Range-Energy Relations for Protons in Various Substances

An expression is obtained for the range-energy relation $R\left(T_p\right)$ for protons ($T_p=\mathrm{proton}\mathrm{kinetic}\mathrm{energy}$) as a function of the mean excitation potential $I$ which enters into the Bethe-Bloch formula for the ionization loss $\frac{\mathrm{dE}}{\mathrm{dx}}$. The expression for $R\left(T_p\right)$ is obtained by an interpolation of the previously calculated range-energy relations for Be, Al, Cu, and Pb. The resulting expression for $R\left(T_p\right)$ can be used for any substance, provided an appropriate value of $I$ is assumed. Values are also obtained for the quantity $q=\left(\frac{I}{R}\right)\left(\frac{\mathrm{dR}}{\mathrm{dI}}\right)$ which gives the fractional change of $R$ for a small variation of the excitation potential $I$.