Prolate, oblate, and triaxial shape coexistence, and the lost magicity of $N=28$ in ${}^{43}$S

We report the low-lying spectrum and collective $\beta$ and $\gamma$ deformation of ${}^{43}$S as investigated by antisymmetrized molecular dynamics. Our result successfully explains the observed data including an isomeric $7/2_1^{-}$ state and illustrates the coexistence of the prolate-deformed ground band with a vanishing $N=28$ shell gap, a triaxially deformed isomeric state, and an oblate-deformed excited band at very low excitation energies.

Figure 1

Observed and calculated low-lying spectra of ${}^{47}$Ca and ${}^{43}$S, respectively. Panels (a) and (b) show the observed spectra of ${}^{47}$Ca and ${}^{43}$S. Panels (c) and (d) show the ${}^{43}$S spectra calculated using triaxial and axial GCM, respectively.

Figure 2

(a) Negative-parity energy surface in the $\beta$-$\gamma$ plane obtained by variation after parity projection. The red line shows the deformation path along which the neutron single-particle energies are shown in Fig. 3. (b)–(f) Energy surfaces and GCM overlaps. Contours show the energy surface at intervals of 1 MeV for the $K$ state which has the largest overlap with each state. Color plots show the GCM overlap with the $K$ state.

Figure 3

Neutron single-particle energies as a function of the quadrupole deformation parameters $\beta$ and $\gamma$ along the fan-shaped path shown in Fig. 2a. The blue (red) line indicates an orbit originating in the spherical $f_{7/2}$ ($p_{3/2}$) orbit. Lines (with open and solid circles) show unoccupied levels (levels occupied by one and two neutrons).