Recently it is claimed that there is a significant systematic error from excited state contributions in the nucleus correlation functions by comparing with calculations using the exponential and wall source operators. However, the wall source result is obtained in much earlier time than the plateau region. In order to investigate the systematic error in the plateau region, we calculate the correlation functions with both the operators in quenched QCD at 0.8 GeV pion mass and in $N_f=2+1$ QCD at 0.7 GeV pion mass in high accuracy.
In this report we present preliminary results of those calculations, and show that the energy shift obtained from the two sources agree with each other, if those are determined from a region, where both the nucleon and two-nucleon correlation functions have plateaus.