Rigorous upper and lower bounds to dipole oscillator strengths have been calculated for 17 of the low-lying singlet and triplet transitions in He and ${\mathrm{Li}}^{+}$ using accurate Hylleraas-type wave functions of some 135-138 terms. About a third of the calculated $f$ values can be guaranteed to 1% or better, and in the best case (${\mathrm{Li}}^{+} 2{}_{}{}^3{}_{}{}^{}S\to 2{}_{}{}^3{}_{}{}^{}P$) the bounds tighten to about 0.05%, some two orders of magnitude better than corresponding experimental determinations. By comparing with an extensive compilation of experimental results, we find the quality of the rigorous bounds to generally match or exceed that of experimental determinations, and about a dozen experiments can be ruled out entirely. Trends with respect to nuclear charge, spin multiplicity, and principal quantum number are examined, and special emphasis is given throughout to sources of uncertainty in the calculated oscillator strengths which are revealed by the error-bound formulas.

• Received 20 August 1973

DOI:https://doi.org/10.1103/PhysRevA.9.118