Shape Changes in the $N=28$ Island of Inversion: Collective Structures Built on Configuration-Coexisting States in ${}^{43}\mathrm{S}$

The neutron-rich nuclei in the $N=28$ island of inversion have attracted considerable experimental and theoretical attention, providing great insight into the evolution of shell structure and nuclear shape in exotic nuclei. In this work, for the first time, quadrupole collectivity is assessed simultaneously on top of the $3/2^{-}$ ground state and the $7/2^{-}$ shape-coexisting isomer of ${}^{43}\mathrm{S}$, putting the unique interpretation of shape and configuration coexistence at $N=27$ and 28 in the sulfur isotopic chain to the test. From an analysis of the electromagnetic transition strengths and quadrupole moments predicted within the shell model, it is shown that the onset of shape coexistence and the emergence of a simple collective structure appear suddenly in ${}^{43}\mathrm{S}$ with no indication of such patterns in the $N=27$ isotone ${}^{45}\mathrm{Ar}$.

Figure 1

Top: Doppler-corrected energy spectrum for ${}^{43}\mathrm{S}$ gated on laboratory-frame scattering angles smaller than 40 mrad. The red curve is the total fit function. The individual geant4 simulations of the observed in-beam and background $\gamma$ decays along with a double exponential background are shown in other colors. Bottom: Low-energy portion of the ${}^{43}\mathrm{S}$ Doppler-corrected energy spectrum. The wide feature present for ${}^{43}\mathrm{S}$ that is absent for ${}^{38}\mathrm{S}$ (see Ref. [41]) is from the continuous decay of the 320-keV isomer along the beam line. The smooth low-energy background is due to bremsstrahlung and other beam-correlated background.

Figure 2

Background-subtracted, Doppler-corrected energy spectrum for ${}^{43}\mathrm{S}$ measured with CAESAR in coincidence with 320-keV $\gamma$ rays detected in the hodoscope at the S800 focal plane from the decay of the isomer. The inset shows the laboratory-frame hodoscope spectrum for coincidences.

Figure 3

SDPF-MU predictions for $B(E2)$ strengths in $e^2{\mathrm{fm}}^4$ for low-lying levels in ${}^{43}\mathrm{S}$ compared with experimental results. The $p$ orbitals have been shifted up by 300 keV to improve agreement with the energy of the $7/2_1^{-}$ isomer (red). This modification has a negligible effect on the calculated transition strengths. Arrow widths are proportional to $B(E2)$.

Figure 4

$E2$ map for ${}^{43}\mathrm{S}$ (a) in the collective model for $K=1/2$ and $7/2$ using $Q_i=50e{\mathrm{fm}}^2$ and (b) for our SDPF-MU calculations ($p$ orbitals moved up by 300 keV). The size of the dots signifies the magnitude of the $Q_s$ moment and the color its sign (blue, negative; red, positive). The $B(E2\downarrow )$ strength connecting the states is indicated by the line thickness. The emergence of the simple collective structure in the complex shell-model calculation is clearly visible. The inset shows the $E2$ map for ${}^{45}\mathrm{Ar}$, exhibiting no such distinct collective structures or shape coexistence.