Nuclear Collective Motion Research Articles

Relationship between the fermion dynamical symmetric model Hamiltonian and nuclear collective motion

In this paper we investigate the role of single-particle energies on the low-lying states of ${}^{132}\mathrm{Ba},$ a typical O(6) nucleus in the IBM and the fermion dynamical symmetric model (FDSM). It is found that one can reproduce the physical quantities of a realistic system with nondegenerate single-particle energies using degenerate single-particle levels and a slightly different parametrization of the two-body interaction. However, if the single-particle splittings are enlarged by a factor of 1.5, the O(6)-like behavior of the nucleus is lost and a model that assumes degenerate levels cannot describe its collective structure. Contributions from interactions other than monopole and quadrupole pairing and a quadrupole-quadrupole force are found to be unimportant. Although the role of the abnormal-parity level depends on the details of the single-particle structure, its effects can be ``compensated'' by using different Hamiltonian parameters and degenerate single-particle levels in a FDSM treatment.

Nucleon pair approximation of the nuclear collective motion

The nucleon pair shell model calculation is performed in terms of the SD collective pairs which are obtained in a suitable way to obtain the maximum collectivity. The method is applied to even-even Sn, Te, Xe, Ba, and Ce isotopes near the $A=130$ region employing the (monopole and quadrupole) pairing plus quadrupole-quadrupole-type interaction with a very few parameters. The structure of energy levels for the quasi-\ensuremath{\gamma} band as well as the ground band is well reproduced in each nucleus. Other properties such as $E2$ transition rates and binding energies also agree with experimental data very well. The overall fit with the experimental data is superior to the previous calculations.

A program for coupled-channel calculations with all order couplings for heavy-ion fusion reactions

A FORTRAN 77 program that calculates fusion cross sections and mean angular momenta of the compound nucleus under the influence of couplings between the relative motion and several nuclear collective motions is presented. The no-Coriolis approximation is employed to reduce the dimension of coupled-channel equations. The program takes into account the effects of nonlinear couplings to all orders, which have been shown to play an important role in heavy-ion fusion reactions at subbarrier energies.

Damping of collective nuclear motion and thermodynamic properties of nuclei beyond mean field

The dynamical description of correlated nuclear motion is based on a set of coupled equations of motion for the one-body density matrix ϱ(11′; t) and the two-body correlation function c 2(12, 1′2′; t), which is obtained from the density-matrix hierarchy beyond conventional mean-field approaches by truncating three-body correlations. The resulting equations non-perturbatively describe particle-particle collisions (short-range correlations) as well as particle-hole interactions (long-range correlations). Within a basis of time-dependent Hartree-Fock states these equations of motion are solved for collective vibrations of 40Ca at several finite thermal excitation energies corresponding to temperatures T = 0 – 6 MeV. Transport coefficients for friction and diffusion are extracted from the explicit solutions in comparison to the solutions of the associated TDHF, VUU, Vlasov or damped quantum oscillator equations of motion. We find that the actual magnitude of the transport coefficients is strongly influenced by particle-hole correlations at low temperature which generate large fluctuations in the nuclear shape degrees of freedom. Thermodynamically, the specific heat and the entropy of the system as a function of temperature does not differ much from the mean-field limit except for a bump in the specific heat around T ⋍ MeV which we attribute to the melting of shell effects in the correlated system.

Investigation on Microscopic Dynamics of Dissipation in Nuclear Collective Motion

Investigation on Microscopic Dynamics of Dissipation in Nuclear Collective Motion

Algebraic Nonlinear Collective Motion

Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3,R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3,R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).

Branching rules for restriction of the Weil representations of Sp(n,R) to its maximal parabolic subgroup CM(n)

The symplectic group Sp(n,R) is the group of linear canonical transformations of a real 2n-dimensional phase space and CM(n)⊂Sp(n,R) is a maximal parabolic subgroup. The symplectic groups are the fundamental dynamical groups of classical and quantal Hamiltonian mechanics. In particular, Sp(3,R) is the dynamical group of the spherical harmonic oscillator and its Weil (harmonic series) representations are important for the microscopic (shell model) description of the collective motions of many-particle systems. The subgroup CM(3)⊂Sp(3,R) also appears in the microscopic theory of nuclear collective motion as the dynamical group of a hydrodynamic model of quadrupole vibrations and rotations of a nucleus. Thus, the Sp(3,R)→CM(3) branching rules are needed in finding the embedding of the hydrodynamic collective model in the microscopic shell model. Some new developments are made in the vector-coherent-state theory of induced representations.

Thomas-Fermi theory of the breathing mode and nuclear incompressibility

A Thomas-Fermi theory with a linear scaling assumption is proposed for the breathing mode of nuclear collective motion. It leads to a general result ${K}_{A}=〈K(\ensuremath{\rho},\ensuremath{\delta})〉{+K}_{\mathrm{GD}}\ensuremath{-}{2E}_{C}/A$ which states that the incompressibility ${K}_{A}$ of a finite nucleus $A$ mainly equals the nuclear matter incompressibility $K(\ensuremath{\rho},\ensuremath{\delta})$ averaged over the nucleon density distribution $\ensuremath{\rho}(\mathbf{r})$ of nucleus $A$, added to a term ${K}_{\mathrm{GD}}$ contributed from the gradients of nucleon densities, with twice the Coulomb energy per nucleon ${E}_{C}/A$ subtracted. The nuclear matter equation of state given by the Thomas-Fermi statistical model with a Seyler-Blanchard-type interaction is employed to calculate the nuclear matter incompressibility $K(\ensuremath{\rho},\ensuremath{\delta})$ and a localized approximation of the Seyler-Blanchard-type interaction, which is shown to be similar to the Skyrme-type interaction, is developed to calculate the value of ${K}_{\mathrm{GD}}.$ ${K}_{\mathrm{GD}}$ and $\ensuremath{-}{2E}_{C}/A$ contribute about 20--10 % and 1--5 %, respectively, to the nuclear incompressibility ${K}_{A},$ from the light to the heavy nuclei. The shell and the even-odd effects are discussed by a scaling model which shows that these effects can be neglected for medium and heavy nuclei. The anharmonic effect is shown to be significant only for light nuclei. The leptodermous expansion of ${K}_{A}$ is obtained and the contribution from the curvature term proportional to ${A}^{\ensuremath{-}2/3}$ is discussed. The calculated isoscalar giant monopole resonance energy ${E}_{M}$ for a variety of nuclei are shown to be in agreement with experimental measurements.

Transverse form factors in the collective and symplectic models

Transverse electron scattering form factors are calculated for 0 + → 2 + excitations in 16O, 24Mg and 40Ca. The objective is to learn about the current flows associated with nuclear collective motions. The 2 + states considered in 16O and 40Ca are giant quadrupole vibrational excitations. In 24Mg, the 2 + state is the first excited rotational state. The form factors have been computed microscopically within the framework of the symplectic model and, in order to interpret the dynamical content of collective flows of the model, the results are compared with form factors calculated with collective models, for different collective flows. For the giant resonance state, we calculate the form factor for irrotational-flow vibrational motion and, for the rotational state, we use the rotor model with both rigid and irrotational current flows.

Giant resonances built on highly excited states: A test-ground for nuclear dynamics

We show that from a study of collective motions built on highly excited states we can extract important information on open problems in structure and dynamics: 1. i) Competition between one-and two-body dissipation and relative temperature dependence 2. ii) Transition in the nature of nuclear collective motions: from pure quantum to classical sound waves 3. iii) Pre-equilibrium effects: the “dynamical” dipole in charge asymmetric entrance channels.

Higher order long range correlations in nuclear structure and dynamics.

An explicit correction term to the ensemble averaged trajectory for the phase space single-particle distribution function due to the presence of the higher order long range correlations is considered. It is demonstrated that this extension of the usually employed transport approaches (BUU, BNV, LV, etc.) has a diffusion structure. The role of higher order correlations in the cases of nuclear collective motion and the mean field decomposition effect in nuclear fragmentation at high temperatures is analyzed. In particular we show the importance of higher order correlations for the transition from zero to first sound regime for propagation of the collective excitation in hot nuclear matter. \textcopyright{} 1996 The American Physical Society.

The many facets of giant resonances at high excitation energies

We show that from a study of collective motions built on highly excited states we can extract important information on open problems in nuclear structure and dynamics: 1. i)Competition between one- and two-body dissipation, 2. ii) Effects of correlations and related density fluctuations, 3. iii) Transition in the nature of nuclear collective motions: from pure quantum to classical sound waves, 4. iv) Pre-equilibrium effects: the “dynamical” dipole in charge asymmetric entrance channels, 5. v) Fusion hindrance from dynamical instabilities. We try also to discuss the relevance of new, more exclusive, experiments and of a larger systematics.

Nonlinear dynamics and nuclear collective motion

To understand the exceedingly rich structure of the quantum excited states in nuclei, the importance of exploring the complex structure of the time-dependent Hartree—Fock (TDHF) manifold is discussed. It is shown that various ideas developed in the general theory of non-linear dynamics (e.g., non-linear resonance, elliptic and hyperbolic fixed points, order-to-chaos transition, etc.,) play a decisive role in obtaining analytic information on the quantum excited states, provided that the corresponding TDHF manifold has a simple potential energy surface (PES) with only one minimum. When the TDHF manifold has a PES with more than two local minima, one is involved into an important problem related with adiabatic versus diabatic collective potentials. The adiabatic collective potential is usually obtained when one numerically solves the constrained Hartree-Fock (CHF) equation within a constraining coordinate space, which has a limited number of degrees of freedom. To explore the dynamical relation between the adiabatic and diabatic single-particle states, one has to analyze the CHF method within the full TDHF manifold, which includes the constraint coordinate space. It turns out that the solutions of the CHF equation give many differentiable surfaces in the TDHF manifold. By using the differentiable property of the CHF solutions in the TDHF manifold, a new method for reaching various HF points is discussed.

Damping of nuclear collective motions within the method of phase-space moments of the Wigner distribution function

Abstract The semiclassical method of the equations of motion for the phase-space moments of the Wigner function is extended to the inclusion of damping mechanisms. The gross structure of the strength function is obtained going beyond the scaling approximation. Two-body correlations are introduced through an extended relaxation-time approximation. A realistic Skyrme-type interaction is used to derive the self-consistent potential. An application is shown to the damping of the giant monopole resonance (GMR) in 208 Pb. The calculated spreading widths with a relaxation-time parameter determined microscopically for the “collisional” damping are very much below the observed values. On the other side, consistency is found between the description of the widths of monopole, quadrupole and octupole giant resonances with an empirical value of the relaxation-time parameter

Mesonic probes

Celebrating the forty years since the landmark paper of Bohr and Mottelson on nuclear collective motion with a perspective which looks both backward and forward, we consider here the role of mesons as nuclear probes. We have had two decades of experiments at the meson factories — LAMPF, PSI & TRIUMF — during which our thinking about the role of mesons in the nucleus has changed dramatically. Twenty years ago the π — N system was believed to be well understood and the pion was heralded as an ideal probe. Now with the advent of the standard model of quarks, leptons and unified forces (and, especially, QCD) the pion is a useful but very complex nuclear probe and we understand little of the π — N system. The evolution of the ideas during the past two decades is described as well as the current issues for mesons as nuclear probes. This perspective comes at a time when large new facilities are emerging to address the new issues of the field — for example, CEBAF, Bates, RHIC, DAΦNE, COSY, MAMI and GSI — and we can look forward to new hadronic probes from the KAON Factory.

Algebraic models of nuclear collective motion

The focus of this review is on the use of algebraic structure in the development of nuclear collective theory. The objective is a theory which takes full advantage of: (a) the geometrical perspectives of the traditional collective model, (b) the independent-particle concepts of the shell model and unified models, and (c) the mathematical tools of the algebraic models. For the purpose of this review, I adopt the premise that the most important correlations in the nucleus, as far as the description of quadrupole vibrations and rotations are concerned, are of the independent-particle, pairing and quadrupole types. I shall concentrate on the complementary approaches adopted in the Interacting Boson Model and in the Symplectic Model and the ways these models relate to the shell model and the Bohr-Mottelson-Frankfurt collective model.

A MASS PARAMETER FOR NUCLEAR COLLECTIVE MOTION FROM THE GENERATOR COORDINATE METHOD

We calculate a mass parameter for nuclear collective motion within the framework of the Generator Coordinate Method. Two alternative phase space normalization schemes are presented, and a simple expression for the collective mass is obtained within the Gaussian Overlap Approximation. As an application, we calculate the mass parameter associated with β vibrations. A systematic study carried out in the mass range 12≤A≤100 shows pronounced shell effects. Our results in the spherical limit are shown to exceed the well known inertia for quadrapole oscillations in an irrotational fluid by a factor 2–3. It is argued that the application of this method to other problems in nuclear structure and reactions should be straightforward.

The microscopic theory of nuclear collective motion

An overview is given of the symplectic model and how, with appropriate generalizations to include intrinsic nucleon spin degrees of freedom and representation mixing, it provides a microscopic interpretation of the nuclear collective model.

Nuclear mass dependence of chaotic dynamics in the Ginocchio model.

The chaotic dynamics in nuclear collective motion is studied in the framework of a schematic shell model which has only monopole and quadrupole degrees of freedom. The model is shown to reproduce the experimentally observed global trend toward less chaotic motion in heavier nuclei. The relation between the current approach and the earlier studies with bosonic models is discussed.

Diabaticity of nuclear motion: problems and perspectives

The assumption of adiabatic motion lies in foundations of many models of nuclear collective motion. To what extend can nuclear modes be treated adiabatically? Due to the richness and complexity of the nuclear many-body problem there is no unique answer to this question. The challenges of nuclear collective dynamics invite exciting interactions between several areas of physics such as nuclear structure, field theory, nonlinear dynamics, transport theory, and quantum chaos.