Double Giant Dipole Resonance Research Articles

Sum Rules of the Multiple Giant Resonance States

Various sum rules for multiple giant dipole resonance states are derived. For the triple giant dipole resonance states, the energy-weighted sum of the transition strengths requires a model to be related to those of the single and double giant dipole resonance states. It is also shown that the non-diagonal matrix elements of the double commutator between the dipole operator and the nuclear Hamiltonian give useful identities for the excitation energy and transition strength of each excited state. Using those identities, the relationship between width of the single dipole state and those of the multiple ones is qualitatively discussed.

Double giant dipole resonance in hot nuclei

Signals from Double Dipole Giant Resonances (DGDR) in hot nuclei have been searched in a γ-γ coincidence experiment using the HECTOR array at the Laboratori Nazionali di Legnaro. The experimental single γ-ray spectrum and the projection of the γ-γ matrix have been compared with a standard Monte Carlo Statistical Model code including only the single GDR excitation. These calculations have been used as background to determine the extra-yield associated with the DGDR de-excitation. Results have been compared with a previous experiment confirming the presence of the DGDR excitation in fusion-evaporation reactions.

Double giant dipole resonance in hot nuclei

Signals from Double Dipole Giant Resonances (DGDR) in hot nuclei have been searched in a γ-γ coincidence experiment using the HECTOR array at the Laboratori Nazionali di Legnaro. The experimental single γ-ray spectrum and the projection of the γ-γ matrix have been compared with a standard Monte Carlo Statistical Model code including only the single GDR excitation. These calculations have been used as background to determine the extra-yield associated with the DGDR de-excitation. Results have been compared with a previous experiment confirming the presence of the DGDR excitation in fusion-evaporation reactions.

Double giant dipole resonance in hot nuclei

Signals from Double Dipole Giant Resonances (DGDR) in hot nuclei have been searched in a γ-γ coincidence experiment using the HECTOR array at the Laboratori Nazionali di Legnaro. The experimental single γ-ray spectrum and the projection of the γ-γ matrix have been compared with a standard Monte Carlo Statistical Model code including only the single GDR excitation. These calculations have been used as background to determine the extra-yield associated with the DGDR de-excitation. Results have been compared with a previous experiment confirming the presence of the DGDR excitation in fusion-evaporation reactions.

Is the Double Giant Dipole Resonance Process Responsiblefor Alpha Emission in Ternary Fission?

The Monte Carlo program built on thedouble giant dipole resonance model proposed by Mouze et al.[Nuovo Cimento A 110(1997)1097] was employed to calculate the energyspectrum of alpha particles emitted in the spontaneous ternaryfission of 252Cf. It has been found that in the case of the zeroorbital angular momentum of alpha particles in the alpha decay of thefragments, the measured alpha spectrum can be reproducedapproximately by the model without any adjustable parameter.

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.

Double giant resonances in nuclei

A brief review of the results of microscopic calculations aimed at describing the characteristics of double giant dipole resonances (DGDR) is presented. Special attention is paid to a systematic microscopic study of the anharmonic properties of DGDRs for nuclei with mass numbers 40≤A≤208. It is found that the corrections of the energy centroid of a DGDR from its harmonic limit are negative, have a value on the order of a few hundred keV, and follow an A−1 dependence.

Observation of a double giant dipole resonance in fusion-evaporation reactions

The emission of two coincident energetic (E≥8 MeV) gamma rays has been observed in the 187 MeV 37Cl+ 120Sn reaction by using the cluster detectors of the EUROBALL III array. Those events are attributed to the decay of the double giant dipole resonance built on highly excited states.

Electromagnetic Cross Sections of Double Giant Dipole Resonances in136Xeand208Pbwithin the Phonon Damping Model

The electromagnetic cross sections of the double giant dipole resonances (DGDR) in 136Xe and 208Pb are calculated using the strength functions obtained within the phonon damping model. The parameters of the model have been selected to describe reasonably well the single giant dipole resonance in these nuclei. The results are found in an overall agreement with the recent experimental data for the DGDR cross sections in exclusive measurements at near-relativistic energies.

Anharmonic properties of the double giant dipole resonance

A systematic microscopic study of the anharmonic properties of the double giant dipole resonance (DGDR) has been carried out, for the first time, for nuclei with mass number A spanning the whole mass table. It is concluded that the corrections of the energy centroid of the Jpi = 0(+) and 2(+) components of the DGDR from its harmonic limit are negative, have a value of the order of a few hundred keV, and follow an A-1 dependence.

SU(2,1) Model of Multiple Giant Dipole Resonance Coulomb Excitation

We construct a three-dimensional analytically soluble model of the nonlinear effects in Coulomb excitation of multiphonon giant dipole resonances (GDR) based on the SU(2,1) algebra. The full three-dimensional model predicts enhancement of the double GDR (DGDR) cross sections at high bombarding energies. Enhancement factors for DGDR measured in 13 different processes with various projectiles and targets at different bombarding energies are well reproduced with the same value of the nonlinearity parameter with the exception of the anomalous case of 136Xe which requires a larger value.

Double giant dipole resonances in time-dependent density-matrix theory

The strength functions of the double giant dipole resonances (DGDR) in 16O and 40Ca are calculated with the use of an extended version of the time-dependent Hartree-Fock theory known as the time-dependent density-matrix theory. The calculations are done in a self-consistent manner, in which the same Skyrme force as that used for a mean-field potential is used as an effective interaction for a two-body correlation function. It is found that the DGDR in 16O has a large width due to the Landau damping, although the centroid energy of the strength distribution is close to twice the energy of the giant dipole resonance (GDR) calculated in RPA. The DGDR in 40Ca is found more harmonic than that in 16O: the strength function of the DGDR in 40Ca is similar to what is predicted from the strength function of the GDR in RPA.

On the spectroscopy of atomic electrons (positrons) in the energy range of 10 to 50 MeV from heavy-ion collisions at intermediate energies

We study the effect of the spreading widths on the excitation probabilities of the double giant dipole resonance. We solve the coupled-channels equations for the excitation of the giant dipole resonance and the double giant dipole resonance. Taking Pb+Pb collisions as example, we study the resulting effect on the excitation amplitudes, and cross sections as a function of the width of the states and of the bombarding energy.

Multiphonon and “Hot”-Phonon Isovector Electric-Dipole Excitations

We argue that a substantial increase in the cross section for Coulomb excitation in the region of the Double Giant Dipole Resonance should be expected from Coulomb excitation of excited states involved in the spreading of the one-phonon resonance, in a manifestation of the Brink–Axel phenomenon. This generates an additional fluctuating amplitude and a corresponding new term to be added incoherently to the usual cross section. The appropriate extension of an applicable reaction calculation is considered in order to estimate this effect.

Microscopic description of multiphonon states excitation in heavy ion collisions

Starting from a microscopic approach based on RPA, we go beyond it by introducing anharmonicity by taking into account the mixing of two-phonon states among themselves and with one-phonon states. By introducing also non linear terms in the external field we show that these new ingredients give an explanation of the puzzle of the excitation cross section of the double giant dipole resonance (DGDR) for the 208 Pb + 208 Pb system at 641 MeV/A.

Damping of the double giant dipole resonance

A microscopic approach is proposed to the damping of the double giant dipole resonance (DGDR). The double-time Green's function method is used to derive a closed set of coupled equations for the propagation of two-phonon excitation through the field of incoherent nucleon pairs. The analytical expressions for the width and energy shift of the DGDR are obtained. The numerical calculations are performed for ${}^{90}\mathrm{Zr},$ ${}^{90}\mathrm{Sn},$ and ${}^{208}\mathrm{Pb}$ for several characteristics of the DGDR at zero as well as nonzero temperatures T. The results are found in reasonable agreement with existing experimental systematics for the width and energy of the DGDR. As compared to the estimation within the harmonic picture, the anharmonicity leads to a noticeable enhancement of the integrated photoabsorption cross section (IPACS) over the DGDR region. The DGDR width is found to increase sharply with increasing T at $T<~3\mathrm{MeV},$ but goes to a saturation at $T>3\mathrm{MeV}$. The harmonic limit for the DGDR width is restored already at $T>~1.5\mathrm{MeV}.$ It is shown that the IPACS of the DGDR can also be enhanced compared to its harmonic value if it is built on a hot GDR.

Excitation and decay of two-phonon giant dipole resonances

In heavy ion collisions at near relativistic energies, electromagnetic excitation of the double giant dipole resonance occurs with large cross sections. We summarize the presently available experimental data and discuss related theoretical efforts. Emphasis is paid to the question of anharmonicities and to the damping of the two-phonon states.

Double giant resonances in deformed nuclei

We report on the first microscopic study of the properties of two-phonon giant resonances in deformed nuclei. The cross sections of the excitation of the giant dipole and the double giant dipole resonances in relativistic heavy ion collisions are calculated. We predict that the double giant dipole resonance has a one-bump structure with a centroid 0.8 MeV higher than twice the energy for the single giant dipole resonance in the reaction under consideration. The width of the double resonance equals 1.33 of that for the single resonance.

Decay theory of double giant resonances

The decay theory of double giant resonances incorporating fluctuation contributions of the Brink-Axel type is developed. The gamma and neutron emission decay of Double Giant Dipole Resonances (DGDR) in 208Pb is discussed in connection with a recent measurement.

Microscopic description of Coulomb and nuclear excitation of multiphonon states in heavy ion collisions

We calculate the inelastic scattering cross sections to one- and two-phonon states in heavy ion collisions. Both Coulomb and nuclear excitations are included and their interplay is studied. Starting from a microscopic approach based on RPA, we go beyond it in order to treat anharmonicities and take explicitly into account the mixing of two-phonon states among themselves and with one-phonon states. Nonlinear terms in the exciting field are also introduced. These anharmonicities and nonlinearities are shown to have important effects on the cross sections both in the low energy part of the spectrum and in the energy region of the Double Giant Dipole Resonance.