Quantum self-organization and nuclear collectivity

The interplay between the single-particle states and the collective modes have been one of the central subjects of nuclear physics since the very beginning. If the single-particle aspect is too strong, for instance, with a large gap between relevant orbits, it certainly suppresses the collective mode. Thus, the single-particle states and the collective modes have been considered to be enemies each other, and the former behaves as the resistance power against the latter. However, an opposing idea has arisen recently. The nuclear force is characterized by a component driving a collective mode, like the quadrupole interaction for the ellipsoidal shape. Recently, the monopole component of nuclear forces has been shown to reduce this resistance power: energies of single-particle orbits can be optimized for a given mode by choosing favorable configurations. In fact, the monopole component of the central and tensor forces show strong orbital dependences, and can move single-particle energies depending on configurations of other nucleons. This mechanism is called the quantum self-organization, and is consistent with the general self-organization concept. Its effect can be seen in the quantum phase transition of Zr isotopes, while the same underlying mechanism promotes the shape evolution in Sm isotopes. These phenomena have been clarified quantitatively by state-of-the-art Monte Carlo Shell Model calculations with reasonable interactions, showing good agreements with experiment. Thus, single-particle states are not necessarily an enemy of the collectivity, but can be a good friend. One of the striking outcome is that contrary to the conventional idea, side bands of rotational nuclei may not be beta or gamma vibration of the ellipsoidal shape, but may be consequences of many-body correlations due to nuclear forces, beyond the liquid drop model. Some other manifestations and possible experimental challenges will be discussed.