Bethe stopping-power formula for structured projectiles
- Sandia National Laboratories, Division 9571, Albuquerque, New Mexico87185-1187 (United States)
It is known that the energy loss in ion-atom collisions is dominated by elastic scattering of one collision partner and excitation or ionization of the second. This is true for both structured and structureless projectiles. Here, I show that this fact leads to a relatively simple extension of the Bethe stopping-power formula for structureless projectiles to structured projectiles. The formula replaces the Bethe mean excitation energy with two other mean energies which reflect the elastic scattering factor of the otherwise structureless projectile. The expression is symmetrical in the center-of-mass system. The formula is in excellent agreement with numerical calculations, when the numerical calculations are asymptotic. To obtain the extended Bethe stopping formula, it is necessary to evaluate integrals over energy and momentum transfer involving generalized oscillator strengths, properly treating the energy-dependent lower limit in the momentum transfer integral. I do this by a constructive procedure using two cutoffs (instead of the traditional one) in momentum transfer. Peek had earlier developed a procedure to address the question of whether the Bethe mean excitation energy calculated with optical oscillator strengths is the same as the Bethe mean excitation energy appearing in the stopping power formula. I show that the result of the constructive procedure agrees with the result of Peek in the asymptotic limit, and I develop a criterion to determine the asymptotic limit. {copyright} {ital 1998} {ital The American Physical Society}
- OSTI ID:
- 625867
- Journal Information:
- Physical Review A, Journal Name: Physical Review A Journal Issue: 4 Vol. 57; ISSN 1050-2947; ISSN PLRAAN
- Country of Publication:
- United States
- Language:
- English
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