Extension of the invariant embedding method for the calculation of particle fluctuations

Paper i proceeding, 2009

Invariant embedding theory is an alternative formulation of particle transport theory. So far the method has exclusively been used for calculating first moments, i.e. expectations. The present paper extends the method to treat fluctuations. A probability balance equation is derived in the traditional invariant embedding approach from which equations for the first and second order densities are derived. It is shown that only the equations for the first order densities are non-linear, while subsequent order densities obey linear equations. With the method, correlations between particles at two different energies and angles, or the higher moments of the emitted multiplicity distribution, such as the variance, from a target bombarded by incident particles can be determined. The approach is illustrated by a simple forward backward scattering model. The possibility of applying the method to finite sized slabs and spheres is also discussed.