We illustrate the effect of back decay in the following simplified
comparison. We consider a case in which a
beam of resonant energy
collides with a D** _{2}** layer of varying thickness, and we wish to describe
the fusion yield in the D

With these assumptions, the fusion yield as a function of layer thickness
in the effective formation model (a) can be expressed as:

where

These expressions can be expanded in series in

Recalling , both models give the same results to leading order. Therefore, in the limit of a thin layer, model (a) can be justified for describing the fusion yield. However, the next-to-leading order corrections become important at

(132) |

resulting in an overestimate of fusion yield with model (a).

In our earlier analysis of the time-of-flight fusion experiments, the
effective rate (model a) was used, and we observed that the calculated
fusion yield was significantly larger than the experimental data. Since our
thickness was comparable to the interaction length ** x_{int}**, the
discussion given here explains the discrepancy. Detailed Monte Carlo
calculations indeed show that the fusion yield is overestimated by nearly
50% in our time-of-flight fusion measurement arrangement, compared to
model (b).

It is interesting to note that Eq. B.5 suggests that, within
model (b) and given the knowledge of
,
one can
determine both
and ** W** by the absolute measurement of the
thickness dependence of fusion yield