Anomalous behavior of the first excited $0^{+}$ state in $N\approx Z$ nuclei

A study of the energies of the first excited $0^{+}$ states in all even-even $Z⩾8$ nuclei reveals an anomalous behavior in some nuclei with $N=Z,Z\pm 2$. We analyze these irregularities in the framework of the shell model. It is shown that proton-neutron correlations play an important role in this phenomenon.

Figure 1

The energy ratio $R_0\equiv E(0_2^{+})/E(2_1^{+})$ as a function of the energy of the first excited $2_1^{+}$ state for all even-even nuclei with $Z\ge 8$. The points above the main trajectory are labeled by their ($Z,N$) values. The solid squares denote the experimental values and the open circles denote the calculated values for some of these nuclei (see text). The three unlabeled, calculated points that lie above the trajectory near E($2_1^{+}$) ∼ 1.0 and 1.3 MeV correspond to ${}^{44,46,48}\mathrm{Ti}$.

Figure 2

The energy ratio $R_{0/2}$ as a function of $R_{4/2}$ for sd and fp shell even-even nuclei with $8\ge Z\ge 30$. Those nuclei with anomalous $R_{0/2}$ values are labeled by their ($Z,N$) values.

Figure 3

Excitation energies of the first excited $0^{+}$ and $2^{+}$ states and as a function of $N\text{−}Z$ for the (a) Ne and Mg, (b) Ti, and (c) Cr and Fe isotopes. Ratio $R_0\equiv E(0_2^{+})/E(2_1^{+})$ as a function of $N\text{−}Z$ for the (d) Ne and Mg, (e) Ti, and (f) Cr and Fe isotopes. The solid and open symbols denote the experimental and calculated values, respectively. The cross symbols in (b) and (e) correspond to the second excited $0^{+}$ state in the Ti isotopes.

Figure 4

Correlation energy differences $\langle V_{\mathrm{int}}\rangle$ and the corresponding $T=0$ and $T=1$ components for the (a) Ne and (b) Mg isotopes.

Figure 5

(a) Excitation energies of the $0_2^{+}$ and $2_1^{+}$ states and the corresponding $R_{0/2}$ ratios for the $N=Z$ sd-shell nuclei. The solid and open symbols denote the experimental and calculated values, respectively. (b) Correlation energy differences $\langle V_{\mathrm{int}}\rangle$ and the corresponding $T=0$ and $T=1$ components for the $N=Z$ sd-shell nuclei.