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.     

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.     

Fluid-dynamical description of nuclear collective excitations

The role of antisymmetric tensor fields in the gauging of groups is related to theorems on cohomology theory, and Cartan integrable systems are discussed. Examples are given. Various possibilities to gauge d = 11 supergravity by decontracting its underlying group are considered. In particular the simple supergroups Osp (1 | 64) and SU(32 | 1) yield a negative result, but a certain non-semisimple supergroup containing Osp (1 | 32) is proposed as a viable candidate. The corresponding action would no longer contain the 3-index photon A_μν?, but instead a second spin $\text{3}\text{2}$ field η_μ and boson fields $\text{B}{}_{\mathrm{\mu }}{}^{\mathrm{a1a2}}$ and $\text{B}{}_{\mathrm{\mu }}{}^{\mathrm{a1\dots a5}}$. A first order formalism for d = 11 is presented. It is to be used for an improved form of dimensional reduction.     

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.     

On the nuclear polarization potential for heavy-ion scattering

The real polarization potential ΔV due to transfer reactions is studied using a microscopic semiclassical formalism. It is found that ΔV is typically of the same order of magnitude as the corresponding absorptive potential W. Different types of possible energy dependences for ΔV and W are explored qualitatively. Specific calculations for ¹⁶O + ²⁰⁸Pb and ¹⁶O + ⁶⁰Ni scattering show features similar to those which have been deduced empirically.     

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.     

Estimation of nuclear effects in heavy-ion elastic scattering

The elastic scattering of heavy ions interacting by a central complex nuclear potential is calculated in first-order perturbation theory. The differential cross section can be expressed by simple analytical formulas for a Yukawa-type potential as well as for a Woods-Saxon potential. This leads to a very easy estimate of the nuclear effects, if the energy of the projectile is in the neighbourhood of the Coulomb barrier. It is shown that the derived expressions are quite accurate compared to a full numerical solution of the Schrödinger equation, as long as the elastic cross section deviates less than about 50 % from the pure Rutherford cross section.     

Theory of resonant inelastic x-ray scattering by collective magnetic excitations

I present a tractable theory for the resonant inelastic x-ray scattering (RIXS) of magnons. The low-energy transition operator is written as a product of local spin operators and fundamental x-ray absorption spectral functions. This leads to simple selection rules. The scattering cross section linear (quadratic) in spin operators is proportional to the fundamental magnetic circular (linear) dichroic spectral function. RIXS is a novel tool to measure magnetic quasiparticles (magnons) and the incoherent spectral weight, as well as multiple magnons up to very high energy losses, in small samples, thin films, and multilayers, complementary to neutron scattering.     

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.     

Excitation of collective nuclear states by fast particles

The elastic and inelastic scattering of a fast particle by a vibrating nucleus is discussed in the semicalssical approximation. For elastic scattering it is shown that the effect of the vibrations can be described by an effective deformed optical potential which is axially symmetric about the incident direction. Explicit results are obtained for inelastic scattering. In an appendix, the validity of the semiclassical approximation for potential scattering is discussed and numerical tests made.     

Interband collective electronic excitations in resonant Raman scattering of two-subband quantum wires

Using the bosonization technique, a theory for the collective excitations of the interacting electrons in quantum wires with two subbands occupied is developed. The dispersion relations for the inter-subband charge and spin density excitations are determined. The results are used to interpret the features observed in recent measurements of the Raman spectra of AlGaAs/GaAs quantum wires, particularly for photon energies near band gap resonance. It is shown that peaks previously identified as “single particle excitations” are signatures of higher order collective spin density excitations. Predictions about the observability of the interband modes are made. Received 8 February 1999     

Description of elastic heavy-ion scattering within the Glauber-Sitenko approach

Analytic expressions for the amplitudes of elastic nucleus-nucleus scattering for various collision regimes are derived within the Glauber-Sitenko approach. The procedure used to do this employs an extended optical potential of the Woods-Saxon type and takes into account the deflection of trajectories by a strong Coulomb field. A comparison of the analytically calculated cross sections with numerical results and experimental data shows that the approach in question can be successfully used in the energy range from 10 to 100 MeV per nucleon. It is demonstrated that, for a preset potential, it is possible to find angular ranges dominated by specific patterns of scattering, such as classical or rainbow scattering and Fresnel or Fraunhofer diffraction.     

A new particle-hole approach to collective states

The relevance of the particle-hole space is demonstrated by showing that in some commonly used formalisms the first excited state lies entirely within the particle-hole space generated from the correlated ground state. This property is proved for several cases of angularmomentum projection — projected Hartree-Fock method (PHF) — and for the generator coordinate method in the Gaussian overlap approximation, while in other cases it has been verified only numerically. A new method is presented for the approximate calculation of energies and transition amplitudes of particle-hole excited states. Only hermitian one-body operators are used to generate the excited states. The two-body density matrix of a correlated state approximating the ground state is required as input data. The formula is tested on the 2⁺ and 3^? states of ⁸Be and ¹²C by using the PHF ground state. Where comparison is possible the method gives better agreement with PHF and experiment than the extended random-phase approximation.     

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.     

Dual boson approach to collective excitations in correlated fermionic systems

We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in the so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to an extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to “bare” RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.     

Inelastic light scattering by collective excitations in the fractional quantum Hall regime

We report an inelastic light scattering study of long wavelength collective gap excitations of fractional quantum Hall (FQH) states at ν=p/(2p+1) for . The ν-dependence of the gap energy suggests a collapse of the collective excitation gap near . In a range of filling factors close to , where the FQH gap is believed to collapse, we observe a collective excitation mode that exists only at temperatures below 150 mK.