The structure of ${}^{36}$Ca under the Coulomb magnifying glass

Abstract

Detailed spectroscopy of the neutron-deficient nucleus ${}^{36}$Ca was obtained up to 9 MeV using the ${}^{37}$Ca($p$,$d$)${}^{36}$Ca and the ${}^{38}$Ca($p$,$t$)${}^{36}$Ca transfer reactions. The radioactive nuclei, produced by the LISE spectrometer at GANIL, interacted with the protons of the liquid Hydrogen target CRYPTA, to produce light ejectiles (the deuteron $d$ or triton $t$) that were detected in the MUST2 detector array, in coincidence with the heavy residues %identified by a zero degree detection system. %States have been measured up to 9 MeV. Our main findings are: i) a similar shift in energy for the 1${}_1^{+}$ and 2${}_1^{+}$ states by about -250 keV, as compared to the mirror nucleus ${}^{36}$S, ii) the discovery of an intruder 0${}_2^{+}$ state at 2.83(13) MeV, which appears below the first 2${}^{+}$ state, in contradiction with the situation in ${}^{36}$S, and iii) a tentative 0${}_3^{+}$ state at 4.83(17) MeV, proposed to exhibit a bubble structure with two neutron vacancies in the 2s${}_{1/2}$ orbit. The inversion between the 0${}_2^{+}$ and 2${}_1^{+}$ states is due to the large mirror energy difference (MED) of -516(130) keV for the former. This feature is reproduced by Shell Model (SM) calculations, using the $sd$-$pf$ valence space, predicting an almost pure intruder nature for the 0${}_2^{+}$ state, with two protons (neutrons) being excited across the $Z$=20 magic closure in ${}^{36}$Ca (${}^{36}$S). This mirror system has the largest MEDs ever observed, if one excludes the few cases induced by the effect of the continuum.

Paper of 5 pages, 3 figures. Contains also a supplementary material of 3 pages and 4 figures