$N=16$ Magicity Revealed at the Proton Drip Line through the Study of ${}^{35}\mathrm{Ca}$

The last proton bound calcium isotope ${}^{35}\mathrm{Ca}$ has been studied for the first time, using the ${}^{37}\mathrm{Ca}(p,t){}^{35}\mathrm{Ca}$ two neutron transfer reaction. The radioactive ${}^{37}\mathrm{Ca}$ nuclei, produced by the LISE spectrometer at GANIL, interacted with the protons of the liquid hydrogen target CRYPTA, to produce tritons $t$ that were detected in the MUST2 detector array, in coincidence with the heavy residues Ca or Ar. The atomic mass of ${}^{35}\mathrm{Ca}$ and the energy of its first $3/2^{+}$ state are reported. A large $N=16$ gap of 4.61(11) MeV is deduced from the mass measurement, which together with other measured properties, makes ${}^{36}\mathrm{Ca}$ a doubly magic nucleus. The $N=16$ shell gaps in ${}^{36}\mathrm{Ca}$ and ${}^{24}\mathrm{O}$ are of similar amplitude, at both edges of the valley of stability. This feature is discussed in terms of nuclear forces involved, within state-of-the-art shell model calculations. Even though the global agreement with data is quite convincing, the calculations underestimate the size of the $N=16$ gap in ${}^{36}\mathrm{Ca}$ by 840 keV.

Figure 1

(a),(b) Excitation energy spectrum of ${}^{35}\mathrm{Ca}$ obtained from the ${}^{37}\mathrm{Ca}(p,t)$ transfer reaction with a gate on outgoing Ca (a) and Ar (b). The red lines show the best fit obtained while individual contributions are shown with different color. (c),(d) The experimental differential cross section obtained for the ground state (c) and the first excited state (d) identified in ${}^{35}\mathrm{Ca}$ using the ${}^{37}\mathrm{Ca}(p,t){}^{35}\mathrm{Ca}$ reaction is shown with the black points. A fit to the cross section is shown using the DWBA calculations performed for an $L=0$ (green) and an $L=2$ (blue) transfer.

Figure 2

Top: experimental (black) and theoretical (red) one-neutron separation energy $S_n$ along the calcium isotopic chain. Bottom: $\mathrm{\Delta }{S}_n$ and energy of the first $2^{+}$ excited state of even-even Ca isotopes. Theoretical $\mathrm{\Delta }{S}_n$ values are shown in red.

Figure 3

The effective single particle energies (ESPE) of the neutron $d_{5/2}$, $s_{1/2}$, and $d_{3/2}$ orbitals at $N=16$ in the $sdpf\text{−}u\text{−}mix$ interaction are shown with the full colored line, relative to the $s_{1/2}$ one. The red dashed lines shows experimental $\mathrm{\Delta }{S}_n$ values along $N=16$ at subshell closures.