Correlation effects in sequential energy branching: an exact model of the Fano statistics

TL;DR

This paper presents an exact model for correlation effects in energy branching processes, showing that correlations significantly influence the Fano factor and impact the energy resolution in semiconductor gamma detectors.

Contribution

It introduces an exactly solvable model that accounts for correlations in energy branching, improving the accuracy of Fano factor estimates over traditional uncorrelated models.

Findings

Correlation effects significantly alter the Fano factor.

Nearest-neighbor correlations improve Fano factor accuracy.

Implications for energy resolution in gamma detectors.

Abstract

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.