Structure of ${}^{36}\mathrm{Ca}$ under the Coulomb Magnifying Glass

Detailed spectroscopy of the neutron-deficient nucleus ${}^{36}\mathrm{Ca}$ was obtained up to 9 MeV using the ${}^{37}\mathrm{Ca}(p,d){}^{36}\mathrm{Ca}$ and the ${}^{38}\mathrm{Ca}(p,t){}^{36}\mathrm{Ca}$ 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. Our main findings are (i) a similar shift in energy for the $1_1^{+}$ and $2_1^{+}$ states by about $-250\mathrm{keV}$, as compared with the mirror nucleus ${}^{36}\mathrm{S}$; (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 ${}^{36}\mathrm{S}$; 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 $-516(130)\mathrm{keV}$ for the former. This feature is reproduced by shell model calculations, using the $sd\text{−}pf$ 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 ${}^{36}\mathrm{Ca}$ (${}^{36}\mathrm{S}$). This mirror system has the largest MEDs ever observed, if one excludes the few cases induced by the effect of the continuum.

Figure 1

(a) Excitation energy spectrum $E_x$ of ${}^{36}\mathrm{Ca}$ obtained from the $(p,d)$ transfer reaction with a gate on outgoing Ca, K, and Ar. (b) One-proton energy spectrum [to which ${\mathrm{S}}_p({}^{36}\mathrm{Ca})=2599.6(61)\mathrm{keV}$ has been added] obtained from the $(p,d)$ reaction with a gate on outgoing K isotopes. $E_x$ spectrum from the $(p,t)$ reaction and gated on outgoing Ca is shown in (c), while the one in (d) is gated on outgoing Ar and the detection of one proton with a center-of-mass energy between 1 and 2 MeV. Individual contributions to the fits are shown with different color codes.

Figure 2

Differential cross sections of the states identified in ${}^{36}\mathrm{Ca}$ using the ${}^{37}\mathrm{Ca}(p,d){}^{36}\mathrm{Ca}$ and ${}^{38}\mathrm{Ca}(p,t){}^{36}\mathrm{Ca}$ transfer reactions are shown in (a)–(d) and (e),(f), respectively. (a)–(d) Blue (green) full lines show the results of the $L=2$ ($L=0$) DWBA calculations fitted to the data. (e),(f) Green and blue full lines correspond to results of the DWBA plus TNA calculations assuming $L=0$ and $L=2$ transfers, respectively. Panel (e) used TNA values directly extracted from the present shell-model calculations, while (f) is a result of fitted values (see text for details).

Figure 3

Partial level scheme of the mirror pair ${}^{36}\mathrm{Ca}\text{−}{}^{36}\mathrm{S}$ obtained experimentally (Exp.) and from shell model calculations (Th.). Energy values for ${}^{36}\mathrm{Ca}$ are those obtained in this Letter.