The monopole effect of the tensor force is presented, exhibiting how spherical single-particle energies are shifted as protons or neutrons occupy certain orbits. An analytic relation for such shifts is shown, and their general features are explained intuitively. Single-particle levels are shown to change in a systematic and robust way, by using the $\pi +\rho$ meson exchange tensor potential, consistently with the chiral perturbation idea. Several examples are compared with experiments.

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.

We study boron, carbon, nitrogen, and oxygen isotopes with a newly constructed shell-model Hamiltonian developed from a monopole-based universal interaction (VMU). The present Hamiltonian can reproduce well the ground-state energies, energy levels, electric quadrupole properties, and spin properties of these nuclei in full psd model space including (0$-${}3)$\hbar${}$\omega${} excitations. Especially, it correctly describes the drip lines of carbon and oxygen isotopes and the spins of the ground states of 10B and 18N while some former interactions such as WBP and WBT fail. We point out that the inclusion of 2$\hbar${}$\omega${} excitations is important in reproducing some of these properties. In the present (0+2)$\hbar${}$\omega${} calculations small but constant E2 effective charges appear to work quite well. As the inclusion of the 2$\hbar${}$\omega${} model space makes a rather minor change, this seems to be related to the smallness of the 4He core. Similarly, the spin g factors are very close to free values. The applicability of tensor and spin-orbit forces in free space, which are taken in the present Hamiltonian, is examined in shell-model calculations.