The low-lying isoscalar giant dipole resonance

This short note is aimed to comment on the recently observed low component of the isoscalar giant dipole resonance in connection with the theoretical predictions made by microscopic and hydrodynamical models. Received: 23 November 2001 / Accepted: 15 February 2002     

Damping of giant dipole resonances at finite temperature

The damping width γ^↓_GDR of the giant dipole resonance, due to its coupling to doorway states, is studied within the framework of the thermal Green's functions theory. It is found that γ^↓_GDR reflects the temperature dependence of the single-particle damping width but, as a consequence of the cancellation effects between self-energy and vertex contributions, the coefficient of such a dependence is so small that it can essentially be neglected, within the temperature range of physical interest.     

Semiclassical description of isoscalar giant multipole resonances

The scaling approximation in a semiclassical theory of nuclear collective motions based on the Vlasov equation is applied to the study of isoscalar giant resonances. Analytic forms are obtained for the frequencies of any multipolarity, expressed just in terms of local density distributions, using realistic nuclear effective forces. The importance of non local interactions and diffuse surfaces is clearly shown. The limits of the scaling picture in describing high multipolarity resonances are finally discussed.     

Energy-weighted RPA sum rules for isoscalar giant resonances

Explicit analytic expressions are derived for the cubic energy-weighted sum rule in RPA and for Skyrme interactions. From these and the once energy-weighted sum rule an average energy for the giant resonance is estimated. The contributions from the deformation of the Fermi sea, and also from the Coulomb, surface and effective mass terms in the interaction are explicitly evaluated. The limited validity of estimates based on the assumption of a uniform density distribution is stressed. The important role of the surface for modes of high multipolarity is shown quantitatively. Using a leptodermous expansion the true volume, surface and higher order terms are obtained.     

Direct neutron decay of the isoscalar giant dipole resonance

The direct and statistical neutron decay of the isoscalar giant dipole resonance has been studied in ⁹⁰Zr, ¹¹⁶Sn, and ²⁰⁸Pb using the (α, α’ n) reaction at a bombarding energy of 200 MeV. The spectra of fast decay neutrons populating valence hole states of the Z, N − 1 nuclei were analyzed, and estimates for the branching ratios were determined. The observation of the nucleon-direct-decay channels helped to select giant-resonance strengths and suppress the underlying background and continuum, which led to an indication of the existence of a new mode with L = 2 character, presumably the overtone of the isoscalar giant quadrupole resonance. The text was submitted by the authors in English.     

A semi-classical model for isoscalar giant resonances at finite temperatures

We present a study of the temperature dependence of the energies of isoscalar giant resonances with multipolarities L = 0, 2, 3 and 4, in the framework of the subtraction procedure of Bonche, Levit and Vautherin (BLV). The method is used to calculate, within a Thomas-Fermi (TF) model at finite temperatures, sum rules of the strength function in the random phase approximation (RPA). Special attention has been paid to the spurious contribution of the gas, which considerably alters the low-energy weighted sum rules, i.e. the low-energy part of the strength function; we find that when this spurious contribution is removed, the resonance energies show a weak dependence on temperature, up to the Coulomb instability onset. The temperature dependence of the nuclear incompressibilities in the scaling and in the constrained models have also been obtained.     

Collective potentials and dipole and quadrupole giant resonances

The dynamic collective model is extended into the energy region immediately above the giant dipole resonances, i.e. into an energy region between 20 and 28 MeV. The total Hamiltonian is constructed and the dynamical problem is solved by diagonalizing the Hamiltonian in the basis of a five-dimensional harmonic oscillator. In schematical studies the splitting of giant quadrupole resonances is shown. For some elements the potential energy surfaces (PES) are constructed within the collective model developed by Gneuss et al. and the quadrupole resonances have been calculated in the framework of the dynamic collective model. In the last part the agreement with experimental data is shown.     

Coulomb excitation of double giant dipole resonances

We implement the Brink–Axel hypothesis for the excitation of the double giant dipole resonance (DGDR): the background states which couple to the one-phonon giant dipole resonance are themselves capable of dipole absorption. These states (and the ones which couple to the two-phonon resonance) are described in terms of the gaussian orthogonal ensemble of random matrices. We use second-order time-dependent perturbation theory and calculate analytically the ensemble-averaged cross section for excitation of the DGDR. Numerical calculations illuminate the mechanism and the dependence of the cross section on the various parameters of the theory, and are specifically performed for the reaction ²⁰⁸Pb + ²⁰⁸Pb at a projectile energy of 640 MeV/nucleon. We show that the contribution of the background states to the excitation of the DGDR is significant. We find that the width of the DGDR, the energy-integrated cross section and the ratio of this quantity over the energy-integrated cross section for the single giant dipole resonance, all agree with experiment within experimental errors. We compare our approach with that of Carlson et al. who have used a similar physical picture.     

Interference of isovector and isoscalar giant quadrupole resonances in Y and Pb

We present the calculations of the fore-aft asymmetry of γ-rays in fast nucleon capture reactions ⁸⁹Y(n, γ)⁹⁰Y, ²⁰⁸Pb(n, γ)²⁰⁹Pb and ²⁰⁸Pb(p, γ)²⁰⁹Bi which are based on a consistent version of the direct-semi-direct (DSD) capture model. The results are in good agreement with observed differential cross sections.     

Far-infrared giant dipole resonances in neutral quantum dots

A resonance behaviour of the far-infrared absorption probability at a frequency N^1/4 is predicted for clusters of N electron–hole pairs (2N110) confined in disk-shaped quantum dots. For radially symmetric dots, the absorption is dominated by a giant dipole resonance, which accounts for more than 98% of the energy-weighted photoabsorption sum rule.     

Separabelized Skyrme interaction and characteristics of giant dipole resonances

The accuracy of eliminating the spurious state from the E1-transition strength distribution is studied within the random phase approximation with separabelized Skyrme forces.     

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.     

Isovector giant dipole resonances in proton-rich Ar and Ca isotopes

The isovector giant dipole resonances(IVGDR)in proton-rich Ar and Ca isotopes have been systematic-ally investigated using the resonant continuum Hartree-F ock+BCS(HF+BCS)and quasiparticle random phase ap-proximation(QRPA)methods.The Skyrme SLy5 and density-dependent contact pairing interactions are employed in the calculations.In addition to the giant dipole resonances at energy around 18 MeV,pygmy dipole resonances(PDR)are found to be located in the energy region below 12 MeV.The calculated energy-weighted moments of PDR in nuclei close to the proton drip-line exhaust about 4%of the TRK sum rule.The strengths decrease with in-creasing mass number in each isotopic chain.The transition densities of the PDR states show that motions of pro-tons and neutrons are in phase in the interiors of nuclei,while the protons give the main contribution at the surface.By analyzing the QRPA amplitudes of proton and neutron 2-quasiparticle configurations for a given low-lying state,we find that only a few proton configurations give significant contributions.They contribute about 95%to the total QRPA amplitudes,which indicates that the collectivity of PDR states is not strong in proton-rich nuclei in the present study.     

Quenching of photon decay in hot giant dipole resonances

The quenching of photon decays in giant dipole resonances (GDR) at high excitation energy (E^*) is explained as due to the competition between γ-ray and particle emission. This effect is related to a large increase of the GDR width with the temperature of the nucleus in presence of a pre-equilibrium mechanism that also tends to reduce the collective dipole strength. A saturation of the GDR width at high excitation energy cannot account for the experimental data. Limiting temperatures for the observation of GDR γ-decays are deduced. The E^*-dependence of photon yields above the GDR region is also discussed.     

Electro-excitation of giant dipole resonances in medium-heavy,spherical nuclei

The collective intermediate structure of the giant resonances in medium-heavy, spherical nuclei, which was discovered by photonuclear experiments, has been explained nearly quantatively by the collective dynamic theory, which takes into account the coupling of giant-dipole and surface-quadrupole resonance.However, photonuclear experiments determine essentially only the excitation energy and the dipole strength of the various levels. In order to gain more insight into the model, electro-excitation experiments should be carried through. At moderate momentum transfer (q = 1 fm⁻¹ to 1.5 fm⁻¹), such experiments could test the details of the transition charge distribution predicted by the collective theory. Since the various giant resonance levels have different admixtures of surface phonons, their transition densities and therefore the resulting cross sections show a different behaviour.     

Energies and moments of giant resonances for isoscalar monopole and quadrupole excitations: A sum-rule approach

An approach to isoscalar giant resonances in terms of their energy moments is proposed. Besides the well-known moment containing the energy to power plus one, moments with powers plus three and minus one are evaluated. Values for the giant resonance energy and a limit on its width are obtained. The approach systematises and unifies various collective theories, and gives a simple derivation of the quadrupole energy as √2 times the oscillator quantum.     

The potential energy surfaces and the giant dipole resonances of46,48,50Ti

The low energy and giant dipole resonance properties of^46,48,50Ti have been investigated within the framework of the collective model of Gneuss and Greiner. The starting potential energy surfaces were taken from Rebel and Habs from which the low energy properties were compared with both an asymmetric rotator model and a shell model calculation. The giant dipole absorption cross sections compared favourably with the experimental data. However, the scarcity of data relating to theγ-scattering from the giant dipole resonance states to the low lying levels made any detailed comparison incomplete.     

Evidence for pygmy and giant dipole resonances in 130Sn and 132Sn

The dipole strength distribution above the one-neutron separation energy was measured in the unstable 130Sn and the double-magic 132Sn isotopes. The results were deduced from Coulomb dissociation of secondary Sn beams with energies around 500 MeV/nucleon, produced by in-flight fission of a primary 238U beam. In addition to the giant dipole resonance, a resonancelike structure ("pygmy resonance") is observed at a lower excitation energy around 10 MeV exhausting a few percent of the isovector E1 energy-weighted sum rule. The results are discussed in the context of a predicted new dipole mode of excess neutrons oscillating out of phase with the core nucleons.