Bounds on mean excitation energies in terms of oscillator-strength moments

The logarithmic mean excitation energies that determine, for fast charged particles, the total inelastic-scattering cross section, the stopping power, and the straggling are bounded from above and below by simple expressions involving moments of the oscillator-strength distribution. A general condition under which the set of elementary inequalities gives tight bounds is indicated, and is illustrated in several examples. Effective oscillator-strength distributions that are constructed on the basis of variational principles lead to tighter bounds in terms of some of the moments and the oscillator strengths for some discrete excitations