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.
Highlights
The underlying mechanisms of the many-body structure of atomic nuclei have been studied over decades as one of the most important objectives of nuclear physics
The relation between the singleparticle states and the collective modes has naturally become of much interest, as described by Bohr and Mottelson in [10] as “the problem of reconciling the simultaneous occurrence of single-particle and collective degrees of freedom and exploring the variety of phenomena that arise from their interplay”
If the splitting is large enough, the many-body structure is dominated by the single-particle energies (SPE): nucleons occupy the lowest single particle states in the ground state, the lowest configuration gives us the first excited state, and so forth
Summary
The underlying mechanisms of the many-body structure of atomic nuclei have been studied over decades as one of the most important objectives of nuclear physics. It has been understood usually that there are two types of dominant motion of nucleons in the atomic nucleus : single-particle states and collective modes. If the splitting is large enough, the many-body structure is dominated by the SPEs: nucleons occupy the lowest single particle states in the ground state, the lowest configuration gives us the first excited state, and so forth. In such cases, the correlations due to the interaction between nucleons may contribute, but their effects are minor, more or less, compared to the effects of SPE splittings. Even when the dimensions are in the order of 1023 for the conventional shell model, the problem can be solved, to a good approximation, with up to approximately 100 MCSM basis vectors
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