Using excitation from five dye lasers, the Yb+ Rydberg series of np(1/
2) and np(3/2) have been achieved. Abnormal branching ratios of np(1/2
):np(3/2) excited from Yb+ 7s(1/2) are found. In the relativistic cent
ral-field independent-particle approximation, oscillator-strength dist
ributions of Yb+, Ba+, and Sr+ are calculated, respectively. The calcu
lated results are in good agreement with our experiment on Yb+ and pre
vious experiments on Ba+ and Sr+ where abnormal branching ratios were
also found. We have found that the abnormal branching ratios are due t
o the appearance of Cooper minima or shape resonances. The results can
be used to estimate the oscillator strength of unsymmetric double Ryd
berg states.