Analysis of level structure and monopole effects in Ca isotopes

Understanding the properties of nuclei near the double magic nucleus ⁴⁰Ca is crucial for both nuclear theory and experiments. In this study, Ca isotopes were investigated using an extended pairing-plus-quadrupole model with monopole corrections. The negative-parity states of ⁴⁴Ca were coupled with the intruder orbital \(g_{9/2}\) $g_{9/2}$ at 4 MeV. The values of \(E_{4+}\) $E_{4+}$ / \(E_{2+}\) $E_{2+}$ agree well with experimental trend from ⁴²Ca to ⁵⁰Ca, considering monopole effects between \(\nu f_{7/2}\) $\nu f_{7/2}$ and \(\nu p_{3/2}\) $\nu p_{3/2}$ ( \(\nu f_{5/2}\) $\nu f_{5/2}$ ). This monopole effect, determined from data of ⁴⁸Ca and ⁵⁰Ca, supports the proposed new nuclear magic number \(N = 34\) $N=34$ by predicting a high-energy \(2^{+}\) $2^{+}$ state in ⁵⁴Ca.