From conventional (neutron-proton) nuclear scissors to spin nuclear scissors

Investigations of the nuclear scissors mode in the frame of the Wigner Function Moments (WFM) method leading to the discovery of the new types of the nuclear collective motion are reviewed. It is demonstrated how the generalization of WFM method to take into account spin degrees of freedom allows one to reproduce all earlier described qualitative features of the conventional (neutron-proton) nuclear scissors (deformation dependence of the energy and transition probabilities, connection with isovector GQR implying the Fermi surface deformation, flows) and allows one to reveal a variety of new collective modes: isovector and isoscalar spin scissors, the relative motion of the orbital angular momentum and spin, isovector and isoscalar spin-vector GQR, spin-flip excitations.     

A one-dimensional statistical model of friction in deeply inelastic heavy ion collisions

We use the semiclassical approximation for the relative motion (which is simplified and taken to be one-dimensional), neglect other collective degrees of freedom, and describe the coupling between relative motion and intrinsic degrees of freedom by a random-matrix model. This leads to an explicit expression for the friction coefficient. Numerical calculations show qualitative agreement with the data.     

Application of a self-consistent theory of large amplitude collective motion to the generalized meshkov-glick-lipkin model

A recent formulation of the theory of large amplitude collective motion in the adiabatic limit is applied to a generalized monopole shell model. Numerical calculations are carried out for the three-level model, approximately equivalent to a classical system with two degrees of freedom. Our results go somewhat beyond previous treatments of this system and provide substantiation for the validity of the method, in suitable parameter ranges, as a way of recognizing and decoupling the collective and the non-collective degrees of freedom.     

Coupling of the rotational motion with the axial vibrations of multipolarity 2 and 4

The unadiabatic effects related to the coupling between the rotational and vibrational degrees of freedom are investigated. The collective Hamiltonian is constructed using the concepts of the Bohr theory and includes the degrees of freedom corresponding to the axial quadrupole and hexadecapole vibrations. The coupling of the nuclear vibrations with the rotational motion is so strong that one has to multiply the inertial parameters and the moment of inertia by the factor 1.7 in order to get the experimental energies spacing in the ground state bands. The dynamical effects to the electric quadrupole and hexadecapole moments are considered. The parameter of unadiabaticityα calculated within the model agrees well with the experimental data.     

The generator-coordinate-method with conjugate parameters and the unification of microscopic theories for large amplitude collective motion

A dynamic theory of large amplitude collective motion of many particle systems is presented which is relevant, for example, to nuclear fission. The theory is microscopic and makes use of a collective path, i.e. a suitably constructed set of distorted nonequilibrium Slater determinants. The approach is a generalization of the generator coordinate method (GCM) and improves its dynamic aspects by extending it to a pair of conjugate generator parameters q and p (DGCM). The problems connected with redundancy and superfluous degrees of freedom are solved by prediagonalizing the local oscillations about each point of the dynamic collective basis | q, p ～. For adiabatic large amplitude collective motion a Schrödinger equation is derived which appears to be nearly identical to the one obtained by a consistent quantization of semiclassical approaches as e.g. the adiabatic time dependent Hartree-Fock theory (ATDHF). In turn a collective path constructed by ATDHF proves to be particularly suited for being used in the present DGCM formalism. Altogether the formalism unifies two classes of microscopic approaches to collective motion, viz. the quantum mechanical GCM and the classical theories like cranking and ATDHF.     

Damping of collective modes in DIC: Quantal versus statistical fluctuations

A model is developed to describe the transformation of relative kinetic energy into intrinsic excitation energy in DIC. Energy dissipation is viewed as an indirect process, in which collective vibrational modes are first excited coherently and then damped due to the coupling to the remaining non-collective degrees of freedom. Both collective and intrinsic degrees of freedom are included explicitly, and the coupling between them is treated in a random-matrix model. Under certain assumptions it is shown that, in the weak-coupling limit, the collective probability distribution in phase space obeys a Fokker-Planek equation. This transport equation is used to derive equations of motion for the expectation values of some “macroscopic” quantities characterizing the process. Some numerical results are presented and a qualitative comparison with the Copenhagen model is attached.     

THE COMPOSITE PARTICLE REPRESENTATION THEORY: (I) The Composite Particle Representation Transformation

A generalization of the quantum mechanical representation transformation is presented, in this paper. It is shown that, as an important example, the Boson-expansion method, commonly employed in nuclear physics, corresponds to such a .generalized transformation. Using this generalization, we were able to construct a special representation called the "Composite Particle Representation". In the composite. particle representation, the composite particle degrees of freedom are included, as well as the original particle degrees of freedom. The former is introduced in order that the motion of certain particle clusters can be described as separate entities in a many-body system. This representation is shown to be exactly equivalent to the usual quantum mechanical .representation which .includes only the original particle degrees of freedom. Many applications of this theory are expected, in particular in the study of hadrons.from the quark point of view and the Interacting Boson Mode1 in nuclei.     

Nuclear dissipation due to bosonic reservoirs at finite temperature: A master equation based on second RPA dynamics

Using the second RPA property that the nuclear intrinsic degrees of freedom (specifically, the quadruples) are invested with bosonic qualities, we describe the nuclear dissipative process as the damping of a collective degree of freedom coupled to a bosonic reservoir at finite temperature. The resulting second RPA master equation within the observed collective subspace agrees exactly in form with the master equation utilized in quantum optics; it describes how a gas of collective RPA phonons relaxes to a Bose-Einstein thermal equilibrium. We further solve this master equation and provide illustrative examples for specific initial conditions. The second RPA approach accounts for quantal fluctuations in addition to the statistical fluctuations, and thus contrasts with the Kramers-Chandrasekhar approach usually utilized in nuclear physics. Furthermore, the second RPA master equation contrasts with the corresponding results of the linear response approach and of the random matrix model.     

An anomalous way to quantize solitons

We picture soliton solutions as collective modes. Their quantization is performed analogously to examples from many-body theory. In contrast to previous approaches we aim for effective actions of both type of degrees of freedom, collective as well as the non-collective ones, plus coupling terms. The procedure used is an adapted version of the Bohm-Pines method, originally developed for treating collective modes of the electron gas, later applied to nuclear transport theory. As one of the novel features we exploit chiral transformations to introduce the collective variables.Dedicated to Prof. Dr. H. J. Mang on the occasion of his 60th birthday     

Hadron structure studied with the electromagnetic probe —from giant resonances to meson production

The development of theoretical photonuclear physics over the last 40 years is illustrated by a few selected examples highlighting a number of important issues like collective motion in nuclei, the role of subnuclear degrees of freedom, relativity and meson production.     

The phase transition to the quark-gluon plasma and its effect on hydrodynamic flow

It is shown that in ideal relativistic hydrodynamics a phase transition from hadron to quark and gluon degrees of freedom in the nuclear matter equation of state leads to a minimum in the excitation function of the transverse collective flow.     

Chaotic motion and collective nuclear rotation

The regular and chaotic motion in the classical and quantal versions of a model hamiltonian with two degrees of freedom are investigated. This model contains a parameter which is identified with a conserved quantum number, the total spin. In particular, transitions between states differing in spin by one unit are studied. The transition is strongly collective for regular motion, and collectivity is destroyed with increasing stochasticity of the model.     

THE GENERATOR COORDINATE METHOD AND NUCLEAR COLLECTIVE MOTIONS (Ⅷ) THE CHOICE AND REPRESENTATION OF COLLECTIVE DEGREES OF FREEDOM

The choice and representation of degrees of freedom of collective motions are thoroughly discussed. Starting from the dynamical group of a shematic model, it is pointed out that the number of independent collective degrees of freedom is uniquely determined, although there exist different continuous variable or boson representations. If more collective degrees of freedom were involved, there must be accompanied conditions.