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 Na31. Theoretical calculations are performed within the interacting shell-model framework in a large valence space, based on a Ca48 core, which encompasses the full pf shell for the protons and the 0f5/2, 1p3/2, 1p1/2, 0g9/2, and 1d5/2 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.

Valuable theoretical predictions of nuclear dipole excitations in the whole nuclear chart are of great interest for different applications, including in particular nuclear astrophysics. Here we extend our large-scale calculations of the $E1$ and $M1$ absorption $\gamma$-ray strength function obtained in the framework of the axially symmetric deformed quasiparticle random-phase approximation (QRPA) based on the finite-range D1M Gogny force to the deexcitation strength function. To do so, shell-model calculations of the deexcitation dipole strength function are performed and their limit at low $\gamma$ energies used to complement phenomenologically the QRPA calculations. We compare our final prediction of the $E1$ and $M1$ strength with available experimental data at low energies and show that a fairly good agreement is obtained. Predictions of the dipole strength function for spherical and deformed nuclei within the valley of $\beta$ stability as well as in the neutron-rich region are discussed and compared with traditional Lorentzian-type prescriptions. Its impact on the total radiative width as well as radiative neutron and proton capture cross sections is studied.

We have performed large-scale shell-model calculations of the half-lives and neutron-branching probabilities of the $r$-process waiting-point nuclei at the magic neutron numbers $N=50$, 82, and 126. The calculations include contributions from allowed Gamow-Teller and first-forbidden transitions. We find good agreement with the measured half-lives for the $N=50$ nuclei with charge numbers $Z=28$\char21{}32 and for the $N=82$ nuclei ${}^{129}$Ag and ${}^{130}$Cd. The contribution of forbidden transitions reduce the half-lives of the $N=126$ waiting-point nuclei significantly, while they have only a small effect on the half-lives of the $N=50$ and 82 $r$-process nuclei.

The lifetimes of the first excited 2+ states in Fe62 and Fe64 have been measured for the first time using the recoil-distance Doppler shift method after multinucleon transfer reactions in inverse kinematics. A sudden increase of collectivity from Fe62 to Fe64 is observed. The experimental results are compared with new large-scale shell-model calculations and Hartree-Fock-Bogolyubov\char21{}based configuration-mixing calculations using the Gogny D1S interaction. The results give a deeper understanding of the mechanism leading to an onset of collectivity near Ni68, which is compared with the situation in the so-called island of inversion around Mg32.

We calculate the low-lying spectra and several high-spin states of zirconium isotopes ($Z=40$) with neutron numbers from $N=50$ to $N=58$ using a large valence space with the ${}^{78}\mathrm{Ni}$ inert core, which a priori allows one to study the interplay between spherical and deformed configurations, necessary for the description of nuclides in this part of the nuclear chart. The effective interaction is derived by monopole corrections of the realistic $G$ matrix. We reproduce essential nuclear properties, such as subshell closures in ${}^{96}\mathrm{Zr}$ and ${}^{98}\mathrm{Zr}$. The spherical-to-deformed shape transition in ${}^{100}\mathrm{Zr}$ is addressed as well.