Accurate Evaluation of Stopping and Straggling Mean Excitation Energies for N, O, H 2 , N 2 , O 2 , NO, NH 3 , H 2 O, and N 2 O Using Dipole Oscillator Strength Distributions: A Test of the Validity of Bragg's Rule

Abstract

Accurate values of the mean excitation energy I/sub 0/ (occurring in the Bethe stopping cross section equation for fast charged particles) and the dipole oscillator strength sum S/sub 1/ and mean excitation energy I/sub 1/ (appearing in the equation for straggling given by Fano) have been determined for N, O, H/sub 2/, O/sub 2/, O/sub 2/, NH/sub 3/, H/sub 2/O, NO, and N/sub 2/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 H/sub 2/, N/sub 2/, and O/sub 2/ as elemental values in the additivity relations, the additivity estimates of S/sub 1/, I/sub 1/, and I/sub 0/ obtained for N, O, NH/sub 3/, H/sub 2/O, NO, and N/sub 2/O agree with the accurate results to within 0.4, 0.9, and 4%, respectively. On the other hand, for the H atommore » large discrepancies (20--30%) between the accurate values for S/sub 1/, I/sub 1/, and I/sub 0/ 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 H/sub 2/, N/sub 2/, and O/sub 2/ calculated Bethe stopping cross sections are compared with experimental results and are used to discuss shell corrections to the Bethe stopping cross section equation.« less