Giant Dipole Resonance In Nuclei Research Articles

Relativistic Coulomb excitation of the giant dipole resonance in nuclei: How to calculate transition probabilities without invoking the Liénard-Wiechert relativistic scalar and vector potentials

The conclusions extracted from a recent study of the excitation of giant dipole resonances in nuclei at relativistic bombarding energies open the way for a further simplification of the problem. It consists in the elimination of the relativistic scalar and vector electromagnetic potentials and the familiar numerical difficulties associated with their presence in the calculation scheme. The inherent advantage of a reformulation of the problem of relativistic Coulomb excitation of giant dipole resonances along these lines is discussed.

Giant resonances at zero and finite temperatures

The recent status of theoretical and experimental studies of giant dipole resonances in nuclei is presented with the emphasis on: (1) giant dipole resonances in highly excited nuclei, (2) multiple-phonon resonances and (3) pygmy dipole resonances in neutron-rich nuclei. In particular, the description of these resonances within the framework of the phonon damping model is discussed in detail.

Relativistic Coulomb excitation of the giant dipole resonance in nuclei: A straightforward approach

We investigate alternatives to the standard formalism used for the study of relativistic Coulomb excitation of the giant dipole resonance in nuclei. The idea is to obtain reasonable results for the probabilities of excitation and cross sections to the one-phonon and two-phonon levels avoiding the substantial complexity of the treatments exploited so far. This is achieved for the relevant range of partial waves up to bombarding energies of at least $5\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$ per nucleon. The transfer of energy to the center of mass of the excited nuclei is also investigated.

Effects of correlations on neutrino opacities in nuclear matter

Including nucleon-nucleon correlations due to both Fermi statistics and nuclear forces, we have developed a general formalism for calculating the neutral-current neutrino-nucleon scattering rates in nuclear matter. We derive corrections to the dynamic structure factors due to both density and spin correlations and find that neutrino-nucleon scattering rates are suppressed by large factors around and above nuclear density. Hence, in particular for the ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ neutrinos, but also for the ${\ensuremath{\nu}}_{e}$ neutrinos, supernova cores are more ``transparent'' than previously thought. The many-body corrections increase with density, decrease with temperature, and are roughly independent of incident neutrino energy. In addition, we find that the spectrum of energy transfers in neutrino scattering is considerably broadened by the interactions in the medium. An identifiable component of this broadening comes from the absorption and emission of quanta of collective modes akin to the Gamow-Teller and giant dipole resonances in nuclei (zero sound; spin sound), with \ifmmode \check{C}\else \v{C}\fi{}erenkov kinematics. Under the assumption that both the charged-current and the neutral-current cross sections are decreased by many-body effects, we calculate a set of ad hoc protoneutron star cooling models to gauge the potential importance of the new opacities to the supernova itself. While the early luminosities are not altered, the luminosities after many hundreds of milliseconds to seconds can be increased by factors that range from 10 to 100 %. Such enhancements may have a bearing on the efficacy of the neutrino-driven supernova mechanism, the delay to explosion, the energy of the explosion, and the strength and relative role of convective overturn at late times. However, the actual consequences, if any, of these new neutrino opacities remain to be determined.

Giant dipole resonance in nuclei with exotic shape

The giant dipole resonance is studied in nuclei with exotic shapes utilizing the Woods-Saxon potential for the single-particle states, and the RPA formalism for the phonon states. Requirements on translational invariance is used to determine the residual interaction including coupling constants. The low-lying resonance component in superdeformed nuclei, which corresponds to vibrations along the longer axis, almost disappears if a strong necking is formed.

Gamma decay of giant dipole resonances and the shapes and fluctuations of hot nuclei

Developments in the study of the gamma decay of Giant Dipole Resonances (GDR) in hot nuclei are discussed. The main emphasis here is on experiments and theoretical efforts aimed at understanding the average shapes and fluctuations of the shapes of excited nuclei from studies of the angular distribution of the high energy gamma rays emitted when Giant Dipole Resonances in nuclei with large thermal energy decay.

Systematics of the double giant dipole resonances in nuclei.

A generalization of the continuum open-shell r-space linear response random-phase approximation method to finite temperatures (i.e., TDRPA method) is applied in a study of the systematics of the electric double giant dipole resonance (DGDR) in magic and open-shell nuclei covering a wide range of nuclear masses. Viewing the DGDR as a single-phonon vibration in a hot nucleus, whose temperature corresponds to the centroid energy of the ground-state (zero-temperature) GDR, the TDRPA equation has been solved for the eleven nuclei whose DGDR state has recently been investigated in pion double-charge-exchange (DCX) experiments. The expected general features of a collective vibration in hot nuclei, particularly the broadening and the downshift of the GDR excitation energy due to increase in temperature, were found to be small, yet quite distinguishable. Except for the lighter nuclei, a reliable estimate for the DGDR energy would be ${\mathit{E}}^{\mathrm{DGDR}}$\ensuremath{\approxeq}2${\mathit{E}}^{\mathrm{GDR}}$ and the estimate for its width would be ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{DGDR}}$\ensuremath{\approxeq} \ensuremath{\surd}2 ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{GDR}}$. However, the changes in the integrated cross sections of the DGDR due to finite temperature are found to be much more significant. An exact ${\mathit{A}}^{\mathrm{\ensuremath{-}}1/6}$ power law for the DGDR energy is suggested by the TDRPA solutions. A gratifying agreement between the TDRPA predictions and experiment has been established for the Q values of the relevant pion DCX reactions after taking into account the proper Coulomb and symmetry energy corrections.

Optical response of metal microclusters: Atomic analog of the giant dipole resonance in nuclei.

From the analogy between the collective vibrations of delocalized electrons against the positive charged background provided by the ions in small metal clusters and the vibrations of protons against neutrons (giant dipole resonance) in nuclei, it is possible to formulate a model for the damping mechanism of plasma oscillations that exhibits an interesting correspondence between atomic and nuclear statistical processes.

Relativistic coulomb excitation of giant resonances in the hydrodynamical model

We investigate the Coulomb excitation of giant dipole resonances in relativistic heavy-ion collisions using a macroscopic hydrodynamical model for the harmonic vibrations of the nuclear fluid. The motion is treated as a combination of the Goldhaber-Teller displacement mode and the Steinwedel-Jensen acoustic mode, and the restoring forces are calculated using the droplet model. This model is used as input to study the characteristics of multiple excitation of giant dipole resonances in nuclei. Possibile signatures for the existence of such states are also discussed quantitatively.

Giant Resonances in Excited Nuclei

An experimental and theoretical review of the giant dipole resonance in nuclei is given. Proton capture reactions and heavy ion fusion are emphasized. Topics considered include statistical models, angular distributions and measurement techniques. (AIP)

Group theoretical models of giant resonance splittings in deformed nuclei

We discuss the coupling between low-lying and high-lying collective modes in nuclei within the framework of group theoretical models. In particular, we study the splitting of the giant dipole resonance in nuclei with an axial and triaxial deformation.

Microscopic derivation of classical equations of motion for many-particle systems

The effects of the internal structure on the classical description of scattering systems consisting of large composite particles are studied. For elastic scattering, the Pauli principle leads to a modification of the double folding potential and of the reduced mass at small distances. For inelastic scattering, the possibility of internal excitation leads to a friction term proportional to the velocity in the classical equation of motion. The magnitude of the friction term is shown to depend on the transition probabilities to excited states. So a microscopic basis is provided for the equations used for the description of heavy-ion scattering. Finally, the formalism is applied to calculations of the line-widths of giant dipole resonances in nuclei.

Excitation of the giant dipole resonance in the scattering of isoscalar projectiles

The excitation of the giant dipole resonance in nuclei with N > Z by isoscalar projectiles α and d is discussed within a simple collective model for isoscalar dipole excitations. Calculations have been performed for 208Pb; they are compared to recent data on the excitation of the new giant resonance at E x = 13.8 MeV. For α scattering the effect of dipole excitation is quite weak but significant contributions are obtained for d scattering.

The Similarities Between Photoabsorption to Bound and Continuum States

The p6 → p5d and d10 → d9f transitions to bound and continuum states are considered and it is shown that the major features in the photoionization of the neutral rare gases are present in the photoabsorption to bound states in the isoelectronic ions. This is a consequence of the collapse of d and f orbitals between the neutral and the ionized members of the particular isoelectronic sequences. It is shown that Hartree-Fock calculations which take into account the proper angular momentum coupling of the final state can account for the gross structure of the photoionization as well as the photoabsorption spectrum to within approximately a factor of 2. Much stronger correlation effects exist in bound spectra. The identification of collective resonances, which should correspond to strong correlation effects, in the continua of the neutral rare gases by other workers is shown to rely on a doubtful analogy with the use of the Random Phase Approximation to interpret the giant dipole resonance in nuclei and on the neglect of exchange in the early calculations of the photoionization cross-sections. Exchange turns out to be extremely important for the 1P terms in p5d and d9f which are the only ones that can be reached by an electric dipole transition from the ground state. It is concluded that it is unnecessary to invoke collective effects to explain the photoionization cross-sections of the rare gases.

A dynamical theory of the giant dipole resonance in nuclei

Calculations of the giant dipole resonance in the particle-hole model, employing empirical values for the unperturbed particle and hole energies have been unsuccessful in pushing the dipole state to a sufficiently high energy. It is argued that unperturbed levels, corresponding to an effective mass of m ∗/m ∼ 0.60–0.64 , should be employed. The couplings of particles and holes to vibrations are the crucial ingredients in these considerations. This also has the consequence of spreading out the M1 strength. A new interpretation of experimental strengths is proposed.

Effective interaction and isospin splitting

Abstract In view of the recently observed isospin splitting in giant dipole resonances in nuclei such as 11B an attempt is made to understand such splittings from the view point of effective interactions. From the simple analysis of central forces it is found that while the Wigner and Bartlett exchange mixtures are irrelevant, the Majorana force (AM) must contribute significantly compared to the Heisenberg force (AH) and that (AM+AB) must always be positive. It is also necessary for the effective force to be of long range.

Correlations of electrons in small molecules

Recent advances in the theory of the giant dipole resonance in nuclei suggest that systems of a small number of fermions interacting through a repulsive residual force should have collective states. The theory is adapted to small molecules, and applied to ethylene (C2H4) with the Coulomb potential replaced by a dipole-dipole interaction. This approximation should reproduce effects due to correlations arising from the long range of the Coulomb potential. The excitation energies of `single-particle-single-hole' triplet states are taken either from experiment or from rough non-empirical values available in the literature. The calculation yields a collective singlet state at about 50 ev, in a region which has not yet been explored experimentally. It suggests also that long range correlations lead to reductions by about a factor 2 in the spacing of the lowest singlet and triplet excited states (as compared with the value for a pure π -> π* excitation) and for the dipole transition moment from the lowest excited singlet to the ground state. These results arise from co-operative interactions of several electrons. The reduction of the strength of the π-π interaction can be expressed as a dielectric effect due to the other electrons.