Single-particle states vs. collective modes: friends or enemies ?

¹ RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
² Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
³ Center for Nuclear Study, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
⁴ Instituut voor Kern- en Stralingsfysica, K. U. Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
⁵ National Superconducting Cyclotron Laboratory,Michigan State University, East Lansing, Michigan 48824, USA

Published online: 16 May 2018

Abstract

The quantum self-organization is introduced as one of the major underlying mechanisms of the quantum many-body systems. In the case of atomic nuclei as an example, two types of the motion of nucleons, single-particle states and collective modes, dominate the structure of the nucleus. The collective mode arises as the balance between the effect of the mode-driving force (e.g., quadrupole force for the ellipsoidal deformation) and the resistance power against it. The single-particle energies are one of the sources to produce such resistance power: a coherent collective motion is more hindered by larger spacings between relevant single particle states. Thus, the single-particle state and the collective mode are “enemies” against each other. However, the nuclear forces are rich enough so as to enhance relevant collective mode by reducing the resistance power by changing single-particle energies for each eigenstate through monopole interactions. This will be verified with the concrete example taken from Zr isotopes. Thus, the quantum self-organization occurs: single-particle energies can be self-organized by (i) two quantum liquids, e.g., protons and neutrons, (ii) monopole interaction (to control resistance). In other words, atomic nuclei are not necessarily like simple rigid vases containing almost free nucleons, in contrast to the naïve Fermi liquid picture. Type II shell evolution is considered to be a simple visible case involving excitations across a (sub)magic gap. The quantum self-organization becomes more important in heavier nuclei where the number of active orbits and the number of active nucleons are larger.