Probing the $N=32$ Shell Closure below the Magic Proton Number $Z=20$: Mass Measurements of the Exotic Isotopes ${}^{52,53}\mathrm{K}$

The recently confirmed neutron-shell closure at $N=32$ has been investigated for the first time below the magic proton number $Z=20$ with mass measurements of the exotic isotopes ${}^{52,53}\mathrm{K}$, the latter being the shortest-lived nuclide investigated at the online mass spectrometer ISOLTRAP. The resulting two-neutron separation energies reveal a 3 MeV shell gap at $N=32$, slightly lower than for ${}^{52}\mathrm{Ca}$, highlighting the doubly magic nature of this nuclide. Skyrme-Hartree-Fock-Bogoliubov and ab initio Gorkov-Green function calculations are challenged by the new measurements but reproduce qualitatively the observed shell effect.

Figure 1

Sketch of the part of the ISOLTRAP setup used for the measurements reported here. For details, see the text.

Figure 2

Time-of-flight spectra for nuclides at mass numbers $A=52$ (top) and $A=53$ (bottom). Vertical lines indicate the ${\mathrm{Cr}}^{+}$ fit ranges.

Figure 3

Two-neutron separation energies for the $Z=18–21$ isotopes from the atomic-mass evaluation 2012 (AME2012, open symbols) [21], recent measurements of ${}^{48,49}\mathrm{Ar}$ by Meisel et al. [24], and the ISOLTRAP data (from Ref. [11] and this work).

Figure 4

Empirical shell gaps for $N=28$ and $N=32$ from the atomic-mass evaluation 2012 (AME2012, open symbols) [21] and the ISOLTRAP data (from Ref. [11] and this work).

Figure 5

Two-neutron separation energies for the isotopic chains of potassium (left axes) and calcium (right axes); note the shifted scales. Open symbols, data from Ref. [21]; filled symbols, calcium data from Ref. [11] and new mass data from this work. Top: With $S_{2n}$ values from HFB calculations using the SLy4 (green lines) and the SLy5 (red lines) interaction, with volume-type delta pairing of strength $V_0=-150\mathrm{MeV}{\mathrm{fm}}^3$ (solid lines) or $V_0=-200\mathrm{MeV}{\mathrm{fm}}^3$ (dashed lines). Bottom: With $S_{2n}$ values obtained from ab initio Gorkov-Green function theory (see the text for details).