Calculations of Energy Levels Using the Weakest Bound Electron Potential Model Theory

In this paper, we introduce a new method for calculation of energy levels in detail and give our results for several iso-spectrum-level series as examples: [He] 2s2p $\text{}^{1}P_{1}$, [He] 2s2p $\text{}^{3}P_{0}$, [He] 2s2p $\text{}^{3}P_{2}$, and [He] 2s3s $\text{}^{3}S_{1}$ series of Be-like sequence; [Ne] $\text{}3s^{2}3d$ $\text{}^{2}D_{3//2}$ series and [Ne] $3s^{2}3d$ $\text{}^{2}D_{5//2}$ series of Al-like sequences; [Ne] 4p $\text{}^{2}P_{1//2}$ series, [Ne] 5d $\text{}^{2}D_{5//2}$ series, and [Ne] 6f $\text{}^{2}F_{7//2}$ series of Na-like sequences. In the method I(Z)=$T_\text{lim} (Z)-T(Z,n)$, where I(Z), $T_\text{lim}(Z)$, and T(Z,n) denote ionization potential, series limit, and energy level of a given member, respectively. The expression of non-relativistic part of I(Z) is derived from weakest bound election potential model theory and relativistic effects of I(Z) are included by using a six-order polynomial in Z. Our results are compared with the experimental data and with those obtained by other theoretical method.