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Physical Review Letters

Regularity-Induced Separation of Intrinsic and Collective Dynamics

Michal Macek, Jan Dobeš, Pavel Stránský, Pavel Cejnar

Published Aug 13, 2010• 27 citations
Publisher

Abstract

We propose that the adiabatic separation of collective and intrinsic motions in many-body systems is related to increased regularity of the intrinsic dynamics. The surmise is verified on the separation of rotations from intrinsic vibrations in the interacting boson model of nuclear structure.
DOI
10.1103/physrevlett.105.072503

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We observe an adiabatic separation of collective rotations built upon a subset of intrinsic vibrational states within the interacting boson model (IBM) in the parameter domains corresponding to axially deformed ground state. The effect is not limited only to the low-lying states and closely follows the variation of quantum and classical measures of regularity. It leads to the existence of rotational bands even close to the highest accessible energies in specific regions within the IBM symmetry triangle. We propose a more general effect of regular intrinsic dynamics on the adiabatic separation of intrinsic and collective motion.
The general problem of dissipation in macroscopic large-amplitude collective motion and its relation to energy diffusion of intrinsic degrees of freedom of a nucleus is studied. By applying the cranking approach to the nuclear many-body system, a set of coupled dynamical equations for the collective classical variable and the quantum mechanical occupancies of the intrinsic nuclear states is derived in the limit of weak coupling of the collective and intrinsic subsystems. Different dynamical regimes of the intrinsic nuclear motion and its consequences on time properties of collective dissipation are discussed.
Low-lying collective states in nuclei are investigated in the framework of the interacting boson model using an ensemble of random many-body interactions. It is shown that whenever the number of bosons is sufficiently large compared to the rank of the interactions, the spectral properties are characterized by a dominance of LP=0+{L}^{P}{=0}^{+}LP=0+ ground states and the occurrence of both vibrational and rotational band structures. This indicates that these features represent a general and robust property of the collective model space.
An effective boson Hamiltonian is derived from the original Hamiltonian of a many-fermion system. The results show that when the intrinsic motion of bosons is collective and the excitation energies of the system are small, the effective boson-boson interaction can be reduced to a two-body interaction while for odd systems or systems with uncorrelated fermions, there is an additional two-body boson-fermion interaction. Both these interactions can be calculated from the original fermion-fermion ones. Thus, the microscopic foundation of the interacting boson model is established without recourse to mapping procedures.NUCLEAR STRUCTURE Interacting boson model, boson fermion hybrid representation, microscopic foundation.
Conventional many-body quantum theory considers, as a rule, a system of particles in the mean field interacting through two-body forces. Recently it was suggested that in nuclear physics many-body forces, first of all three-body ones, are important for saturation of nuclear matter and for many details of nuclear structure. We consider possible influence of three-body forces, regardless of their origin (bare nucleon interactions or effective medium phenomena), on many-body dynamics. The new effects include, but are not limited to, renormalization of pairing and other two-body forces, enhancement of anharmonicity for collective modes, and special features of shell model calculations.