The atomic nucleus is a quantum many-body system whose constituent nucleons (protons and neutrons) are subject to complex nucleon-nucleon interactions that include spin- and isospin-dependent components. For stable nuclei, several decades ago, emerging seemingly regular patterns in some observables could already be described successfully within a shell-model picture that results in particularly stable nuclei at certain magic fillings of the shells with protons and/or neutrons: $N$, $Z=8$, 20, 28, 50, 82, 126. However, in short-lived, so-called exotic nuclei or rare isotopes, characterized by a large $N/Z$ asymmetry and located far from the valley of $\beta$ stability on the nuclear chart, these magic numbers, viewed through observables, were shown to change. These changes in the regime of exotic nuclei offer an unprecedented view at the roles of the various components of the nuclear force when theoretical descriptions are confronted with experimental data on exotic nuclei where certain effects are enhanced. This article reviews the driving forces behind shell evolution from a theoretical point of view and connects this to experimental signatures.

Both one-proton and one-neutron knockout reactions were performed with fast beams of two asymmetric, neutron-deficient rare isotopes produced by projectile fragmentation. The reactions are used to probe the nucleon spectroscopic strengths at both the weakly and strongly bound nucleon Fermi surfaces. The one-proton knockout reactions ${}^9\mathrm{Be}$(${}^{28}\mathrm{S}$,${}^{27}\mathrm{P}$)X and ${}^9\mathrm{Be}$(${}^{24}\mathrm{Si}$,${}^{23}\mathrm{Al}$)X probe the weakly bound valence proton states and the one-neutron knockout reactions and ${}^9\mathrm{Be}$(${}^{28}\mathrm{S}$, ${}^{27}\mathrm{S}$)X and ${}^9\mathrm{Be}$(${}^{24}\mathrm{Si}$, ${}^{23}\mathrm{Si}$)X the strongly bound neutron states in the two systems. The spectroscopic strengths are extracted from the measured cross sections by comparisons with an eikonal reaction theory. The reduction of the experimentally deduced spectroscopic strengths, relative to the predictions of shell-model calculations, is of order 0.8–0.9 in the removal of weakly bound protons and 0.3–0.4 in the knockout of the strongly bound neutrons. These results support previous studies at the extremes of nuclear binding and provide further evidence that in asymmetric nuclear systems the nucleons of the deficient species, at the more-bound Fermi surface are more strongly correlated than those of the more weakly bound excess species.

There is now a large and increasing body of experimental data and theoretical analyses for reactions that remove a single nucleon from an intermediate-energy beam of neutron- or proton-rich nuclei. In each such measurement, one obtains the inclusive cross section for the population of all bound final states of the mass $A-1$ reaction residue. These data, from different regions of the nuclear chart, and that involve weakly and strongly bound nucleons, are compared with theoretical expectations. These calculations include an approximate treatment of the reaction dynamics and shell-model descriptions of the projectile initial state, the bound final states of the residues, and the single-particle strengths computed from their overlap functions. The results are discussed in the light of recent data, more exclusive tests of the eikonal dynamical description, and calculations that take input from more microscopic nuclear structure models.

The even ${}^{52-56}\mathrm{Ti}$ isotopes have been studied with intermediate-energy Coulomb excitation and absolute $B(E2;0^{+}\to 2_1^{+})$ transition rates have been obtained. These data confirm the presence of a subshell closure at neutron number $N=32$ in neutron-rich nuclei above the doubly magic nucleus ${}^{48}\mathrm{Ca}$ and provide no direct evidence for the predicted $N=34$ closure. Large-scale shell model calculations with the most recent effective interactions are unable to reproduce the magnitude of the measured strengths in the semimagic Ti nuclei and their strong variation with neutron number.