**3. The Fe Isotopic Chain**

The first in-beam nuclear spectroscopy of 66Fe and 68Fe was published in 2008 from a measurement performed at NSCL where these two Fe isotopes with 40 and 42 neutrons were populated each in 9Be-induced one- and two-proton knockout reactions, using the laboratory's S800 spectrograph for particle identification and SeGA for in-beam *γ*-ray spectroscopy [33]. For 66Fe, in addition to the tentative 2<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>0</sup><sup>+</sup> <sup>1</sup> and 4<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>2</sup><sup>+</sup> <sup>1</sup> transitions reported earlier from *β* decay [34], a 957(10) keV *γ*-ray was observed in both reactions, while a 1310(15) keV transition was only seen in the one-proton knockout. Within a simple two-proton knockout picture, for two protons removed from the *f*7/2 orbital, one would expect to populate states in 66Fe with spin-parity 6+, 4+, and 2+, suggesting that the 957 keV line depopulates the 6<sup>+</sup> state of 66Fe. Subsequent *β*-decay work limited to lower-spin states seems to suggest that the 1310-keV transition could originate from the second 2<sup>+</sup> level and feeds the first 2<sup>+</sup> state [35]. This first in-beam work predates the publication of the LNPS effective interaction [4] and it is interesting to explore the suggestion that

the 6<sup>+</sup> <sup>1</sup> state was observed. Kotila and Lenzi [36] discuss collective phenomena in Fe and Cr and show that the 6<sup>+</sup> <sup>1</sup> level predicted by the LNPS calculations agrees with the tentatively assigned (6+) state proposed by Adrich et al. in 66Fe [36]. Subsequent inbeam spectroscopy work performed at NSCL explored the 2<sup>+</sup> <sup>1</sup> and 4<sup>+</sup> <sup>1</sup> states of 66Fe in 9Be-induced inelastic scattering [37] and the quadrupole collectivity in intermediate-energy Coulomb excitation [38] and excited-state lifetime measurements [39].

Beyond *N* = 40, in 68Fe, the first observation of *γ*-ray transitions was reported in [33] from 9Be-induced one- and two-proton removal reactions with proposed 2<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>0</sup><sup>+</sup> <sup>1</sup> and 4+ <sup>1</sup> <sup>→</sup> <sup>2</sup><sup>+</sup> <sup>1</sup> decays, later supported by intermediate-energy Coulomb excitation measurements [38] as well as *β* decay [40]. It turned out that the energy of the first 2<sup>+</sup> state in 68Fe is lower than in 66Fe, indicating that the maximum collectivity is assumed beyond *N* = 40. Taking the 4<sup>+</sup> <sup>1</sup> assignment at face value, the *R*4/2 energy ratio increases as well. The shell model calculations with the LNPS effective interaction are in good agreement with the energies and transition strengths, lending even more confidence that the shell evolution past *N* = 40 is captured by the incorporated driving forces [4]. Excited states beyond the tentatively assigned yrast 2<sup>+</sup> and 4<sup>+</sup> remained elusive until a *β*-decay study [41], where a number of low-spin states were proposed. Two candidates for the 6<sup>+</sup> <sup>1</sup> state just emerged recently from a 9Be-induced charge-exchange reaction on 68Co projectiles in the (7−) ground state and a low-spin isomer [42]. Governed by the charge-exchange selection rules, access to never-before observed states was provided, predominantly higher-spin states [42]. The calculations with the LNPS effective interaction show good agreement with the energies of the candidate yrast states up to the suggested candidate 6<sup>+</sup> levels [42]. This reaction mechanism holds great promise to reach beyond the selectivity of knockout reactions and *β* decay, depending on the spin and parity of the projectile initial state.

At *N* = 44, spectroscopy of 70Fe became first possible in 2015 at the RIBF facility at RIKEN using a (*p*, 2*p*) reaction with the MINOS hydrogen target [13] and the DALI2 scintillator array [43] and in the same year with *β* decay at RIKEN [41]. Two transitions were consistently identified in both measurements and proposed to correspond to the 2<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>0</sup><sup>+</sup> 1 and 4<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>2</sup><sup>+</sup> <sup>1</sup> decays, establishing the corresponding states. It took until 2019 to get beyond the yrast 4<sup>+</sup> state and identify a transition on top of the 4<sup>+</sup> level in a 9Be-induced one-proton knockout measurement performed at NSCL with GRETINA and the S800 spectrograph [44]. The measured and calculated partial one-proton removal cross sections were confronted and showed, at first glance, a striking disagreement with high-lying states populated more strongly than the yrast states observed in the measurement. The emerging picture is one that is not unlike the Pandemonium in *β* decay [45], where indiscernible feeding from a multitude of higher-lying states funnels intensity into low-lying states which then appear prominent albeit carrying little direct feeding. This demonstrates that, while one-proton removal is a powerful experimental probe to reach nuclei more neutron-rich than the projectile, the collectivity prevalent in this region of the nuclear chart can lead to fragmentation of the single-particle strength which may then be thinly spread over many states in the reaction residue, leading to a Pandemonium-like feeding scheme when *γ*-ray spectroscopy is used [44].

The most neutron-rich Fe isotope with spectroscopic information is 72Fe, studied at RIBF/RIKEN in the same experiment and with the same approach as 70Fe [43] and two *γ* rays were observed and proposed to correspond to the 2<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>0</sup><sup>+</sup> <sup>1</sup> and 4<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>2</sup><sup>+</sup> 1 transitions, establishing the corresponding states. It will likely take a next-generation rare-isotope facility to move beyond 72Fe with nuclear spectroscopy. A peculiar picture emerges where starting at *N* = 40, the evolution of the 2<sup>+</sup> <sup>1</sup> and 4<sup>+</sup> <sup>1</sup> excitation energies largely stays flat, as shown in Figure 3. Across the Fe isotopic chain, the LNPS shellmodel calculations, using the slightly modified LNPS-m effective interaction, reproduce the measured excitation energies.

**Figure 3.** Evolution of the yrast 2<sup>+</sup> and 4<sup>+</sup> states in the Fe isotopic chain from *N* = 36 to 46, the most neutron-rich Fe isotope with spectroscopic information. The data is confronted with the results of LNPS-m (modified Lenzi-Nowacki-Poves-Sieja) shell-model calculations from reference [43]. LNPSm is a slightly modified version of the original LNPS interaction as detailed in [43]. The calculations reproduce the signature drop in excitation energy at *N* = 40, corresponding to an onset of collectivity, and the subsequent flat evolution.
