The random phase approximation and the separation of collective degrees of freedom

G. F. Bertsch

Koichi Takahashi, Tatsuo Tsukamoto

A method of introducing collective motion into the layered Fermi fluid (LFF) is discussed by concentrating on layer vibrations. By the random phase approximation (RPA), the original dynamical degrees of freedom of particles are separated into collective modes (CMs), uncorrelated (harmonic) oscillator modes (UOMs) and two-dimensional (2D) motions of particles within layers, which leads to a subband structure of particle spectrum. Transverse CMs cause the system's instability in case the interaction potential has too high a repulsive core. A primitive estimation of the correlation energy Δε due to CMs is presented in the Hartree-Fock approximation for a simple toy model with a square well potential. |Δε| is shown to be maximized when CMs are sustained by about one half of particles. There exists a density above which the Fermi surface intersects the lowest two bands and the interaction among CMs and particles will become attractive to provide a possible mechanism of superfluidity and/or superconductivity.

I. Unna

Koichi Takahashi, T. Tsukamoto

A method of introducing collective motion into the layered Fermi fluid (LFF) is discussed by concentrating on layer vibrations. By the random phase approximation (RPA), the original dynamical degrees of freedom of particles are separated into collective modes (CMs), uncorrelated (harmonic) oscillator modes (UOMs) and two-dimensional (2D) motions of particles within layers, which leads to a subband structure of particle spectrum. Transverse CMs cause the system's instability in case the interaction potential has too high a repulsive core. A primitive estimation of the correlation energy Δε due to CMs is presented in the Hartree-Fock approximation for a simple toy model with a square well potential. |Δε| is shown to be maximized when CMs are sustained by about one half of particles. There exists a density above which the Fermi surface intersects the lowest two bands and the interaction among CMs and particles will become attractive to provide a possible mechanism of superfluidity and/or superconductivity.

J. D. Fan, Y. M. Malozovsky

Takashi Nakatsukasa, Niels R. Walet

A model Hamiltonian describing a two-level system with a crossing plus a pairing force is investigated using technique of large-amplitude collective motion. The collective path, which is determined by the decoupling conditions, is found to be almost identical to the one in the Born-Oppenheimer approximation for the case of a strong pairing force. For the weak pairing case, the obtained path describes a diabatic dynamics of the system. PACS number(s): 21.60.-n, 36.40.Sx Nuclei and metallic clusters are finite fermionic many-body systems which support many kinds of collective motion. While properties of high-frequency vibrations (giant resonances) may be well reproduced by the random-phase approximation (RPA), some low-frequency vibrations exhibit an anharmonic nature that the RPA cannot describe. Shape coexistence and fission phenomena in nuclei and clusters also have such a large amplitude nature. In order to investigate these kinds of large amplitude collective motion, one would like to reduce the number of degrees of freedom to a few judiciously chosen collective coordinates. In order to determine the collective coordinates self-consistently, we use the theory of adiabatic