The variation relationship of ion yield for xenon atom under the single ionization in the mid-infrared band versus laser intensity is measured systematically by using the wavelength-tunable strong femtosecond laser pulses. The theoretical calculations based on the PPT and ADK models are done and the theoretical calculation results are compared with the experimental results. It is found that all the calculation results based on the ADK model are consistent with the experimental results in the whole measurement region, while the calculation results based on the ADK model do only when the wavelength is long enough and the intensity is strong enough. The unification for the two models in the deep tunneling ionization regime and the validity for the two models in describing the single ionization of atoms are directly verified in experiments, and thus these two models can be used as a precise tool to calibrate the absolute intensity of long wavelength laser pulses.