The proton stopping cross section of liquid water for the energy range from 40 keV to 10 MeV is calculated by applying the modified local-plasma model and employing a simple model of liquid water. The calculated stopping cross section of liquid water is about 5.6% to 14% lower than the calculated vapor-state results for the range of 80 to 500 keV and is about 8.5% to. 13.4% lower than measured vapor-state results. The present results agree well with the measurements for ice crystals. The mechanism of this physical-state effect is also presented.

Molecular mean excitation energies for ionic bonded molecules calculated according to the local plasma approximation are compared to the Bragg rule. Adjustments of 15% are calculated for LiF in agreement with experiments while 6% adjustments are predicted for HF and 3% for LiH.

Mean excitation energies for stopping by isolated atoms are accurately predicted by the plasma absorption spectrum associated with the atomic orbitals when the plasma frequency shift due to individual electron motion proposed by Pines [Phys. Rev. 92, 626 (1953)] is incorporated.

A modified local-plasma model, based on the works of Lindhard and Winther, and Bethe, Brown, and Walske is established. The Gordon-Kim model for molecular-electron density is used to calculate stopping power of N2, 02, and water vapor for protons of energy ranging from 40 keV to 2.5 MeV, resulting in good agreement with experimental data. Deviations from Bragg's rule are evaluated and are discussed under the present theoretical model.

The basic model of Lindhard and Scharff, known as the local plasma model, is utilized to study the effects of the chemical and physical state of the medium on its stopping power. Unlike previous work with the local plasma model, in which individual electron shifts in the plasma frequency were estimated empirically, the Pines correction derived for a degenerate Fermi gas is shown herein to provide a reasonable estimate even on the atomic scale. Thus, the model is moved to a completely theoretical base requiring no empirical adjustments, adjustments characteristics of past applications. The principal remaining error is in the overestimation of the low-energy absorption properties characteristic of the plasma model in the region of the atomic discrete spectrum, although higher energy phenomena are accurately represented and even excitation-to-ionization ratios are given with fair accuracy. Mean excitation energies for covalently bonded gases and solids, ionic gases and crystals, and metals are calculated using first-order models of the bonded states for which reasonable agreement with the recently evaluated data of Seltzer and Berger is obtained. Hence the methods described herein allow reasonable estimates of mean excitation energy for any physical-chemical combination of material media for stopping power applications.