Nuclear Structure in Even-Even Nuclei, $24\le Z\le 72$

Analysis of the spectra of excited nuclei has been used for decades to reveal trends and build models. Power regressions of the form $E(J)=a(\sqrt {J(J+1)} )^b$ fitted to the \textit{yrast} line of isotopes reveal an average $b$ of $_{\sim }\raise0.5ex\hbox{$\scriptstyle 4$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 3$}$. It should be noted that this is the value predicted for large angular momenta by the Variable Moment of Inertia model [1,2]. A second plot of $\mathop R\nolimits_J \quad (\mathop R\nolimits_J =\mathop E\nolimits_{\mathop J\nolimits_1^+ } /\mathop E\nolimits_{\mathop 2\nolimits_1^+ } )$ vs. $J$ reveals curves described by power regressions where $0.66\le b\le 1.81$. Graphs of $b$ vs. neutron number ($N)$ reveal V-shaped patterns for many nuclei, with the lowest exponent corresponding to a magic $N$. In addition, sharp jumps in exponents are seen at the $(N=88)\to (N=90)$ transition point in several nuclei. A third chart -- an abbreviated energy level diagram including $\mathop 0\nolimits_1^+ $,$\mathop 0\nolimits_2^+ $,$\mathop 2\nolimits_1^+ $,$\mathop 2\nolimits_2^+ $, and $\mathop 4\nolimits_1^+ $states illustrates the energy increases at magic numbers, along with the near-degenerate two-phonon triplet of $\mathop 0\nolimits_2^+ $, $\mathop 2\nolimits_2^+ $, and $\mathop 4\nolimits_1^+ $ - most clearly observed in isotopes of Z=28,34,36,38,44,46, and 48. Lastly, a fourth chart of $\mathop E\nolimits_{\mathop 3\nolimits_1^- } $ against $\mathop E\nolimits_{\mathop 2\nolimits_1^+ } $ shows positive correlation that is well described by equation $E(\mathop 3\nolimits^- )=A-\frac{\mathop B\nolimits^2 }{E(\mathop 2\nolimits_1^+ )}$ - not only for Z=54 [3] but also for Z=36,42-52, and 68. Data obtained through ENSDF database. [1] M.A.J.Mariscotti,G.Sharff-Goldhaber and B.Buck, \textit{Phys.Rev.}\textbf{178,1864}(1969). [2] M.I. Stockmann and V.G.Zelevinsky, \textit{Phys.Lett.}\textbf{41B},19(1972). [3] W.F. Mueller et al.,\textit{Phys.Rev.C} \textbf{73}, 014316(2006).