Moment theory bounds on the mean energies of stopping, straggling, and molecular excitation

Abstract

Quantum mechanical sum rules and results from the theory of moments are employed in the construction of rigorous upper and lower bounds on the mean energies of stopping, straggling, and molecular excitation appropriate for the passage of fast charged particles through matter. The bounds are constructed with effective excitation spectra chosen to satisfy known oscillator strength sum rules, in accordance with the dictates of the theory of moments, thereby circumventing the formally required spectral distribution of dipole oscillator strengths. Accurate results are obtained in the cases of atomic and molecular hydrogen and the inert gases with a minimum of computational effort, demonstrating that the moment theory approach for determining charged particle mean penetration energies compares favourably with ab initio theoretical, semi-empirical, and closely related linear programming methods.