Proton Stopping Powers in Some Low-Z Elements

Abstract

For some calculations, the proton stopping power in tissue must be known accurately. The composition of tissue was assumed to be constituted of 11 elements; the proton stopping powers were available for hydrogen, carbon, nitrogen, and oxygen. Those for the remaining 7 elements for the energy range 0.5 to 10 MeV at intervals of 0.5 MeV are evaluated and presented in this paper. Corrections such as the Barkas effect correction, Bloch's correction, and shell correction are evaluated and used in the calculation of proton stopping powers. Corrections for the Bethe formula for heavy ions were suggested by Barkas et al. (Phys. Rev. Lett. 11, 26, 1963) when they observed that the stopping powers for positive ions were larger than those for the negative ions with identical velocities. They suggested that a charge-dependent correction term be incorporated in the Bethe formula. Theoretical estimates of this correction derived by Ashley et al. (Phys. Rev. 85, 2392-2397, 1972) were used in the calculation of the Barkas effect. The Barkas effect correction depends on projectile velocity and Z. It decreases with energy. To account for the discrepancy between the classical and the quantum mechanical treatment of the Bethe formula, Bloch (Ann. Phys. 285, Chap. 18, 1933) suggested a correction to the stopping-power formula; this correction is also evaluated in this paper. Bloch's correction also decreases with energy. The shell correction needed for the binding of the electrons in the target atom is also calculated using Walske's asymptotic formula taking into account the screening effect of the atomic electrons of the K and L shells of the target atom. A computer program was written to calculate the stopping powers of protons with all these corrections for seven low-Z elements which are part of the tissue composition. These values are compared with those of other authors, and fairly good agreement is found. The lack of sufficient experimental information and uncertainty in the mean excitation energy values and shell corrections area are some of the causes for the differences in the evaluation of stopping power by the different authors.