Binding-energy independence of reduced single particle strengths derived from $(p,d)$ reactions

An overall reduction factor (ORF) is introduced for studying the quenching of single particle strengths through nucleon transfer reactions. The ORF includes contributions of all the probed bound states of the residual nucleus in a transfer reaction and permits a proper comparison with results of inclusive knockout reactions. A systematic analysis is made with 103 sets of angular distribution data of $(p,d)$ reactions on 21 even-even targets with atomic mass numbers from 8 to 56 using the consistent three-body model reaction methodology proposed in [J. Lee, J.A. Tostevin, B.A. Brown, et al., Phys. Rev. C 73, 044608 (2006)]. The extracted ORFs are found to be nearly independent on the nuclear isospin asymmetry, which is different from the systematics of inclusive knockout reactions but is consistent with the recent measurement of $(d,t)$, $(d,3He)$, $(p,2p)$, and $(p,pn)$ reactions on nitrogen and oxygen isotopes and textit{ab initio} calculations.