Absolute optical oscillator strengths for the electronic excitation of atoms at high resolution: Experimental methods and measurements for helium

An alternative method is described for the measurement of absolute optical oscillator strengths (cross sections) for electronic excitation of free atoms and molecules throughout the discrete region of the valence-shell spectrum at high energy resolution (full width at half maximum of 0.048 eV). The technique, utilizing the virtual-photon field of a fast electron inelastically scattered at negligible momentum transfer, avoids many of the difficulties associated with the various direct optical techniques that have traditionally been used for absolute optical oscillator strength measurements. The method is also free of the bandwidth (line saturation) effects that can seriously limit the accuracy of photoabsorption cross-section measurements for discrete transitions of narrow linewidth obtained using the Beer-Lambert law [${\mathit{I}}_{0}$/I=exp(nl${\mathrm{\ensuremath{\sigma}}}_{\mathit{p}}$)]. Since the line-saturation effects are not widely appreciated and are only usually considered in the context of peak heights, a detailed analysis of this problem is presented, with consideration of the integrated cross section (oscillator strength) over the profile of each discrete peak.The suitability of the high-resolution dipole (e,e) method for general application to atomic and molecular electronic spectra is evaluated by test measurements of the absolute dipole (optical) oscillator strengths for the photoexcitation and photoionization of helium, since for this atom detailed quantum-mechanical calculations using highly correlated wave functions have been reported. The absolute scale is obtained from the Thomas-Reiche-Kuhn sum-rule normalization of the Bethe-Born transformed electron-energy-loss spectrum and does not involve the difficult determinations of photon flux or target density. The measured dipole oscillator strengths for helium excitation (1 $^{1}$S\ensuremath{\rightarrow}n $^{1}$P, n=2--7) are in excellent quantitative agreement with the calculations reported by Schiff and Pekeris [Phys. Rev. 134, A368 (1964)] and by Fernley, Taylor, and Seaton [J. Phys. B 20, 6457 (1987)]. The absolute measurements are also compared with other experimental and theoretical oscillator strength determinations for photoexcitation and photoionization processes in helium up to 180 eV, including the 2snp and 3snp autoionizing resonances in the 59--72-eV energy region.