Upper and Lower Bounds to Atomic and Molecular Properties. I. Be-Sequence Oscillator Strengths (Dipole-Length Formulation) for the1s 22s 2S1−1s 22s 2p P1Transition

Wave functions, which include interelectron coordinates $r_{\mathrm{ij}}$ explicitly, are calculated for the $1s^{ 2}2s^{ 2}{}_{}{}^1{}_{}{}^{}S$ and $1s^{ 2}2s 2p {}_{}{}^1{}_{}{}^{}P$ states of Be I, C III, and O V. These wave functions are used to calculate oscillator strengths, including upper and lower bounds, for the lowest ${}_{}{}^1{}_{}{}^{}S-{}_{}{}^1{}_{}{}^{}P$ transition. Interpolation techniques are used to make a graphical study of the oscillator-strength behavior along the isoelectronic sequence. Comparisons are made with previous experimental and theoretical results. The results of this study are oscillator strengths for the $1s^{ 2}2s^{ 2} {}_{}{}^1{}_{}{}^{}S\to 1s^{ 2}2s 2p {}_{}{}^1{}_{}{}^{}P$ Be isoelectronic sequence with rigorous upper and lower bounds of (7-10)% and probable accuracy ≤ 2%.