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Although the shell model is fundamental to our understanding of nuclear structure, the breakdown of traditional magic numbers far from stability provides insight into the nature of the underlying nuclear interactions and acts as a tool to test existing models. Islands of inversion (IoI) in the nuclear landscape are characterized by the presence of deformed multi-particle multi-hole (npnh) ground states instead of the (0p0h) configurations predicted by spherical mean-field calculations. This is typically driven by the strong nuclear quadrupole-quadrupole interaction that induces shape transitions, wherein these highly correlated “intruder” states become more bound than spherical ones.
In the N=40 region, the relatively large energy gap separating the pf shell from the $\nu g_{9/2}$ orbital points towards a strong sub shell closure at N=40 which has been supported by the observation of a high-lying 2$^{+}$ state and low B(E2) value in $^{68}$Ni (Z=28) [1]. However, systematics of E(2+) and B(E2) values have indicated a sudden increase in collectivity below Z=28 when approaching N=40, seen especially in the rapid drop of E(2+) in Fe (Z=26) and Cr (Z=24) isotopes [2,3]. This is attributed to the neutron occupation of intruder states from a higher shell, similar to the IoI around N=20 [4, 5]. Shape coexistence also manifests in nuclei at the boundaries of IoIs [6]. In the N=40 region, low-lying 0$^{+}$ excited states, which are traditional indicators of shape coexistence have been identified up to A=66 [7, 8]. In $^{68}$Fe, a state at 2035 keV is tentatively assigned as 0$^{+}$ or 2$^{+}$ and the confirmation of this spin would indicate whether this trend extends past N=40.
To explore these phenomena, an experiment was performed at TRIUMF-ISAC using the GRIFFIN spectrometer that utilized the $\beta$- and $\beta$n decay of $^{68}$Mn to populate excited states in $^{67,68}$Fe, $^{67,68}$Co and $^{67,68}$Ni. This experiment produced the highest-statistics data set to date for these isotopes. Consequently, we have greatly expanded the level scheme of $^{68}$Fe and measured key spectroscopic quantities. Angular correlation analysis performed using the 64 HPGe crystals of GRIFFIN has provided new information on the spin assignment of the proposed 0$_{2}^{+}$ state, resulting in a reinterpretation of shape coexistence in this nucleus. Furthermore, the first direct measurement of the lifetime of the 2$_{1}^{+}$ level in $^{68}$Fe was performed using $\beta\gamma\gamma$ fast-timing analysis, and B(E2; 2$_{1}^{+}$ $\rightarrow$ 0$_{1}^{+}$) was subsequently calculated. The associated nuclear structure implications and other results from the analysis will be presented and discussed.
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[6] M. Rocchini et al. In: Phys. Rev. Lett. 130 (12 Mar. 2023), p. 122502.
[7] Balraj Singh. In: Nuclear Data Sheets 108.2 (2007), pp. 197–364.
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