Island of inversion around<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Cr</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>64</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>

We study the development of collectivity in the neutron-rich nuclei around $N=40$, where the experimental and theoretical evidence suggest a rapid shape change from the spherical to the rotational regime, in analogy to what happens at the island of inversion surrounding $^{31}\mathrm{Na}$. Theoretical calculations are performed within the interacting shell-model framework in a large valence space, based on a $^{48}\mathrm{Ca}$ core, which encompasses the full $\mathit{pf}$ shell for the protons and the $0{f}_{5/2}$, $1{p}_{3/2}$, $1{p}_{1/2}$, $0{g}_{9/2}$, and $1{d}_{5/2}$ orbits for the neutrons. The effective interaction is based on a G matrix obtained from a realistic nucleon-nucleon potential whose monopole part is corrected empirically to produce effective single-particle energies compatible with the experimental data. We find a good agreement between the theoretical results and the available experimental data. We predict the onset of deformation at different neutron numbers for the various isotopic chains. The maximum collectivity occurs in the chromium isotopes where the large deformation regime already starts at $N=38$. The shell evolution responsible for the observed shape changes is discussed in detail, in parallel to the situation in the $N=20$ region.

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