Interpolation of oscillator-strength sum-rule data using scaled hydrogenic moments: Stopping and straggling mean excitation energies

The derivative of the quantity S(k), where S(k) is the sum of dipole oscillator strengths weighted by the kth power of the excitation energy, provides a convenient technique for calculating stopping and straggling mean excitation energies. This implies knowledge of the S(k) for all k within a certain range that is usually obtained by interpolating the S(k) values available for integer k. A method that relates the components of S(k) for equivalent electrons of a target atom, S/sub j/(k), to that of a hydrogenic ion with nuclear charge number Z/sub j/(k) is constructed. This approach requires certain matrix elements and expectation values involving all occupied target orbitals plus any unoccupied target orbitals that have the same principal quantum number as an occupied orbital and a nonzero dipole matrix element with this occupied orbital. It is shown here that the resulting curve of Z/sub j/(k) versus k can be interpolated with greater accuracy than can S(k) or S/sub j/(k). The relationship between S/sub j/(k) and Z/sub j/(k) constructed here implies an S(k) curve for all k and, consequently, the stopping and straggling mean excitation energies. The average errors for interpolating Z/sub j/(k) as compared to S/sub j/(k) are improved by factors of 2--4 for a large range of targets. However, there are individual targets for which this error trend is reversed