Shell-structure inertia for slow collective motion

The modified shell correction method is suggested for the calculation of transport coefficients in a slow nuclear collective dynamics. For the multipole low-lying vibrations near the spherical shape of a nucleus, the smooth transport coefficients corresponding to the extended Thomas-Fermi approach are used as a macroscopic background. The time-dependent mean field is approximated through the infinitely deep square-well potential for the calculation of the shell corrections. Significant shell effects in stiffness and inertia are found at small temperatures. These effects disappear approximately at the same large enough temperature as in the free energy. It is shown that the collective inertia is substantially larger than that of irrotational flow owing to the consistency condition of particle density and potential variations. The collective vibration energies and reduced friction and effective damping coefficients with accounting for the shell effects are in better agreement with allowance data than that found from the hydrodynamic model. The text was submitted by the authors in English.     

Generalized cranking model for collective nuclear motion

The Inglis cranking model is generalized to take into account effects of any velocity dependence present in the single-particle potential and the reaction of the pairing field to the collective motion. The generalized model is applied to translations, rotations and some special types of vibrations. Some of our results and our numerical calculations are obtained with a harmonic-oscillator single-particle potential. Unlike the inertia calculated with the Inglis cranking model, the inertia calculated with the generalized cranking model is independent of the effective mass and approaches the irrotational value in the limit of large pairing.     

Dissipation of nuclear collective motion

The collective transport theory provides a framework for understanding damped collective motion. The irreversibility of collective motion is traced to the fact that the nucleus is an open system. The finite lifetime of single-particle excitations causes the relaxation of the nuclear collective response. Both vibrational states and damped heavy-ion collisions can be understood quantitatively by computations without free parameters.     

Particle motion in guide potentials and the collective nuclear motion

The motion of a particle which is constrained by a guide potential to move on a curve is studied in the framework of the Generator Coordinate Method (GCM). In the limit of narrow guide potentials a differential equation for the wave function of the constrained motion is obtained which differs from the corresponding Schrödinger equation by an additional potential. This additional potential is due to the embedding of the curve in the space and depends on the form of the guide potential and on the curvature of the curve. Nonadiabatic transitions in the constrained motion are possible for finite widths of the guide potential. The coupling terms are given explicitly and it is shown that an adiabatic limit exists. Since the GCM can equally well describe the collective motion of nuclei, some insight into the more complicated problem of collective motion is obtained from its analogies to the studied problem of constrained particle motion: The collective motion of a nucleus can be considered as the motion of a particle with variable mass along a curve in a guide potential which is given by the interaction potential between the nucleons. It is shown that Schrödinger's quantized kinetic energy is correctly used in the cranking model and that the additional potential terms mentioned above are included there by the definition of the collective potential energy. Approximations to the idealized GCM used here are discussed and the connection with the method of Born, Oppenheimer and Villars is indicated.     

Boson description of nuclear collective motion

Nuclear system with octupole-octupole interaction is studied by means of the boson expansion method. Expressions of the fourth-order collective Hamiltonian and third-order octupole moment operator are derived. For¹¹²Cd and¹⁴⁸Sm, characteristics of octupole vibrational spectra are discussed in comparison with the quadrupole vibration.     

Boson description of nuclear collective motion

Nuclear system interacting via quadrupole and octupole particle-hole forces is studied by the boson expansion technique. Energy spectra of the negative parity yrast band and the ground state band are calculated and compared with experiment for¹⁰⁰Ru,¹¹²Cd,¹⁵⁰Sm and¹⁵⁰Gd. ExperimentalB(E1)/B(E2) ratios show strong hindrance for E1 transitions, and are used to deduce the static polarizability of E1 transitions.     

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.     

Damping of nuclear collective and single-particle motion

The collective motion of the nuclear system is studied. In the independent-particle model, the motion is completely reversible. The neglected residual interactions couple the ph states to more complicated states. This coupling is taken into account by the optical model potential assuming independent decay of particle and hole states. Irreversibility is thereby introduced and damping of collective motion described in terms of the widths of the ph states. The validity of the assumption of independent decay is discussed. It is argued that spreading widths to low-frequency collective states are not part of the optical model, and do not contribute to damping of collective motion.     

Microscopic nuclear collective motion studied by classical equations of motion

The time-dependent variation principle is used to obtain generally non-canonical equations of motion from any class of quantum states which are parameterized by a set of continuous complex quantities. A class of states is presented whose associated classical dynamics is described by the five collective quadrupole degrees of freedom. Information about the classical dynamics of the system can be obtained from the non-canonical equations by finding physically interesting quantities which are coordinate independent and which characterize the low-energy collective motion. Approximate collective hamiltonians, of either a Bohr-Mottelson or an IBM type, can be found by insisting that the interesting physical quantities which describe the low-energy classical behavior of the many-body system are the same as those describing the classical behavior of the system given by the collective hamiltonian. The method is applied to two simple schematic models, one vibrational and one rotational, and IBM hamiltonians are obtained.     

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.     

Theory of non-adiabatic cranking and nuclear collective motion

The cranking model is extended to the case of a general non-adiabatic motion. The time-dependent many-body Schrödinger equation is solved, where the time dependence of the collective motion is determined by the classical Lagrange equations of motion. The Lagrangian is obtained from the expectation value of the energy. In the case of one collective degree of freedom the condition that the expectation value of the energy is constant in time is sufficient to determine the collective motion. An iteration procedure is applied, of which the zeroth order is shown to be the common cranking formula. In an alternative approach the energy conservation is expressed in differential form. This leads in the case of one collective degree of freedom to a set of coupled, non-linear first-order differential equations in time for the expansion coefficients of the many-body wave function and for the collective variable. As an illustrative example we solve the case of two coupled linear harmonic oscillators.     

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.     

Memory effects in nuclear Fermi-liquid

The kinetic theory is applied to the nuclear Fermi liquid. The nuclear collective dynamics is treated in terms of the observable variables: particle density, current density, pressure etc. The influence of Fermi-surface distortion, relaxation processes and memory effects on the nuclear dynamics is studied. We show that the presence of the dynamic Fermi-surface distortion gives rise to some important consequences in the nuclear dynamics which are absent in classical liquids. We discuss the nuclear small amplitude excitations, the spinodal instability, the nuclear fission and the bubble instability in heated Fermi-liquid in presence of the memory effects.     

Surveying the role of excitation energy in probing nuclear dissipation

A dynamical Langevin model is employed to calculate the excess of the evaporation residue cross sections of the ^194Pb nucleus over that predicted by the standard statistical model as a function of nuclear dissipation strength. It is shown that large excitation energy can increase the effects of nuclear dissipation on the excess of the evaporation residues and the sensitivity of this excess to the dissipation strength,and that more higher excitation energies have little contribution to further raising this sensitivity. These results suggest that on the experimental side,producing those compound systems with moderate excitation energy is sucient for a good determination of the pre-saddle nuclear dissipation strength by measuring the evaporation residue cross section,and that forming an extremely highly excited system does not considerably improve the sensitivity of evaporation residues to the dissipation strength.     

Memory effects in nuclear friction

The status of the problem of describing the dissipative phenomena in nuclear reactions is discussed from experimental and theoretical points of view. Dynamical effects in the initial phase of a fusion reaction are presented showing the evolution of two colliding ¹⁰⁰Mo ions. The role of elastic forces associated with the Fermi surface deformation is shown by comparing the results obtained with and without taking into account the memory effects. The evolution of the unified nuclear system formed after establishing contact between ions is shown to be also strongly influenced by elastic forces associated with the Fermi surface deformations and with related memory effects. Examples are given in which the Fermi surface deformations lead to phenomena usually attributed to the excitation energy and deformation dependence of the friction parameter.     

Surveying the role of excitation energy in probing nuclear dissipation

A dynamical Langevin model is employed to calculate the excess of the evaporation residue cross sections of the 194pb nucleus over that predicted by the standard statistical model as a function of nuclear dissipation strength. It is shown that large excitation energy can increase the effects of nuclear dissipation on the excess of the evaporation residues and the sensitivity of this excess to the dissipation strength, and that more higher excitation energies have little contribution to further raising this sensitivity. These results suggest that on the experimental side, producing those compound systems with moderate excitation energy is sufficient for a good determination of the pre-saddle nuclear dissipation strength by measuring the evaporation residue cross section, and that forming an extremely highly excited system does not considerably improve the sensitivity of evaporation residues to the dissipation strength.