The variation of excitation energies \(E_{2^{+}}\) of yrast \(2^{+}\) states and ratios \(R=\frac{E_{4^{+}}}{E_{2^{+}}}\) with neutron number N, valence neutrons \(N_{n}\)/\(N_{\nu }\) and valence protons \(N_{p}\) /\(N_{\pi }\) of nuclei having valence nucleons in the same shell is studied. It is noticed that the depression in \(E_{2^{+}}\) and ascension in R appear in isobars that differ from the predictions of the \(N_{p}N_{n}\) scheme in which isotones are expected. The depression in \(E_{2^{+}}\) and ascension in R can be correlated with the number of valence nucleons \(M_{T}\), \(N_{p}=N_{n}\) and \(\left( N_{p}N_{n}\right) _{\max }\) depending on the isotope and mass region considered, where \(M_{T}\) is the half of the total number of valence nucleons that can be accommodated in the considered shell.

yrast \(2^{+}\)态的激发能\(E_{2^{+}}\)变化及比率\(R=\frac{E_{4^{+}}}{E_{ 2^{+}}}\) ，中子数为N，价中子\(N_{n}\) / \(N_{\nu }\)和价质子\(N_{p}\) / \(N_{研究了在同一壳层中具有价核子的核的\pi }\) 。值得注意的是，\(E_{2^{+}}\)中的下降和R中的上升出现在等压线中，与\(N_{p}N_{n}\)方案的预测不同，其中等压线为预期的。\(E_{2^{+}}\)中的凹陷和R中的上升可以与价核子数\(M_{T}\)、\(N_{p}=N_{n}\)相关和\(\left( N_{p}N_{n}\right) _{\max }\)取决于所考虑的同位素和质量区域，其中\(M_{T}\)是总数的一半可以容纳在所考虑的壳层中的价核子。