From comparing the energy expression within the quantum defect theory (QDT) and the theory of the weakest bound electron potential model (WBEPM), we try to introduce a ad-justing coefficient k which can reflect the screening effects in the real atomic or ionic system. The calculation of expectation values of the radius and others shows that the coefficient k in-troduced not only makes accurate the describing of Rydbery series when using the parameters of isoelectronic series ; but also reveals the difference and relation between these two series. Another main content of this paper is about the adjustment of the number of nodes in eigen-functions of the valence electrons for atoms.