A detailed kinematics characterization of reaction (1.7) requires the specification of both the kinetic energy and the momentum of the initial state of the reactants a and b as well as-depending upon the reaction details desired-the appropriate
field forces which may act on the particles. However, some useful relations about the energies of the reaction products d and e can be obtained for the simple case in which the reacting particles possess negligible kinetic energies relative to the Q-value of the reaction, i. e. Eka + Ek, b « Qab, and in which the total energy liberated is shared by the two reaction products d and e in the form of their kinetic energy. Under these conditions, Eqs.(1.14) and (1.15a) give

Tmdvd +ттеу2е = Qab • (1.17a)

Then, restricting this analysis to the case that the centre of mass be at rest, Fig. 1.2, momentum conservation provides for

md’Vd = me’Ve ■ (1.17b)

Before Collision:

ma, Ag, Zg mb> Ab, Zjj

After Collision:

:k, d

Fig. 1.2: Kinematic depiction of a head-on nuclear fusion reaction with the centre of mass

at rest.

For the specific case of d-t fusion, Eq. (1.5), for which Q* = 17.6 MeV, the neutron and alpha particle kinetic energies are therefore found to be

Ek, n ~jQdt ~ 14-1 MeV, Екм =1<2л = Зі MeV. (U9)

Thus, an 80 — 20% energy partitioning occurs between the reaction products.