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The calcium isotopes are an ideal system to investigate the evolution of shell structure and magic numbers. Although the properties of surface nucleons in calcium have been well studied, probing the structure of deeply bound nucleons remains a challenge. Here, we report on the first measurement of unbound states in 53Ca and 55Ca, populated from 54,56Ca(p,pn) reactions at a beam energy of around 216 MeV/nucleon at the RIKEN Radioactive Isotopes Beam Factory. The resonance properties, partial cross sections, and momentum distributions of these unbound states were analyzed. Orbital angular momentum l assignments were extracted from momentum distributions based on calculations using the distorted wave impulse approximation (DWIA) reaction model. The resonances at excitation energies of 5516(41)keV in 53Ca and 6000(250)keV in 55Ca indicate a significant l =3 component, providing the first experimental evidence for the ν0f7/2 single-particle strength of unbound hole states in the neutron-rich Ca isotopes. The observed excitation energies and cross-sections point towards extremely localized and well separated strength distributions, with some fragmentation for the ν0f7/2 orbital in 55Ca. These results are in good agreement with predictions from shell-model calculations using the effective GXPF1Bs interaction and ab initio calculations and diverge markedly from the experimental distributions in the nickel isotones at Z=28.

Gamma decays were observed in 56Ca and 58Ca following quasi-free one-proton knockout reactions from 57,59Sc beams at ≈200 MeV/nucleon. For 56Ca, a γ ray transition was measured to be 1456(12) keV, while for 58Ca an indication for a transition was observed at 1115(34) keV. Both transitions were tentatively assigned as the 21+→0gs+ 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 21+ 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 0f5/2 and 0g9/2 orbitals, are almost degenerate. This degeneracy precludes the possibility for a doubly magic 60Ca and potentially drives the dripline of Ca isotopes to 70Ca or even beyond.

We report on the first γ-ray spectroscopy of 51,53K produced via the 52,54Ca(p,2p) reactions at ∼250 MeV/nucleon. Unambiguous final-state angular-momentum assignments were achieved for beam intensities down to few particles per second by using a new technique based on reaction vertex tracking combined with a thick liquid-hydrogen target. Through γ-ray spectroscopy and exclusive parallel momentum distribution analysis, 3/2+ ground states and 1/2+ first excited states in 51,53K were established quantifying the natural ordering of the 1d3/2 and 2s1/2 proton-hole states that are restored at N = 32 and 34. State-of-the-art ab initio calculations and shell-model calculations with improved phenomenological effective interactions reproduce the present data and predict consistently the increase of the E(1/21+) - E(3/21+) energy differences towards N = 40. Keywords: Spectroscopy, Shell evolution, 51K, 53K