Nuclear Collective Dynamics Research Articles

Nuclear Collective Dynamics in Transport Model With the Lattice Hamiltonian Method

We review the recent progress on studying the nuclear collective dynamics by solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation with the lattice Hamiltonian method treating the collision term by the full-ensemble stochastic collision approach. This lattice BUU (LBUU) method has recently been developed and implemented in a GPU parallel computing technique, and achieves a rather stable nuclear ground-state evolution and high accuracy in evaluating the nucleon-nucleon (NN) collision term. This new LBUU method has been applied to investigate the nuclear isoscalar giant monopole resonances and isovector giant dipole resonances. While the calculations with the LBUU method without the NN collision term (i.e., the lattice Hamiltonian Vlasov method) describe reasonably the excitation energies of nuclear giant resonances, the full LBUU calculations can well reproduce the width of the giant dipole resonance of $^{208}$Pb by including a collisional damping from NN scattering. The observed strong correlation between the width of nuclear giant dipole resonance and the NN elastic cross section suggests that the NN elastic scattering plays an important role in nuclear collective dynamics, and the width of nuclear giant dipole resonance provides a good probe of the in-medium NN elastic cross section.

Excited-state quantum phase transitions in systems with two degrees of freedom. III. Interacting boson systems

The series of articles [Ann. Phys. 345, 73 (2014) and 356, 57 (2015)] devoted to excited-state quantum phase transitions (ESQPTs) in systems with $f=2$ degrees of freedom is continued by studying the interacting boson model of nuclear collective dynamics as an example of a truly many-body system. The intrinsic Hamiltonian formalism with angular momentum fixed to $L=0$ is used to produce a generic first-order ground-state quantum phase transition with an adjustable energy barrier between the competing equilibrium configurations. The associated ESQPTs are shown to result from various classical stationary points of the model Hamiltonian, whose analysis is more complex than in previous cases because of (i) a non-trivial decomposition to kinetic and potential energy terms and (ii) the boundedness of the associated classical phase space. Finite-size effects resulting from a partial separability of both degrees of freedom are analyzed. The features studied here are inherent in a great majority of interacting boson systems.

Nuclear collective dynamics in the lattice Hamiltonian Vlasov method

The lattice Hamiltonian method is developed for solving the Vlasov equation with nuclear mean-field based on the Skyrme pseudopotential up to next-to-next-to-next-to leading order. The ground states of nuclei are obtained through varying the total energy with respect to the density distribution of nucleons. Owing to the self-consistent treatment of initial nuclear ground state and the exact energy conservation in the lattice Hamiltonian method, the present framework of solving the Vlasov equation exhibits very stable nuclear ground state evolution. As a first application of the new lattice Hamiltonian Vlasov method, we explore the iso-scalar giant monopole and iso-vector giant dipole modes of finite nuclei. The obtained results are shown to be comparable to that from random-phase approximation and consistent with the experimental data, indicating the capability of the present method in dealing with the long-time near-equilibrium nuclear dynamics.

Measurement of azimuthal flow of soft and high-pT charged particles in 5.02 TeV Pb+Pb collisions with the ATLAS detector

The experimental data collected by the ATLAS experiment during the 2015 heavy ion LHC run offers new opportunities to study properties of Quark-Gluon Plasma at unprecedented high temperatures and densities. Study of the azimuthal anisotropy of produced particles not only constrains our understanding of initial conditions of nuclear collisions and soft particle collective dynamics, but also sheds light on jet-quenching phenomena via measurement of flow harmonics at high transverse momenta. A new ATLAS measurement of elliptic flow and higher-order Fourier harmonics of charged particles in Pb+Pb collisions at sNN=5.02 TeV in a wide range of transverse momenta, pseudorapidity (|η|<2.5) and collision centrality is presented. These measurements are based on the Scalar Product and Two Particle Correlation methods. The results obtained are compared with experimental results at lower collision energies.

Semiclassical approaches to nuclear dynamics

The extended Gutzwiller trajectory approach is presented for the semiclassical description of nuclear collective dynamics, in line with the main topics of the fruitful activity of V.G. Solovjov. Within the Fermi-liquid droplet model, the leptodermous effective surface approximation was applied to calculations of energies, sum rules and transition densities for the neutron-proton asymmetry of the isovector giant-dipole resonance and found to be in good agreement with the experimental data. By using the Strutinsky shell correction method, the semiclassical collective transport coefficients such as nuclear inertia, friction, stiffness, and moments of inertia can be derived beyond the quantum perturbation approximation of the response function theory and the cranking model.The averaged particle-number dependence of the low-lying collective vibrational states are described in good agreement with basic experimental data, mainly due to an enhancement of the collective inertia as compared to its irrotational flow value. Shell components of the moment of inertia are derived in terms of the periodic-orbit free-energy shell corrections. A good agreement between the semiclassical extended Thomas-Fermi moments of inertia with shell corrections and the quantum results is obtained for different nuclear deformations and particle numbers. Shell effects are shown to be exponentially dampted out with increasing temperature in all the transport coefficients.

Nuclear collective dynamics within Vlasov approach

We discuss, in an investigation based on Vlasov equation, the properties of the isovector modes in nuclear matter and atomic nuclei in relation with the symmetry energy. We obtain numerically the dipole response and determine the strength function for various systems, including a chain of Sn isotopes. We consider for the symmetry energy three parametrizations with density providing similar values at saturation but which manifest very different slopes around this point. In this way we can explore how the slope affects the collective response of finite nuclear systems. We focus first on the dipole polarizability and show that while the model is able to describe the expected mass dependence, A^{5/3}, it also demonstrates that this quantity is sensitive to the slope parameter of the symmetry energy. Then, by considering the Sn isotopic chain, we investigate the emergence of a collective mode, the Pygmy Dipole Resonance (PDR), when the number of neutrons in excess increases. We show that the total energy-weighted sum rule exhausted by this mode has a linear dependence with the square of isospin I=(N-Z)/A, again sensitive to the slope of the symmetry energy with density. Therefore the polarization effects in the isovector density have to play an important role in the dynamics of PDR. These results provide additional hints in the investigations aiming to extract the properties of symmetry energy below saturation.

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.

Ab initio No-core Shell Model Calculations in a SU(3)-based Coupling Scheme

We use powerful algorithms of computational group theory to perform ab initio configuration-interaction calculations in a SU(3)-based symmetry-adapted many-particle basis. We demonstrate that eigenfunctions for the low-lying states of 6Li, 8Be, 12C, and 16O exhibit a strong dominance of low proton, neutron, and total intrinsic spins that carry the same spatial deformation as the leading symplectic Sp(3,ℝ) irreducible representations. Our findings imply that only a small fraction of the complete model space is needed to model nuclear collective dynamics, deformation, and α-particle clustering even if one uses modern realistic interactions that do not preserve SU(3) symmetry. This in turn points to the importance of using a symmetry-adapted framework, one based on a LS coupling scheme with the associated spatial configurations organized according to deformation.

Symmetry-adapted no-core shell model applications for light nuclei with QCD-inspired interactions

We use powerful computational and group-theoretical algorithms to perform ab initio CI (configuration-interaction) calculations in a model space spanned by SU(3) symmetry-adapted many-body configurations with the JISP16 nucleon–nucleon interaction. We demonstrate that the results for the ground states of light nuclei up through A=16 exhibit a strong dominance of low-spin and high-deformation configurations together with an evident symplectic structure. We also find states among the lowest-lying 0+ eigenstates of 12C and 16O that are clearly dominated by α-clustering correlations. Our findings imply that only a small fraction of the full model space is needed to model nuclear collective dynamics, including deformations and α-particle clustering, even if one uses modern realistic interactions that do not preserve SU(3) symmetry. This, in turn, points to the importance of using a symmetry-adapted CI framework, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation.

Skyrme energy-density functional approach to collective dynamics

Our recent developments for the microscopic description of nuclear collective dynamics in the framework of the time-dependent density functional theory is presented. It is shown that the quasiparticle random-phase approximation is ready for the systematic investigation of the giant resonances in the entire mass region of nuclear chart and that the collective Hamiltonian approach gives the quantitative description of the low-lying states in transitional nuclei with the Skyrme and pairing energy density functionals as a microscopic input. We put emphasis on necessity of the massive use of high performance computers to carry out such microscopic calculations.

Quadrupole collectivity in the two-body random ensemble

We conduct a systematic investigation of the nuclear collective dynamics that emerges in systems with two-body random interactions. We explore the development of the mean field and study its geometry. We investigate multipole collectivities in the many-body spectra and their dependence on the underlying two-body interaction Hamiltonian. The quadrupole-quadrupole interaction component appears to be dynamically dominating in the two-body random ensemble. This quadrupole coherence leads to rotational spectral features and thus suggests the formation of the deformed mean-field of a specific geometry.

SYMMETRY VS. CHAOS IN COLLECTIVE DYNAMICS

Models of nuclear collective dynamics are used to study the interplay of order (approximate dynamical symmetry) and chaos in general physical systems. We report on some recent results obtained within the interacting boson model and the geometric model.

Skyrme energy-density functional approach to nuclear collective dynamics

Skyrme energy-density functional approach to nuclear collective dynamics

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.

Semiclassical inertia of nuclear collective dynamics

For the low-lying collective excitations in nuclei, the transport coefficients, such as the stiffness, the inertia, and the friction, are derived within the periodic-orbit theory in the lowest orders of semiclassical expansion corresponding to the extended Thomas—Fermi approach. The multipole vibrations near the spherical shape are described in the mean-field approximation through the infinitely deep square-well potential and Strutinsky averaging of the transport coefficients. Owing to the consistency condition, the collective inertia for sufficiently increased particle numbers and temperatures is substantially larger than that of irrotational flow. The average energies of collective vibrations, reduced friction, and effective damping coefficients are in better agreement with experimental data than those found from the hydrodynamic model.

Mass parameters for large amplitude collective motion: A perturbative microscopic approach

The adiabatic limit of the time-dependent Hartree–Fock–Bogoliubov approximation is studied in the canonical basis for a rather wide class of collective modes. As a first step towards a fully selfconsistent solution, we study mass parameters where the effects due to the time-odd part of the mean fields are neglected, but where the static rearrangement of the generalized cranking operator is taken into account. Corresponding inertia parameters are compared with those resulting from currently used ansatz in microscopic accounts of the low energy nuclear collective dynamics. For the particular case of the axial quadrupole motion and using the Gogny D1S effective interaction, we show that our mass parameters exhibit strong variations as functions of the deformation whose origins are traced back to the rearrangement of both the Hartree–Fock and pairing fields. The physical consequences of these variations depend of the time scales of the studied collective motions and are illustrated in the context of superdeformed states in the A∼150 region and of the lifetime of a fission isomer in the actinide region.

On the stability of global non-radial pulsations of neutron stars

A neutron star is the cosmic nuclear object in which the energy of gravitational pull is brought to equilibrium by elastic energy stored in the neutron Fermi-continuum. Evidence for the viscoelastic behaviour of a stellar nuclear matter provides a seismological model of pulsar glitches interpreted as a sudden release of the elastic energy. In laboratory nuclear physics, the signatures of viscoelasticity of nuclear matter are found in the current investigations on the collective nuclear dynamics, in which a heavy nucleus is modelled by a spherical piece of viscoelastic Fermi-continuum compressed to the normal nuclear density. It is plausible to expect, therefore, that the motions of self-gravitating nuclear matter constituting the interior of neutron stars should be governed by the equations of an elastic solid, rather than by hydrodynamic equations describing the behaviour of gaseous plasma inside the main sequence stars. In this paper, we present arguments that elastodynamic equations, originally introduced in the context of nuclear collective dynamics, can provide a proper account of elasticity in the large scale motions of neutron matter under its own gravity. Emphasis is placed on mathematical physics underlying the constructive description of the continuum mechanics and the rheology of macroscopic nuclear matter. The capability of the elastodynamic approach is examined by analysis of oscillatory dynamics of a neutron star in the standard homogenous model, operating with a spherical mass of self-gravitating degenerate neutron matter whose viscoelastic behaviour is described in terms of the spheroidal and torsional gravitational-elastic eigenmodes, inherenly related to viscoelasticy. The energy variational principle is utilized to compute the frequencies of viscoelastic gravitational pulsations and their relaxation time. The method is demonstrated for both the idealized homogeneous model and the neutron star models constructed on realistic equations of state. Finally, we derive analytic conditions for the stability of a neutron star to linear elastic deformations accompanying the non-radial pulsations, and discuss the fingerprints of these pulsations in the electromagnetic activity of radiopulsars.

Prospact and Retrospect on Development of the Microscopic Theory of Nuclear Collective Dynamics

Prospact and Retrospect on Development of the Microscopic Theory of Nuclear Collective Dynamics

Dynamic response function and large-amplitude dissipative collective motion.

Aiming at exploring microscopic dynamics responsible for the dissipative large-amplitude collective motion, the dynamic response and correlation functions are introduced within the general theory of nuclear coupled-master equations. The theory is based on the microscopic theory of nuclear collective dynamics which has been developed within the time-dependent Hartree-Fock (TDHF) theory for disclosing the complex structure of the TDHF manifold. A systematic numerical method for calculating the dynamic response and correlation functions is proposed. By performing numerical calculation for a simple model Hamiltonian, it is pointed out that the dynamic response function gives important information in understanding the large-amplitude dissipative collective motion which is described by an ensemble of trajectories within the TDHF manifold.

Nuclear Collective Dynamics of Shape Phase Transition. I

The quasi-bands structure for the transition from spherical to deformed shape in Sm isotopes is studied by making use of the self-consistent collective coordinate method. The five-quadrupole collective coordinates and momenta are explicitly treated and they are canonically transformed into the intrinsic shape and rotational degrees of freedom with respect to the body-fixed reference frame. From the analysis of the collective kinetic energy in the intrinsic system, the higher-order anharmonic terms including the coupling with two-quasi-particle non-collective states play an essential role in the description of the mass parameters and rotational moments of inertia.