Level Structures of ${}^{56,58}$Ca Cast Doubt on a doubly magic ${}^{60}$Ca

Abstract

Gamma decays were observed in ${}^{56}$Ca and ${}^{58}$Ca following quasi-free one-proton knockout reactions from ${}^{57,59}$Sc beams at $\approx 200$ MeV/nucleon. For ${}^{56}$Ca, a $\gamma$ ray transition was measured to be 1456(12) keV, while for ${}^{58}$Ca an indication for a transition was observed at 1115(34) keV. Both transitions were tentatively assigned as the $2_1^{+}\to 0_{gs}^{+}$ decays, and were compared to results from ab initio and conventional shell-model approaches. A shell-model calculation in a wide model space with a marginally modified effective nucleon-nucleon interaction depicts excellent agreement with experiment for $2_1^{+}$ level energies, two-neutron separation energies, and reaction cross sections, corroborating the formation of a new nuclear shell above the $N$ = 34 shell. Its constituents, the $0f_{5/2}$ and $0g_{9/2}$ orbitals, are almost degenerate. This degeneracy precludes the possibility for a doubly magic ${}^{60}$Ca and potentially drives the dripline of Ca isotopes to ${}^{70}$Ca or even beyond.

8 pages, 3 figures

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