Accurate values of the mean excitation energy I0 (occurring in the Bethe stopping cross section equation for fast charged particles) and the dipole oscillator strength sum S1 and mean excitation energy I1 (appearing in the equation for straggling given by Fano) have been determined for N, O, H2, N2, O2, NH3, H2 O, NO, and N2 O using dipole oscillator strength distributions. For energies for which the Bethe stopping theory is valid these results allow a quantitative test to be made of the reliability of Bragg's rule and of the analogous additivity rule for straggling. Difficulties arising from problems associated with the use of experimental stopping cross sections and the treatment of shell corrections, that have introduced uncertainty in previous studies of Bragg's rule, are avoided in the present work. Using the accurate results obtained for H2, N2, and O2 as elemental values in the additivity relations, the additivity estimates of S1, I1, and I0 obtained for N, O, NH3, H2 O, NO, and N2 O agree with the accurate results to within 0.4, 0.9, and 4%, respectively. On the other hand, for the H atom large discrepancies (20-30%) between the accurate values for S1, I1, and I0 and the estimates obtained by additivity occur and are due to major modifications in the electronic wavefunction in regions close to the proton that are caused by chemical binding. For heavier atoms this effect is relatively unimportant. For H2, N2, and O2 calculated Bethe stopping cross sections are compared with experimental results and are used to discuss shell corrections to the Bethe stopping cross section equation.

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