Test of the validity of Bragg’s rule for mean excitation energies of small molecules and ions

Abstract

The purpose of this paper is to identify the fragmentation patterns of molecules and ions that give the best fulfilment of a Bragg’s rule estimation of the mean excitation energy of the molecules and ions. We investigate the effect of chemical binding on the validity of Bragg’s rule for the calculation of stopping cross sections and mean excitation energies. As test cases we use a series of small molecules and molecular ions, primarily carbon and nitrogen hydrides. We are using several nuclear fragments of the same molecule or ion to test the dependence of Bragg’s rule on the binding energy of the molecules/ions. The mean excitation energies of the molecules/ions and their fragments are computed with the same method. We find that neglect of chemical binding nearly always results in an underestimation of the mean excitation energies. We also find that the fully atomic decomposition of any molecule, but a diatomic molecule never gives the best fulfilment of Bragg’s rule. The best fulfilment of Bragg’s rule is obtained when using a fragmentation pattern with as few bonds as possible broken and when the choice of fragments is guided by chemical knowledge and intuition. By investigating several alternative fragmentation patterns for a molecule/ion, guidelines for choice of optimal Bragg rule fragmentation are suggested. Using the best fragmentation pattern for the tested molecules and ions, the error in the mean excitation energy is of the order of 5% or less, implying an error of not more than 1% in the pure Bethe stopping power because of applying Bragg’s rule.