We are very grateful to the RIKEN Nishina Center accelerator staff for providing the stable and high-intensity zinc beam and to the BigRIPS team for the smooth operation of the secondary beams. The development of MINOS has been supported by the European Research Council through the ERC Grant No. MINOS-258567. Green's function calculations were performed using HPC resources from GENCI-TGCC, France (Projects A0030507392 and A0050507392) and from the DiRAC Data Intensive service at Leicester, UK (funded by the UK BEIS via STFC capital grants ST/K000373/1 and ST/R002363/1 and STFC DiRAC Operations grant ST/R001014/1). This work (C. B.) was also supported by the United Kingdom Science and Technology Facilities Council (STFC) under Grants No. ST/P005314/1 and No. ST/L005816/1. K. O. acknowledges the support by Grant-in-Aid for Scientific Research JP16K05352. Y. L. S. acknowledges the support of Marie Skłodowska-Curie Individual Fellowship (H2020-MSCA-IF-2015-705023) from the European Union and the support from the Helmholtz International Center for FAIR. The valuable discussions with C. Qi are gratefully acknowledged. H. N. L. acknowledges the support from the Enhanced Eurotalents program (PCOFUND-GA-2013-600382) co-funded by CEA and the European Union. H. N. L. and A. O. acknowledge the support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project No. 279384907-SFB 1245. Y. L. S. and A. O. acknowledge the support from the Alexander von Humboldt Foundation. L. X. C. and B. D. L would like to thank MOST for its support through the Physics Development Program Grant No. ĐTĐLCN.25/18. I.G. has been supported by HIC for FAIR and HRZZ under project No. 1257 and 7194. K. I. H., D. K. and S. Y. P. acknowledge the support from the NRF grant funded by the Korea government (No. 2017R1A2B2012382 and 2019M7A1A1033186). F. B. acknowledge the support from the RIKEN Special Postdoctoral Researcher Program. D.S. was supported by projects No. GINOP-2.3.3-15-2016-00034 and No. K128947. V. V. acknowledges support from the Spanish Ministerio de Economía y Competitividad under Contract No. FPA2017-84756-C4-2-P. V. W. acknowledges support from BMBF grants 05P15RDFN1, 05P19RDFN1 and DFG grant SFB 1245. P. K. acknowledges support from HGS-HIRe and BMBF grant 05P19RDFN1. This work was also supported by NKFIH (128072).

We report on the first γ-ray spectroscopy of K produced via the Ca(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 K were established quantifying the natural ordering of the 1d and 2s 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(1/2 ) - E(3/2 ) energy differences towards N = 40.

7 pags., 3 figs., 1 tab.