Lewis theory for energy straggling in thin layers

A Lewis-moments theory for energy straggling is developed that underpins the observed numerical accuracy of moment-preserving approximations for computing charged particle energy-loss distributions in thin layers. Specifically, we prove that for a certain class of straggling models, if an approximate straggling model has identical collisional energy-loss moments as the exact or analog model through a fixed order N, then the corresponding energy-moments of the energy-loss distributions are identical to order N.