Isoscalar Giant Resonance Research Articles

Collective properties of low-lying octupole excitations in 20882Pb 126, 6020Ca 40 and 288O 20

The octupole strengths of three nuclei: β-stable nucleus 208 82Pb 126, neutron skin nucleus 60 20Ca 40 and neutron drip line nucleus 28 8O 20 are studied by using the self-consistent Hartree–Fock calculation with the random phase approximation. The collective properties of low-lying excitations are analyzed by particle–vibration coupling. The results show that there is the coexistence of the collective excitations and the decoupled strong continuum strength near the threshold in the lowest isoscalar states in 60 20Ca 40 and 28 8O 20. For these three nuclei, both the low-lying isoscalar states and giant isoscalar resonance carry isovector strength. The ratio B(IV)/ B(IS) is checked and it is found that, for 208 82Pb 126, the ratio is equal to (( N− Z)/ A) 2 in good accuracy, while for 60 20Ca 40 and 28 8O 20, the ratios are much larger than (( N− Z)/ A) 2. The study shows that the enhancement of the ratio is due to the excess neutrons that have small binding energies in 60 20Ca 40 and 28 8O 20.

Self-consistent Hartree-Fock based random phase approximation and the spurious state mixing

We use a fully self-consistent Hartree$-$Fock (HF) based continuum random phase approximation (CRPA) to calculate strength functions $S(E)$ and transition densities $\rho_t(r)$ for isoscalar giant resonances with multipolarities $L = 0$, 1 and 2 in $^{80}Zr$ nucleus. In particular, we consider the effects of spurious state mixing (SSM) in the isoscalar giant dipole resonance (ISGDR) and extend the projection method to determine the mixing amplitude of spurious state so that properly normalized $S(E)$ and $\rho_t(r)$ having no contribution due to SSM can be obtained. For the calculation to be highly accurate we use a very fine radial mesh (0.04 fm) and zero smearing width in HF$-$CRPA calculations. We first use our most accurate results as a basis to establish the credibility of the projection method, employed to eliminate the SSM, and then to investigate the consequences of the common violation of self-consistency, in actual implementation of HF based CRPA and discretized RPA (DRPA), as often encountered in the published literature. The HF$-$DRPA calculations are carried out using a typical box size of 12 fm and a very large box of 72 fm, for different values of particle-hole energy cutoff ranging from 50 to 600 MeV.

Isoscalar giant dipole resonance in [formula omitted]Pb via inelastic α scattering at 400 MeV and nuclear incompressibility

The isoscalar giant dipole resonance (ISGDR) in 208Pb has been investigated with inelastic α-scattering of 400 MeV at extremely forward angles, including 0°. Energy spectra, virtually free from instrumental background, have been obtained and the ISGDR strength distribution has been extracted using a multipole-decomposition analysis (MDA). A difference-of-spectra approach yields the same ISGDR centroid energy as with MDA. These results lead to a value for nuclear incompressibility that is consistent for both the isoscalar dipole and monopole modes.

Compressional-mode giant resonances in deformed nuclei

Background-free inelastic scattering spectra have been obtained for the Sm isotopes with 400 MeV α particles at forward angles (including 0°) to investigate the effect of deformation on the compressional-mode giant resonances. The strength distributions for the isoscalar giant resonances (L⩽3) have been extracted for the spherical nucleus 144Sm and the deformed nucleus 154Sm. We have observed that the effects of deformation are different for the low- and high-excitation-energy components of the isoscalar giant dipole resonance in 154Sm. Evidence for the theoretically predicted coupling between the isoscalar dipole resonance and the high-energy octupole resonance is reported.

Nuclear Equation of State and Compression Modes

The nuclear matter (N = Z and no Coulomb interaction) incompressibility coefficient, K nm , which is directly related to the curvature of the nuclear matter equation of state, is a very important physical quantity in the study of properties of nuclei, supernova collapse, neutron stars and heavy-ion collisions. We review the current status of K nm and the experimental and theoretical methods used to determine the value of K nm from the excitation crosssections σ(E) and the transition strength distributions S(E) of compression modes in nuclei. In particular, we will consider the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) and provide a simple explanation to the long standing problem of the conflicting results obtained for K nm , deduced from experimental data on excitation cross sections for the ISGMR and data for the ISGDR.

Exploration of resonant continuum and giant resonance in the relativistic approach

Single-particle resonant-states in the continuum are determined by solving scattering states of the Dirac equation with proper asymptotic conditions in the relativistic mean field theory (RMF). The regular and irregular solutions of the Dirac equation at a large radius where the nuclear potentials vanish are relativistic Coulomb wave functions, which are calculated numerically. Energies, widths and wave functions of single-particle resonance states in the continuum for ^{120}Sn are studied in the RMF with the parameter set of NL3. The isoscalar giant octupole resonance of ^{120}Sn is investigated in a fully consistent relativistic random phase approximation. Comparing the results with including full continuum states and only those single-particle resonances we find that the contributions from those resonant-states dominate in the nuclear giant resonant processes.

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.

Isoscalar giant dipole resonance and nuclear matter incompressibility coefficient

We present results of microscopic calculations of the strength function, S(E), and alpha-particle excitation cross sections sigma(E) for the isoscalar giant dipole resonance (ISGDR). An accurate and a general method to eliminate the contributions of spurious state mixing is presented and used in the calculations. Our results provide a resolution to the long standing problem that the nuclear matter incompressibility coefficient, K, deduced from sigma(E) data for the ISGDR is significantly smaller than that deduced from data for the isoscalar giant monopole resonance (ISGMR).

Toroidal dipole resonances in the relativistic random phase approximation

The isoscalar toroidal dipole strength distributions in spherical nuclei are calculated in the framework of a fully consistent relativistic random phase approximation. It is suggested that the recently observed ``low-lying component of the isoscalar dipole mode'' might correspond to the toroidal giant dipole resonance. Although predicted by several theoretical models, the existence of toroidal resonances has not yet been confirmed in experiment. The strong mixing between the toroidal resonance and the dipole compression mode might help to explain the large discrepancy between theory and experiment on the position of isoscalar giant dipole resonances.

Scaling calculation of isoscalar giant resonances in relativistic Thomas–Fermi theory

We derive analytical expressions for the excitation energy of the isoscalar giant monopole and quadrupole resonances in finite nuclei, by using the scaling method and the extended Thomas–Fermi approach to relativistic mean-field theory. We study the ability of several nonlinear σ– ω parameter sets of common use in reproducing the experimental data. For monopole oscillations the calculations agree better with experiment when the nuclear matter incompressibility of the relativistic interaction lies in the range 220–260 MeV. The breathing-mode energies of the scaling method compare satisfactorily with those obtained in relativistic RPA and time-dependent mean-field calculations. For quadrupole oscillations, all the analyzed nonlinear parameter sets reproduce the empirical trends reasonably well.

Properties of the isoscalar giant dipole resonance

The main properties (strength function, energy-dependent transition density, branching ratios for direct nucleon decay) of the isoscalar giant dipole resonance in several medium-heavy mass spherical nuclei are described within a continuum random-phase approximation approach, taking into account the smearing effect. All model parameters used in the calculations are taken from independent data. The calculation results are compared with available experimental data.

Compression modes and the nuclear matter incompressibility coefficient

We review the current status of the nuclear matter (N=Z and no Coulomb interaction) incompressibility coefficient, K nm , and describe the theoretical and the experimental methods used to determine K nm from properties of compression modes in nuclei. In particular we consider the long standing problem of the conflicting results obtained for K nm , deduced from experimental data on excitation cross sections for the isoscalar giant monopole resonance (ISGMR) and data for the isoscalar giant dipole resonance (ISGDR).

IsoscalarE0,E1,andE2strength in40Ca

The giant resonance region from $10<{E}_{x}<55\mathrm{MeV}$ in ${}^{40}\mathrm{Ca}$ has been studied with inelastic scattering of 240-MeV \ensuremath{\alpha} particles at small angles including 0\ifmmode^\circ\else\textdegree\fi{}. Strength corresponding to $97\ifmmode\pm\else\textpm\fi{}11%,$ $108\ifmmode\pm\else\textpm\fi{}12%,$ and $62+10--20%$ of the isoscalar $E0,$ $E2,$ and $E1$ sum rules, respectively, was identified with centroids of $19.18\ifmmode\pm\else\textpm\fi{}0.37\mathrm{MeV},$ $17.84\ifmmode\pm\else\textpm\fi{}0.43\mathrm{MeV},$ $23.36\ifmmode\pm\else\textpm\fi{}0.70\mathrm{MeV},$ and rms widths of $4.88\ifmmode\pm\else\textpm\fi{}0.57\mathrm{MeV},$ $2.89\ifmmode\pm\else\textpm\fi{}0.60\mathrm{MeV},$ and $5.34\ifmmode\pm\else\textpm\fi{}0.90\mathrm{MeV}.$

Isoscalar giant resonances and nuclear matter compressibility

Isoscalar giant resonances and nuclear matter compressibility

Sensitivity of the isoscalar giant dipole resonance to optical potentials

Sensitivity of the isoscalar giant dipole resonance to optical potentials

The Isoscalar Giant Dipole Resonance: Where We Are and Where We AreHeaded

Over the past few years, very good evidence has emerged for the Isoscalar Giant Dipole Resonance from small-angle inelastic scattering of α particles between 50–100 MeV/nucleon. A reconciliation between the available theoretical predictions and the experimental results still remains far from satisfactory, however, and there are interesting implications of the observed ISGDR strengths on the experimental determination of the incompressibility of nuclear matter. Some possible future measurements are also discussed.

Excitation Modes of Nuclei Far from Stability*

Excitation modes of nuclei far from stability are studied performing the Hartree-Fock plus RPA calculation with the Skyrme interaction. It is found that there are giant excitation peaks, referred to as giant neutron modes, below the isoscalar giant resonances in nuclei with the neutron skin, and that these peaks consist practically of neutron excitations only. Their transition densities are shown to be extended radially in comparison to those of the isoscalar giant resonances. A strong correlation between the sum of the transition strength of the giant neutron modes and the number of neutrons in the neutron skin is found. It is also found that the neutron modes can be seen in excitations with various multipolarities. However, the magnitude of each neutron mode varies according to its multipolarity. Proton mode excitations can be formed in proton-rich nuclei similarly to nuclei with the neutron skin, but their strengths are not so prominent as those of the neutron modes.

Isoscalar dipole mode in relativistic random phase approximation

The isoscalar giant dipole resonance structure in 208Pb is calculated in the framework of a fully consistent relativistic random phase approximation, based on effective mean-field Lagrangians with nonlinear meson self-interaction terms. The results are compared with recent experimental data and with calculations performed in the Hartree–Fock plus RPA framework. Two basic isoscalar dipole modes are identified from the analysis of the velocity distributions. The discrepancy between the calculated strength distributions and current experimental data is discussed, as well as the implications for the determination of the nuclear matter incompressibility.

Polarization associated with the coupling to isoscalar dipole compression mode

The effect of core polarization on isoscalar dipole one-particle moments due to the coupling with isoscalar giant dipole resonance (compression mode) is estimated. Numerical calculations with the core nucleus ${}_{82}^{208}{\mathrm{Pb}}_{126}$ show that a small enhancement of one-particle moments is obtained, of which the magnitude depends sensitively on relevant one-particle orbitals. The results are important for a microscopic understanding of the electric dipole moments (Schiff moments) measured for nuclei in this mass region.

On dipole compression modes in nuclei

Isoscalar dipole strength distributions in spherical medium- and heavy-mass nuclei are calculated within random phase approximation (RPA) or quasiparticle RPA. Different Skyrme-type interactions corresponding to incompressibilities in the range 200–250 MeV are used. The results are discussed in comparison with existing data on isoscalar giant dipole resonances. Two main issues are raised, firstly the calculated giant resonance energies are somewhat higher than the observed ones, and secondly a sizable fraction of strength is predicted below 20 MeV which needs to be experimentally confirmed.