Sum rules for nuclear collective excitations

Characterizations of the response function and of integral properties of the strength function via a moment expansion are discussed. Sum rule expressions for the moments in the RPA are derived. The validity of these sum rules for both density independent and density dependent interactions is proved. For forces of the Skyrme type, analytic expressions for the plus three energy weighted sum rules are given for isoscalar monopole and quadrupole operators. From these, a close relationship between the monopole and quadrupole energies is shown and their dependence on incompressibility and effective mass is studied. The inverse energy weighted sum rule is computed numerically for the monopole operator, and an upper bound for the width of the monopole resonance is given. Finally the reliability of moments given by the RPA with effective interactions is discussed using simple soluble models for the hamiltonian, and also by comparison with experimental data.     

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.     

Retardation effects in damping of nuclear collective excitations

We expand the nonmarkovian collision integral in terms of multipolarities of the distortion of the Fermi surface. It is shown that damping of zero-sound is determined by all multipolarities of the Fermi-surface deformation. For large zero-sound velocity with respect to the Fermi velocity the relaxation time is related to the quadrupole deformation of the Fermi surface. The contributions of collisions to the total widths of the giant multipole resonances are calculated in a semiclassical macroscopic nuclear model.     

The tensor force and collective excitations in nuclear matter

The formalism for the particle-hole Green function is developed to handle the nucleon-nucleon tensor potential in order to investigate both the ring correlation energy and collective excitations in nuclear matter. The formalism is exact for direct ring diagrams. An approximation for exchange ring diagrams is also introduced. The one-pion-exchange potential with cut-off radius is used throughout. No collective excitations are found coming from the tensor force.     

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.     

High-energy approach for heavy-ion scattering with excitations of nuclear collective states

A phenomenological optical potential is generalized to include the Coulomb and nuclear interactions caused by the dynamical deformation of its surface. In the high-energy approach, analytical expressions for elastic and inelastic scattering amplitudes are obtained, where all the orders in the deformation parameters are included. The multistep effect of the 2⁺ rotational state excitation on elastic scattering is analyzed. Calculations of inelastic cross sections for the ¹⁷O ions scattered on different nuclei at about tens of MeV/nucleon or higher are compared with experimental data, and the important role of the Coulomb excitation is established. The text was submitted by the authors in English.     

Fluid-dynamical description of the gap fluctuations of twotrapped fermion species

We apply a recent generalisation of the fluid-dynamical scheme developed for two trapped fermion species with pairing interactions to examine the fluctuations of the gap density coupled to the particle transition density at low energy. The dynamical scheme satisfies Kohn’s theorem for both the particle density and the pairing gap. We analyse the form of the gap fluctuations in a spherical trap in terms of their multipolarity and the interaction strength, and find that coupling to the particle density produces considerable stiffness of the gap transition density together with compression towards the centre of the trap.     

Inelastic scattering of heavy ions at intermediate energies with excitations of nuclear collective states

Excitation of low-lying nuclear collective states upon scattering of heavy ions with energies of several tens of MeV/nucleon has been studied. The interaction potential leading to excitation is chosen in the form of a derivative of the microscopic (or semimicroscopic) nucleus-nucleus double-folding optical potential. Elastic and inelastic scattering cross sections have been calculated within the high-energy approximation; the inelastic scattering amplitude was obtained in the first order in the deformation parameter. The cross sections are compared with the experimental data on scattering of ¹⁷O from a series of nuclei with excitation of the 2⁺ level.     

Macroscopic equations of motion and dynamic polarizability in the study of nuclear collective excitations

Time dependent Hartree-Fock equations are derived using a variational principle over a restricted part of the space of the Slater determinants, in the limit of small deformations (RPA). When an external oscillating field interacts with the nucleus, this method leads to an explicit expression of the nuclear response function (dynamic polarizability) as a function of the external frequency and of the deformation field, defining the nuclear deformation induced by the interaction. A linear differential equation for the deformation field is also obtained: in the limit ω → ∞ it has analytical solutions which satisfy the energy-weighted sum rule, evaluated in a HF ground state, in both isoscalar and isovector modes.     

Atomic collective excitations in liquid lead

The atomic dynamics of liquid lead at the temperature T = 600 K has been simulated on the basis of the embedded atom model potential (the “embedded” atom model making it possible to effectively take into account the many-particle interactions) in order to study the mechanisms of formation of the atomic collective excitations. Spectra of the dynamic structure factor S(k, ω) and the spectral densities of the time correlation functions of the longitudinal \(\tilde C_L\) (k, ω) and transverse \(\tilde C_T\) (k, ω) currents have been calculated for the wavenumber region 0.11 Å^?1 ≤ k ≤ 2.01 Å^?1. It has been established that the dynamics of density fluctuations is characterized by two dispersion “acoustic-like” branches of the longitudinal and transverse polarization.     

Multistep variational approach to collective excitations

We discuss a multistep variational approach to collective excitations. The approach is developed in a boson formalism (bosons representing particle-hole excitations) and based on an iterative sequence of diagonalizations in subspaces of the full boson space. Purpose of these diagonalizations is that of searching for the best approximation of the ground state of the system. The procedure also leads us to define a set of excited states and, at the same time, of operators which generate these states as a result of their action on the ground state. We examine the cases in which these operators carry one-particle one-hole and up to two-particle two-hole excitations. We also explore the possibility of associating bosons to Tamm-Dancoff excitations and of describing the spectrum in terms of only a selected group of these. Tests within an exactly solvable three-level model are provided.     

Optically-driven cooling for collective atomic excitations

We explore how to cool collective atomic excitations in an optically-driven three-level atomic ensemble, which may be described by a model of two coupled harmonic oscillators (HOs) with a time-dependent coupling. Moreover, the model of two coupled HOs is further generalized to address the resolved sideband cooling issues, where the lower-frequency HO can be cooled whenever the cooling process dominates over the heating one during the sideband transitions. Unusually, due to the absence of the heating process, the optimal result for cooling collective excitations in an atomic ensemble could break the standard resolved sideband cooling limit for general models of two coupled HOs.     

Theory of collective excitations in simple liquids

We present a parameter-free theory of the collective excitations in simple liquids such as liquid metals or rare gases. The theory is based on the mode-coupling theory (MCT), which has been previously applied successfully for explaining the liquid-to glass transition. The only input is the liquid structure factor. We achieve good agreement both for the liquid dispersion (maximum of the longitudinal current spectrum) and width (damping) with experimental findings. The time-dependent memory function predicted by MCT has a two-step exponential decay as previously found in computer simulations. Furthermore MCT predicts a scaling of the liquid dispersion with the effective hard-sphere diameter of the materials. This scaling is obeyed by the available experimental data.     

Unified description of 0+ states in a large class of nuclear collective models

A remarkably simple regularity in the energies of 0+ states in a broad class of collective models is discussed. A single formula for all 0+ states in flat-bottomed infinite potentials that depends only on the number of dimensions and a simpler expression applicable to all three interacting boson approximation symmetries in the large N(B) limit are presented. Finally, a connection between the energy expression for 0+ states given by the X5 model and the predictions of the interacting boson approximation near the critical point of the first order phase transition is explored.