On the theory of collective motion in nuclei. II. Quantum theory

The collective Hamiltonian is assumed to be invariant under the orthogonal group O(A ? 1, $\text{R}$). It is shown that the quantum collective dynamics can be formulated on a coset space of the symplectic group $\text{sp}$(6, $\text{R}$) of dimension 12, 16 or 18. The first case corresponds to the collective dynamics based on closed shells and leads to a Hilbert space of analytic functions in six complex collective quasiparticle variables. Dequantization of this scheme yields the classical dynamics described in I. In the limit A ? 1 one obtains a system of s- and d-bosons with symmetry group $\text{u}$ (6) in the collective state space.     

On the hexadecapole collective motion in spherical nuclei

The hexadecapole-collective motion in spherical nuclei is discussed. Numerical calculations are presented and compared with available experimental data.     

On the theory of collective motion in nuclei. III. From Hamiltonian dynamics to vortex-free fluidity

It is assumed that the Hamiltonian for collective motion in nuclei is invariant under the orthogonal group O(n, $\text{R}$). For degenerate orbits in phase space it is shown that the classical Hamiltonian equations reduce to the equations of a vortex-free fluid with a velocity field determined by independent equations of motion.     

Macroscopic description of collective motion in fast-rotating nuclei

The distorted Fermi-surface model is generalized to study rotating nuclei. The Chandrasekhar-Lebovitz method is used to solve the equations of nuclear hydrodynamics. A complete analysis of possible stationary ellipsoidal configurations is presented showing such phenomena as giant back-bending and shape isomerism. The normal oscillation modes of quadrupole symmetry are analysed: it is shown that besides the modes corresponding to the quadrupole giant resonance (QGR) split due to the centrifugal and Coriolis forces, the model predicts the appearance of two additional low-lying modes. The nonvibrational modes are analysed, and the corresponding inertia parameters are calculated. The electric quadrupole transitions in rotating nuclei are studied; according to the model the E2 transitions follow very closely the yrast-line both in the axial noncollectively-rotating nuclei and in the three-axial nuclei.     

On the theory of collective motion in a system of interacting particles

Collective variables are introduced: coordinates and momenta, which in fact are canonical variables. These variables are used to write a Hamiltonian describing collective motions in a classical system of interacting particles.The author is grateful to K. A. Valiev for his supervision and constant interest in the work.     

Microscopic description of collective motion in pf shell nuclei

Rotational and vibrational excitations in pf shell nuclei are studied by means of the generator coordinate method. The generator coordinates are the pairing energies and the quadrupole moments of constrained Hartree-Bogoliubov states, projected onto good angular momenta and particle numbers. The Kuo interaction and the one modified by McGrory are used. The vibrational character of the yrast energies appears to be produced by mixing prolate and oblate wave functions. Pairing correlations are essential for this mixing. In contrast to the yrast states the excitation energies of the higher states depend strongly on the interaction used. They show good agreement with experiment, particularly in the case of ⁴⁸Ti with the Kuo force. The calculated B(E2) values exhibit a rotational band structure in general, even if the energies look more vibrational. The force dependence of the excitation energies can qualitatively be understood by inspection of the intrinsic energy surface.     

Boson description of nuclear collective motion. I

As the first part of the series on the application of the boson expansion method to the nuclear collective motion, the method of Kishimoto and Tamura is illustrated by taking a simple case of boson expansion up to second order. By taking into account the effect of particle channel by the projection technique, the lowest mode is shown to have the same property as the RPA phonon.     

A geometric classical model of collective motion in nuclei

A collective phase space of dimension 12 is introduced to study a classical model of nuclear collective motion. The model employs the 6 components of the coordinate quadrupole and 6 corresponding generalized momenta and can be related to properties of closed-shell nuclei. Vibrational and rotational coordinates are introduced, and purely rotational solutions are studied. The model demonstrates hamiltonian non-rigid motion with a fixed shape of the nucleus. The relation between the coordinate quadrupole tensor and the ellipsoids related to the angular momentum and angular velocity is analyzed for simple forms of the collective potential.     

Uniqueness of the collective submanifold in the adiabatic theory of large amplitude collective motion

It is emphasized that the conditions for the existence of a collective submanifold which follow from adiabatic time-dependent Hartree-Fock theory are precisely the conditions for the existence of a manifold of solutions of Hamilton's equations confined to a surface of reduced dimensionality. A constructive procedure, valid in any number of dimensions and involving the concept of the multidimensional valley, is developed to determine whether a given system admits such a manifold. It is extended to include the idea of the approximate manifold, and an application to a generalized landscape model is described.     

On the theory of Brownian motion. I. Interaction between Brownian particles

The molecular theory of the Brownian motion of heavy particles in a homogeneous solvent of light particles is extended to cover the case of interactions between the Brownian particles. This will have physical effects in the concentration dependence of the Brownian particle self-diffusion coefficient. A density expansion for the Brownian particle friction coefficient is derived, and an approximation permitting the first density correction to be calculated is suggested.This work, part of research supported by NSF Grant GP-8497, was done under the tenure of a National Science Foundation Senior Postdoctoral Fellowship, and of a sabbatical leave granted by the University of Oregon.     

Relativistic mean-field description of collective motion in nuclei: the pion field

The influence of the pion field on isovector dipole and spin-dipole collective oscillations is investigated in a time-dependent model based on relativistic mean field theory. We find that the inclusion of the long range pion-nucleon interaction provides an additional strong damping mechanism for the isovector dipole vibrations. The inclusion of the pion field has also a strong effect on the dynamics of spin-dipole vibrations, and in particular on the splitting of excitation energies of theJ ^π (0^?,1^?,2^?) components of the isovector spin-dipole resonance.     

Damping of nuclear collective motion in the extended mean-field theory

The dissipation mechanism in slow nuclear collective motion is studied in the frame of the extended mean-field theory. The collective motion is treated explicitly by employing a travelling single-particle representation in the semi-classical approximation. The rate of change of the collective kinetic energy is determined by: (i) one-body dissipation, which reflects uncorrelated particle-hole excitations as a result of the collisions of particles with the mean field, (ii) two-body dissipation, which consists of simultaneous 2 particle-2 hole excitations via direct coupling of the residual two-body interactions, and (iii) potential dissipation due to the redistribution of the single-particle energies as a result of the random two-body collisions. In contrast to the first two processes the potential dissipation exhibits memory effects due to the large values of the local equilibration times.     

A quantum model of collective motion in nuclei and its dequantization

Collective coherent states of Perelomov type are denned by acting with unitary operators from a representation of the symplectic group on the ground state of closed-shell nuclei. A dequantization scheme associates with quantum observables classical ones, and with the state space a phase space and a generalized classical dynamics. Applications to the nuclei ⁴He, ¹⁶O and ⁴⁰Ca are derived from microscopic interactions.     

On collective two-phonon states in deformed nuclei

The centroid energies of the two-phonon states in doubly even deformed nuclei are calculated within the quasiparticle-phonon nuclear model taking into account the Pauli principle in the two-phonon components of the wave functions. It is shown that the collective two-phonon energies are shifted by 1–2 MeV to higher energies due to the Pauli principle. A strong fragmentation of the two-phonon collective states over many nuclear levels occurs at the excitation energies of 3–4 MeV. It is concluded that the two-phonon states cannot exist in deformed nuclei. The analysis of the available experimental data on the two-phonon states shows that the experimental data do not contradict the results of these calculations.     

On the description of dissipative collective motion

We use a recently developed time-dependent projection method to describe the dissipation of collective motion coupled to an intrinsic system. The underlying physical picture is similar to that of the linear response approach. Our approach is, however, different from the conceptual point of view. We do not resort to a quasistatic picture but use instead a time-dependent projector. Furthermore, we project on a model space which includes the intrinsic hamiltonian in addition to the collective subspace. In this way we obtain a Fokker-Planck equation for the collective variables which is coupled to a transport equation describing the evolution of the temperature of the intrinsic system.     

Large amplitude collective motion in nuclei and metallic clusters — Applicability of adiabatic theory for a pairing model

A model Hamiltonian describing a two-level system with a crossing plus a pairing force is investigated using the 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. Presented by T. Nakatsukasa at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997. This work is supported by EPSRC (UK).     

Microscopic study of fermionic collective motion: (I). Functional representation of collective motion

Based on the shell structure of the finite nuclear many fermion system (FMFS), the coherent states related to the Spin(2r) group are defined. The global and local functional representations of the FMFS state-vectors and operators, defined on the coset space Spin(2r)/U(r), are constructed. The nonuniqueness of the coherent state functional representations is overcome by the imposition of a consistency condition on the wave functions. The influence of the boundary of the coset space Spin(2r)/U(r) on the local functional representation is physically removed only for the bound states of FMFS. The reason for the non-hermitian behavior of the local functional representation is exposed. Finally, using Bargmann's theory, the boson representation of FMFS are directly calculated from the local functional representation of FMFS. Thus, in this paper, we have demonstrated that the kinematics of the collective behavior of FMFS can be described in three non-equivalent representations: the fermion representation, the global functional representation and the local functional representation.