**4. The Cr Isotopes**

In the heart of the *N* = 40 island of inversion, the nucleus 64Cr eluded spectroscopy until 2010. In fact, Adrich et al. attempted to populate 64Cr in the two-proton removal from 66Fe. This measurement failed as the cross section turned out to be only 0.13(5) mb, an order of magnitude smaller than the cross section leading from 68Ni to 66Fe along *N* = 40 [33]. The conclusion at the time was that the cross section is small due to a structural mismatch between the 66Fe ground state and the bound states of 64Cr. This early idea was partially supported in 2010 through the LNPS effective interaction which predicts significant differences in the neutron 2p2h and 6p6h content in the ground states of 66Fe and 64Cr, hinting indeed at a potentially reduced overlap of the neutron wave functions [4]. The first spectroscopy of 64Cr was then accomplished via 9Be-induced inelastic scattering at NSCL where candidates for 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> <sup>1</sup> transitions were identified. While published in the same year, this data did not enter the development of the LNPS effective interaction and so the close match between experiment and calculation can be viewed as a stunningly successful prediction [4]. The 2<sup>+</sup> <sup>1</sup> state and the energy of the candidate 4<sup>+</sup> <sup>1</sup> level were since confirmed in intermediate-energy Coulomb excitation [38] and *β* decay [46], respectively. The first one- and two-proton knockout study into 64Cr, using GRETINA and the S800, revealed a high *γ*-ray transition density, indicative of a rather complex and dense level scheme [47]. A quantitative knockout study was not possible as the knockout reaction channels may have contained small contaminations from 64Cr populated in fragmentation of other projectiles in the cocktail beam [47]. A study of the *B*(*E*2) transition strength predicted by the LNPS shell-model calculations revealed several very interesting collective band structures, resembling a gamma and beta band but with deviations from the textbook expectations for such structures [47]. These proposed bands are barely linked via *E*2 transitions. Identifying these predicted collective structures in measurements has to remain a challenge for future studies and next-generation rare-isotope facilities where these states can be accessed with reactions at low beam energies such as deep-inelastic scattering [47].

The most neutron-rich Cr isotope with spectroscopic information is 66Cr studied at RIBF/RIKEN with *γ*-ray spectroscopy following a (*p*, 2*p*) reaction [43]. Candidate transitions for 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> <sup>1</sup> decays were proposed, in agreement with slightly modified LNPS shell-model calculations, termed LNPS-m in [43]. The Cr isotopes mirror the observations for the Fe isotopic chain, with a rather flat evolution of the 2<sup>+</sup> <sup>1</sup> and 4+ <sup>1</sup> energies, but starting at *N* = 38 already instead of at *N* = 40 as for the Fe chain; see Figure 4.

**Figure 4.** Evolution of the yrast 2<sup>+</sup> and 4<sup>+</sup> states in the Cr isotopic chain from *N* = 36 to 44, the most neutron-rich Cr isotope with spectroscopic information. The data is confronted with the results of LNPS-m shell-model calculations from reference [43]. LNPS-m is a slightly modified version of the original LNPS interaction as discussed in [43]. The calculations reproduce the signature drop in excitation energy at *N* = 38, corresponding to an onset of collectivity, and the subsequent flat evolution. Note that the onset of collectivity in Cr sets in already at *N* = 38, unlike for the Fe isotopes.

#### **5. The Ti Isotopic Chain**

The *N* = 38 Ti isotope 60Ti was studied in the 9Be-induced one-proton knockout at NSCL using GRETINA at the S800 spectrograph, providing the first spectroscopy of this nucleus [48]. One *γ*-ray peak was observed which was argued to be a doublet of two transitions corresponding to the 2<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>0</sup><sup>+</sup> <sup>1</sup> transition and perhaps the decay of the 4<sup>+</sup> <sup>1</sup> level. This measurement exploited the knockout reaction mechanism and compared calculated and measured partial cross sections [48]. The comparison supported the suggestion of a doublet as well as the spin assignments for the candidate states and the expectation for the inclusive cross section. This analysis provided a unique benchmark for the LNPS effective interaction that goes beyond excitation energies and includes wave-function overlaps, at the time the closest to 60Ca as possible.

At *N* = 40, 62Ti was accessed with *γ*-ray spectroscopy only recently, using a (*p*, 2*p*) reaction with the MINOS target and the DALI2 scintillator array at SAMURAI [49]. Candidate *γ*-ray decays attributed 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> <sup>1</sup> transitions were proposed. As in the work on 60Ti [48], also for 62Ti the direct nature of the reaction was exploited, comparing measured and calculated partial cross sections that probe the wave-function overlaps between projectile ground state and knockout residue final states. A 63V ground-state spin assignment *J* = 3/2− was found the most likely given the calculated cross section distributions for the other alternatives [49]. Along the *N* = 40 isotone line, 62Ti is the last extrapolation point towards the elusive 60Ca (see Figure 5), which was proven to exist only recently with implications for the dripline in the Ca isotopic chain [50].

**Figure 5.** Evolution of the 2<sup>+</sup> and 4<sup>+</sup> energies in the *N* = 40 isotones from Ca to Zn as predicted by LNPS shell-model calculations presented in reference [49] in comparison to data, where 62Ti is the most neutron-rich in the chain. The excellent agreement lends confidence in the prediction for the elusive nucleus 60Ca which was only recently identified [50].

#### **6. Complementary Descriptions of the Region**

While this review focuses on the shell-model description of the nuclei above, the reader is referred to an interesting discussion of the Cr and Fe isotopic chains in the framework of the proton neutron interacting boson model (IBM-2) by Kotila and Lenzi [36]. Among the discussed collective observables, for example, the measured as well calculated energy ratios *R*4/2 and *R*6/4 within the shell-model and the IBM-2 are examined from *N* = 30 − 40 [36]. Complementary to the effective-interaction shell model and the IBM, Coraggio et al. [51] performed pioneering realistic shell-model calculations starting from a low-momentum potential derived from the high-precision CD-Bonn free nucleon-nucleon interaction. The energies of the first 2<sup>+</sup> states and *B*(*E*2) strengths are calculated inside the *N* = 40 island of inversion and the best agreement is reached with the largest possible model space [51]. These calculations were extended for 68,70Fe and confronted with experiment in [41]. The level structures of odd-Z 63,65,67Mn isotopes located on the nuclear chart just between the collective Cr and Fe isotopic chains were shown to be consistent with strongly coupled rotational bands built on a state with *K* quantum number *K* = 5/2 [52], providing yet another means to characterize the collectivity that has become a hallmark of the region.
