  Correlation effects in in the fluctuation of the number of particles in the
process of energy branching by sequential impact ionizations are studied using
an exactly soluble model of random parking on a line. The Fano factor F
calculated in an uncorrelated final-state "shot-glass" model does not give an
accurate answer even with the exact gap-distribution statistics. Allowing for
the nearest-neighbor correlation effects gives a correction to F that brings F
very close to its exact value. We discuss the implications of our results for
energy resolution of semiconductor gamma detectors, where the value of F is of
the essence. We argue that F is controlled by correlations in the cascade
energy branching process and hence the widely used final-state model estimates
are not reliable -- especially in the practically relevant cases when the
energy branching is terminated by competition between impact ionization and
phonon emission.
