For the soft process, the

particle spectrum appears with the characteristics of thermal emission phenomenon.

For example, if we assume that a QD has an equidistant (degenerate) single

particle spectrum with the gap [[delta].sub.e] = 30 meV for electrons and [[delta].sub.h] = 15meV for holes and U = 200 meV depth, the number of respective single particle states is [N.sub.e] = 20 and [N.sub.h] = 80 while the total number of excitonic states is approximately [N.sub.e][N.sub.h] = 1600.

At what equivalent concentration level is the particle spectrum compromised by the remote scattering of beam electrons into the skirt?

After determining the operational blank, a representative spectrum should be compared to each measured particle spectrum. Examples are shown for several of the particles in Fig.

For sufficiently small particles, the remote skirt spectrum from the bulk carbon substrate will eventually dominate the particle spectrum. After the operational parameters of beam energy, environmental gas species, gas pressure, and beam path length have been chosen, the remaining variable to reduce the skirt contribution to the composite spectrum is to modify the substrate itself.

Now let us analyze the particle spectrum associated with the deformed Lagrangian (13).

Since we are interested in the particle spectrum we have to look at the pole structure of the saturated propagator, in this vein it is not difficult to see that there is a simple pole at [k.sup.2] = 0 (for all N) and that there are additional poles identified as the zeros of [F.sub.N]([k.sup.2]; 0; 1).