-N (n,p) 14-C 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/...tic_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