Simplest photonuclear reactions accompanied by the excitation of isovector giant dipole and quadrupole resonances: Semimicroscopic description

A semimicroscopic approach based on the continuum version of the random-phase approximation (CRPA) and on a semiphenomenological inclusion of the fragmentation effect is applied to describing cross sections for photoabsorption and direct plus semidirect and inverse reactions accompanied by the excitation of isovector giant dipole and quadrupole resonances. In addition to the spinless part of the Landau-Migdal interaction and a partly self-consistent phenomenological mean field of the nucleus, that version of the approach which is used here takes into account isovector separable velocity-dependent forces, as well as the effect of the fragmentation shift of the giant-resonance energy. The results obtained by calculating various features of the aforementioned cross sections for a number of magic and semimagic medium-mass nuclei are compared with respective experimental data.     

Pygmy dipole resonance in nuclei

A brief survey of the state of the modern microscopic theory of the so-called pygmy dipole resonance in nuclei is given—in particular, some unresolved problems are listed. It is emphasized that, in order to explain the pygmy dipole resonance, it is necessary but not sufficient to take into account the coupling of single-particle degrees of freedom to photon degrees of freedom. The results of the calculations performed for the first time for the isovector pygmy dipole resonance and the isovector electric giant dipole resonance in ¹²⁴Sn within a self-consistent approach involving, in addition to the standard quasiparticle random-phase approximation, a single-particle continuum and quasiparticle-phonon coupling of single-particle degrees of freedom to phonon degrees of freedom are presented. The results are found to be in satisfactory agreement with experimental data. The calculation of the isoscalar strength function in the energy region of the pygmy dipole resonance revealed that the nuclear-structure mechanism does not provide the isoscalar-strength suppression observed at energies in excess of 7 MeV in (α, α′γ) reactions; therefore, this suppression may stem from the reaction mechanism.     

Fine Structure and Collectivity of the Levels of the Pygmy Dipole Resonance in <Superscript>208</Superscript>Pb in a Self-Consistent Model

A novel fully self-consistent microscopic approach based on the energy density functional method is employed to calculate the fine structure of the pygmy dipole resonance in ²⁰⁸Pb, i.e., the energies and reduced probabilities of E1 transitions for the states with energies below 10 MeV. The approach includes the random-phase approximation, quasiparticle–phonon interaction and the single-particle continuum. The theoretical results are compared to the available high-resolution data and found to agree with measured integral characteristics of the pygmy dipole resonance at energies above 5.7 MeV. Residual spin–spin forces are quantified, and their contribution is found to be significant at both low and high energies. A recently proposed criterion is employed to analyze the collectivity of the 1^–states in ²⁰⁸Pb.     

Self-consistent approaches in the microscopic theory of the nucleus: Static moments of odd-odd nuclei

Self-consistent mean-field theory and the method of the energy density functional, which are two modern self-consistent approaches in the microscopic theory of the nucleus that possess the highest predictive power for describing unstable nuclei, are briefly discussed. Themost recent results of calculations performed within these approaches are presented. The mean energies of E1 excitations in the range of 0–30 MeV are calculated for 15 stable and unstable tin isotopes (A = 100–176) on the basis of the self-consistent version of the generalized theory of finite Fermi systems by employing SLy4 Skyrme forces. A parameter-dependent expression that takes into account the existence of a pygmy dipole resonance is obtained for this quantity. The density-functional method is used within the self-consistent theory of finite Fermi systems on the basis of the Fayans-Tolokonnikov-Trykov-Zawischa functional in order to calculate the ground-state static quadrupole and magnetic moments of odd and odd-odd stable and unstable spherical near-magic nuclei. Good agreement with available experimental data is attained. The respective features are predicted for unstable nuclei.     

On the properties of charge-exchange dipole excitations and the T > component of a giant dipole resonance in spherical nuclei

Within the semimicroscopic approach based on the random-phase approximation that takes exactly into account a single-particle continuum and on a phenomenological inclusion of the fragmentation effect, it is proposed to describe the strength functions for charge-exchange giant dipole resonances and cross sections for photoabsorption and for partial “direct + semidirect” (γ, p) reactions in the vicinity of a giant E1 resonance with allowance for the isospin-splitting effect. The results of the calculations performed for some magic and semimagic nuclei without resort to free parameters are compared with available experimental data.     

Collective excitations in neutron-rich nuclei within the model of a Fermi liquid drop

We discuss a new mechanism of splitting of giant multipole resonances (GMR) in spherical neutron-rich nuclei. This mechanism is associated with the basic properties of an asymmetric drop of nuclear Fermi liquid. In addition to well-known isospin shell-model predictions, our approach can be used to describe the GMR splitting phenomenon in the wide nuclear-mass region A ～ 40–240. For the dipole isovector modes, the splitting energy, the relative strength of resonance peaks, and the contribution to the energy-weighted sum rules are in agreement with experimental data for the integrated cross sections for photonuclear (γ, n) and (γ, p) reactions.     

Proton electric pygmy dipole resonance

The evolution of the low-lying E1 strength in proton-rich nuclei is analyzed in the framework of the self-consistent relativistic Hartree-Bogoliubov model and the relativistic quasiparticle random-phase approximation (RQRPA). Model calculations are performed for a series of N=20 isotones and Z=18 isotopes. For nuclei close to the proton drip line, the occurrence of pronounced dipole peaks is predicted in the low-energy region below 10 MeV excitation energy. From the analysis of the proton and neutron transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance.     

Formation of isomeric states in (γ, γ′) reactions at energies around the giant dipole resonance

The population of isomeric states in (γ, γ′) photonuclear reactions at energies around the giant dipole resonance is considered for ¹¹⁵In and ¹⁸⁰Hf nuclei. The results are compared with previously published experimental and theoretical data. The behavior of the excitation function suggests an increase in the cross section for the formation of high-spin isomeric states in the giant-dipole-resonance region.     

Temperature dependence of collective states in the random-phase approximation

We investigate the temperature dependence of collective states in the framework of the random-phase approximation at finite temperature. We show that sum rules can be extended to collective energies at finite temperature. Numerical methods are developed to solve the RPA equations at finite temperature. Results are presented and discussed in the case of ⁴⁰Ca for isovector dipole and isoscalar octupole vibrations, using oscillator wave functions and a zero-range force. We show that the broadening of giant dipole resonances observed experimentally, appears as a natural consequence of the structure of the RPA equations. Comparison is made with the schematic model for which the temperature dependence of collective states can be worked out analytically.     

Deducing the nuclear-matter incompressibility coefficient from data on isoscalar compression modes

Accurate assessment of the value of the incompressibility coefficient, K, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei, by employing the microscopic theory based on the random-phase approximation (RPA).     

Direct experimental estimate of parameters that determine the cascade gamma decay of compound states of heavy nuclei

A method is proposed for simultaneously determining the interval of the most probable values of the density of levels excited in the radiative capture of slow neutrons and the sum of radiative E1 and M1 strength functions in the excitation-energy interval extending nearly up to the neutron binding energy. Experimental data on the intensities of two-step photon cascades between the compound state and a given low-lying level of the nucleus being studied are analyzed together with the total radiative widths of neutron resonances. Such an analysis can be performed for nuclei having an arbitrary level density, including deformed ones. The resulting data demonstrate that there are significant deviations from the predictions of commonly accepted level-density models—for example, the Fermi gas model—and specify the range of nuclei and the regions of their excitation energies where a further experimental investigation can furnish new important information about the properties of nuclear matter.     

Radiative strength function and the pygmy dipole resonance in <Superscript>208</Superscript>Pb and <Superscript>70</Superscript>Ni

The pygmy-resonance parameters and the E1 strength function are derived for ²⁰⁸Pb using a fully self-consistent microscopic formalism recently developed for magic nuclei, which takes into account quasiparticle phonon interactions (or coupling to phonons) in addition to the random phase approximation. For the radiative strength function of ²⁰⁸Pb at energies above 5 MeV, the experimental data of the Oslo group are adequately described by our predictions, whereby the important role of coupling to phonons is confirmed. By comparing the measurements based on the (³He, ³He′γ) and (γ, γ′) reactions, we discuss the physical properties of the radiative strength function measured for ²⁰⁸Pb. For the neutron-rich ⁷⁰Ni nucleus, predictions for the radiative strength function and the pygmy resonance are obtained using a partially self-consistent approach, which invokes the Skyrme forces in deriving the mean field, effective nucleon–nucleon interaction, and phonon characteristics.     

Description of cross sections for photonuclear reactions in the energy range between 7 and 140 MeV

A combination of the exciton and evaporation models is used to describe photonuclear reactions induced in light, medium-mass, and heavy nuclei by photons of energy in the range 7 ≤ E _γ ≤ 140 MeV. Two mechanisms of the photoexcitation of nuclei are considered. These are the formation of a giant dipole resonance at energies in the range E _γ ? 30 MeV and quasideuteron photoabsorption, which is dominant at energies in the region E _γ ? 40 MeV. The density of particle-hole states, which appears in the exciton model, is calculated on the basis of the Fermi gas model. The emission of two preequilibrium particles is taken into account in describing the quasideuteron reaction channel. The effect of isospin conservation on giant-dipole-resonance decay accompanied by photonucleon emission is examined. The model in question is used to describe cross sections for photon-induced reactions on ²⁶Mg, ⁵⁴Fe, ^{112,118,119,124}Sn, and ¹⁸¹Ta nuclei.     

Collective excitations in the unitary correlation operator method and relativistic QRPA studies of exotic nuclei

The collective excitation phenomena in atomic nuclei are studied in two different formulations of the random-phase approximation (RPA): (i) RPA based on correlated realistic nucleon-nucleon interactions constructed within the unitary correlation operator method (UCOM) and (ii) relativistic RPA derived from effective Lagrangians with density-dependent meson-exchange interactions. The former includes the dominant interaction-induced short-range central and tensor correlations by means of unitary transformation. It is shown that UCOM-RPA correlations induced by collective nuclear vibrations recover a part of the residual long-range correlations that are not explicitly included in the UCOM Hartree-Fock ground state. Both RPA models are employed in studies of the isoscalar giant monopole resonance in closed-shell nuclei across the nuclide chart, with an emphasis on the sensitivity of its properties on the constraints for the range of the UCOM correlation functions. Within the relativistic quasiparticle RPA (RQRPA) based on the relativistic Hartree-Bogolyubov model, the occurrence of pronounced low-lying dipole excitations is predicted in nuclei towards the proton drip line. From the analysis of the transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance. The text was submitted by the authors in English.