Research

Quantum many-body theory for nuclear collective dynamics

What is the shape of a nucleus? 

The equilibrium shape of the classical liquid drop is spherical. When it rotates, it becomes oblate due to the effect of the centrifugal force. In contrast, the majority of nuclei prefer a prolate shape, except for those located near the closed shells of the j-j coupling shell model. Notably, even nuclei with spherical ground states exhibit deformed shapes in their excited states. The deformed shapes appear due to quantal shell effects associated with the single-particle motions in the mean field. Since the nucleus is a finite system, the single-particle states form a shell structure. The spherical shell structure in the j-j coupling shell model gradually changes with the growth of deformation in the mean field, giving rise to deformed shell structures and deformed magic numbers at specific deformed shapes. The gain of binding energies associated with deformed magic numbers appearing at various deformed shapes for certain combinations of protons and neutrons stabilizes the deformed shape.

Emergence of collective rotational motions

Spontaneous symmetry breaking (SSB) and the emergence of the massless collective modes that restore broken symmetry are central concepts in modern physics. Bohr and Mottelson notably highlighted how nuclear rotations exemplify these dynamics within finite quantum systems. Breaking the spherical symmetry in the self-consistent mean field enables us to define the orientation degrees of freedom that specify the orientation of the body-fixed frame relative to the laboratory frame, called the intrinsic frame of reference. The intrinsic frame can be defined as a principal-axis frame of the deformed self-consistent mean field generated by all the nucleons. It is important to keep in mind that SSB can remain veiled in quantum systems, i.e., the experimental measurements probe the states in the laboratory frame, which preserves the symmetries of the original Hamiltonian. Thus, nuclear rotations may be viewed as rotational motions of the self-consistent mean field relative to the laboratory frame.

Collective modes of excitation

The low-frequency quadrupole vibrations can be regarded as soft modes of the phase transition generating equilibrium deformations in the mean field. In nuclei situated in the transitional region from spherical to deformed, the amplitudes of shape fluctuation about the equilibrium shape increase significantly. The large shape fluctuations occur also in weakly deformed nuclei where the gains of binding energy due to the symmetry breaking are comparable in magnitude to the vibrational zero-point energies. Such transitional situations are abundant in nuclear charts and excitation spectra of these nuclei provide an invaluable opportunity to investigate the process of the quantum phase transition through the change of spectra with nucleon number. Vibrational and rotational motions of a nucleus can be described as time-evolutions of a deformable self-consistent mean field.