Let us consider an epithermal collision between
and a DX molecule,
with a
lab energy
(velocity
). Throughout
this appendix, solid state effects such as lattice binding and phonon
exchange are neglected unless otherwise specified.
Resonant scattering may occur via the following sequence of processes:
(1) the molecular complex (MMC) is formed in a collision
,
(2) MMC receives a recoil from the impact of ,
(3) MMC may be (partly) thermalized via collisions with the rest of the
target molecules,
(4) ro-vibrational states of MMC may change as a result of collisions
with other molecules, and
(5) back decay occurs leaving molecule DX in either the ground state
(elastic channel) or in an excited state (inelastic).
The energy of the
after back decay is important. It can be shown
that if the
energy is the same before and after the back decay, the
effective formation approximation gives the correct fusion yield (condition
(b) above). However, if the
energy changes such that it is removed
from the resonant region, the effective formation approximation fails as we
shall see. It should be noted that resonant structure has a narrow width
for low temperature targets, therefore a small change in the
energy
is sufficient to remove it from the resonance.
Even in the completely elastic case (no MMC thermalization, no MMC
relaxation, and back decay via the elastic channel), the mean energy of in the lab frame is significantly reduced after back decay, because of recoil
of the MMC in process (2) and that of DX in (5). In reality, MMC
thermalization, MMC ro-vibrational relaxation, and back decay via inelastic
channels, all give contributions to reducing the
energy, hence the
is likely to be removed from the resonance region.