Isoscalar Giant Monopole Resonance Research Articles

Deformation effects in Giant Monopole Resonance

The isoscalar giant monopole resonance (GMR) in Samarium isotopes (from spherical 144Sm to deformed 148-154Sm) is investigated within the Skyrme random-phase- approximation (RPA) for a variety of Skyrme forces. The exact RPA and its separable version (SRPA) are used for spherical and deformed nuclei, respectively. Consistently with earlier investigations, the quadrupole deformation is shown to yield two effects: the GMR broadens and attains a two-peak structure due to the coupling with the quadrupole giant resonance.

The Determination of the Bulk Symmetry Incompressibility from the Isoscalar Giant Monopole Resonance Revisited

The Determination of the Bulk Symmetry Incompressibility from the Isoscalar Giant Monopole Resonance Revisited

Tensor force effect on incompressibility of bubble nucleus

The tensor force effect on the isoscalar giant monopole resonance (ISGMR) of 46 Ar is investigated in the framework of Hartree–Fock (HF) + random phase approximation (RPA) approach with the Skyrme interactions SLy5, SLy5+T and SLy5+ T w. By using the ISGMR excitation energy, the incompressibility value of 46 Ar is extracted. It is shown that the incompressibility is enhanced with the SLy5+T interaction compared to the one with the SLy5 interaction. However, the SLy5+ T w interaction makes the incompressibility smaller because of the bubble structure of 46 Ar .

Self-consistent Hartree-Fock and RPA Green's function method indicate no pygmy resonance in the monopole response of neutron-rich Ni isotopes

The RPA monopole strength as well as the unperturbed particle-hole excitation strength is studied, in which the strength in the continuum is properly treated without discretizing unbound particle spectra. The model is the sef-consistent Hartree-Fock calculation and the RPA Green's function method with Skyrme interactions. Numerical examples are the Ni-isotopes, especially $^{68}_{28}$Ni$_{40}$, in which an experimental observation of low-lying socalled "pigmy resonance" with an appreciable amount of monopole strength at 12.9 $\pm$ 1.0 MeV was recently reported. In the present study it is concluded that sharp monopole peaks with the width of the order of 1 MeV can hardly be expected for $^{68}$Ni in that energy region. Instead, a broad shoulder of monopole strength consisting of neutron excitations to non-resonant one-particle states (called "threshold strength") with relatively low angular-momenta $(\ell, j)$ is obtained in the continuum energy region above the particle threshold, which is considerably lower than that of isoscalar giant monopole resonance. In the case of monopole excitations of $^{68}$Ni there are no unperturbed particle-hole states below 20 MeV, in which the particle expresses a neutron (or proton) resonant state. It is emphasized that in the theoretical estimate a proper treatment of the continuum is extremely important.

Measurement of the isoscalar monopole response in the neutron-rich nucleus 68Ni.

The isoscalar monopole response has been measured in the unstable nucleus (68)Ni using inelastic alpha scattering at 50A MeV in inverse kinematics with the active target MAYA at GANIL. The isoscalar giant monopole resonance (ISGMR) centroid was determined to be 21.1 ± 1.9 MeV and indications for a soft monopole mode are provided for the first time at 12.9 ± 1.0 MeV. Analysis of the corresponding angular distributions using distorted-wave-born approximation with random-phase approximation transition densities indicates that the L = 0 multipolarity dominates the cross section for the ISGMR and significantly contributes to the low-energy mode. The L=0 part of this low-energy mode, the soft monopole mode, is dominated by neutron excitations. This demonstrates the relevance of inelastic alpha scattering in inverse kinematics in order to probe both the ISGMR and isoscalar soft modes in neutron-rich nuclei.

Excitation of giant monopole resonance in 208Pb and 116Sn using inelastic deuteron scattering

The excitation of the isoscalar giant monopole resonance (ISGMR) in 208Pb and 116Sn has been investigated using small-angle (including 0°) inelastic scattering of 100 MeV/u deuteron and multipole-decomposition analysis (MDA). The extracted strength distributions agree well with those from inelastic scattering of 100 MeV/u α particles. These measurements establish deuteron inelastic scattering at Ed∼100 MeV/u as a suitable probe for extraction of the ISGMR strength with MDA, making feasible the investigation of this resonance in radioactive isotopes in inverse kinematics.

Symmetry energy constraints from giant resonances: A relativistic mean-field theory overview

Giant resonances encapsulate the dynamic response of the nuclear ground state to external perturbations. As such, they offer a unique view of the nucleus that is often not accessible otherwise. Although interesting in their own right, giant resonances are also enormously valuable in providing stringent constraints on the equation of state of asymmetric matter. We this view in mind, we focus on two modes of excitation that are essential in reaching this goal: the isoscalar giant monopole resonance (GMR) and the isovector giant dipole resonance (GDR). GMR energies in heavy nuclei are sensitive to the symmetry energy because they probe the incompressibility of neutron-rich matter. Unfortunately, access to the symmetry energy is hindered by the relatively low neutron-proton asymmetry of stable nuclei. Thus, the measurement of GMR energies in exotic nuclei is strongly encouraged. In the case of the GDR, we find the electric dipole polarizability of paramount importance. Indeed, the electric dipole polarizability appears as one of two laboratory observables -- with the neutron-skin thickness being the other -- that are highly sensitive to the density dependence of the symmetry energy. Finally, we identify the softness of skin and the nature of the pygmy resonance as important unsolved problems in nuclear structure.

Isoscalar and Isovector Giant Monopole Resonances from a Continuum Hartree-Fock Method

We motivate and summarise some recent results in the application of formally exact boundary conditions in nuclear time-dependent Hartree-Fock calculations, mak- ing use of Laplace transformations to calculate the values of the wave functions at the boundaries. We have realised the method in the case of giant monopole resonances of spherically-symmetric nuclei, and present strength functions of 16 O and 40 Ca using a sim- plified version of the Skyrme force, showing that no artefacts from discretisation occur as contaminatnts

Isoscalar giant monopole resonance for drip-line and super heavy nuclei in the framework of relativistic mean field formalism with scaling calculation

AbstractWe study the isoscalar giant monopole resonance for drip-lines and super heavy nuclei in the framework of relativistic mean field theory with a scaling approach. The well known extended Thomas-Fermi approximation in the nonlinear σ-ω model is used to estimate the giant monopole excitation energy for some selected light spherical nuclei starting from the region of proton to neutron drip-lines. The application is extended to the super heavy region for Z=114 and 120, which are predicted by several models as the next proton magic numbers beyond Z=82. We compared the excitation energy obtained by four successful force parameters NL1, NL3, NL3*, and FSUGold. The monopole energy decreases toward the proton and neutron drip-lines in an isotopic chain for lighter mass nuclei, in contrast to a monotonic decrease for super heavy isotopes. The maximum and minimum monopole excitation energies are obtained for nuclei with minimum and maximum isospin in an isotopic chain, respectively.

Isoscalar giant monopole resonance in Sn isotopes using a quantum molecular dynamics model

The isoscalar giant monopole resonance (GMR) in Sn isotopes and other nuclei is investigated in the framework of the isospin-dependent quantum molecular dynamics (IQMD) model. The spectrum of GMR is calculated by taking the rms radius of a nucleus as its monopole moment. The peak energy, the FWHM, and the strength of the GMR extracted by a Gaussian fit to the spectrum have been studied. The GMR peak energies for Sn isotopes from the calculations using a mass-number-dependent Gaussian wave-packet width ${\ensuremath{\sigma}}_{r}$ for nucleons are found to be overestimated and show a weak dependence on the mass number compared with the experimental data. However, it is found that experimental data of the GMR peak energies for ${}^{56}$Ni, ${}^{90}$Zr, and ${}^{208}$Pb as well as Sn isotopes can be nicely reproduced after taking into account the isospin dependence in isotope chains in addition to the mass-number dependence of ${\ensuremath{\sigma}}_{r}$ for nucleons in the IQMD model calculation.

Determination of the density dependence of the nuclear incompressibility

Background: The determination of the density dependence of the nuclear incompressibility can be investigated using the isoscalar giant monopole resonance.Purpose: The importance of the so-called crossing density at subsaturation density is underlined.Methods: The measurements of the isoscalar giant monopole resonance (GMR), also called the breathing mode, are analyzed with respect to their constraints on the quantity ${M}_{c}$, e.g., the density dependence of the nuclear incompressibility around the so-called crossing density ${\ensuremath{\rho}}_{c}=0.1$ fm${}^{\ensuremath{-}3}$.Results: The correlation between the centroid of the GMR, ${E}_{\mathrm{GMR}}$, and ${M}_{c}$ is shown to be more accurate than the one between ${E}_{\mathrm{GMR}}$ and the incompressibility modulus at saturation density, ${K}_{\ensuremath{\infty}}$, giving rise to an improved determination on the nuclear equation of state. The relationship between ${M}_{c}$ and ${K}_{\ensuremath{\infty}}$ is given as a function of the skewness parameter ${Q}_{\ensuremath{\infty}}$ associated with the density dependence of the equation of state. The large variation of ${Q}_{\ensuremath{\infty}}$ among different energy density functionals directly impacts the knowledge of ${K}_{\ensuremath{\infty}}$: A better knowledge of ${Q}_{\ensuremath{\infty}}$ is required to deduce more accurately ${K}_{\ensuremath{\infty}}$. Using the local density approximation, a simple and accurate expression relating ${E}_{\mathrm{GMR}}$ and the quantity ${M}_{c}$ is derived and successfully compared to the fully microscopic predictions.Conclusions: The measurement of the GMR constrains the slope of the incompressibility ${M}_{c}$ at the crossing density rather than the incompressibility modulus at the saturation density.

Shape evolution of giant resonances in Nd and Sm isotopes

Giant multipole resonances in Nd and Sm isotopes are studied by employing the quasiparticle-random-phase approximation on the basis of the Skyrme energy-density-functional method. Deformation effects on giant resonances are investigated in these isotopes which manifest a typical nuclear shape change from spherical to prolate shapes. The peak energy, the broadening, and the deformation splitting of the isoscalar giant monopole (ISGMR) and quadrupole (ISGQR) resonances agree well with measurements. The magnitude of the peak splitting and the fraction of the energy-weighted strength in the lower peak of the ISGMR reflect the nuclear deformation. The experimental data on ISGMR, ISGDR, and ISGQR are consistent with the nuclear-matter incompressibility $K \simeq 210-230$ MeV and the effective mass $m^*_0/m \simeq 0.8-0.9$. However, the high-energy octupole resonance (HEOR) in $^{144}$Sm seems to indicates a smaller effective mass, $m^*_0/m \simeq 0.7-0.8$. A further precise measurement of HEOR is desired to determine the effective mass.

Testing the mutually enhanced magicity effect in nuclear incompressibility via the giant monopole resonance in the 204,206,208Pb isotopes

Using inelastic α-scattering at extremely forward angles, including 0°, the strength distributions of the isoscalar giant monopole resonance (ISGMR) have been measured in the 204,206,208Pb isotopes in order to examine the proposed mutually enhanced magicity (MEM) effect on the nuclear incompressibility. The MEM effect had been suggested as a likely explanation of the “softness” of nuclear incompressibility observed in the ISGMR measurements in the Sn and Cd isotopes. Our experimental results rule out any manifestation of the MEM effect in nuclear incompressibility and leave the question of the softness of the open-shell nuclei unresolved still.

New Kohn-Sham density functional based on microscopic nuclear and neutron matter equations of state

Given the promising features of the recently proposed Barcelona-Catania-Paris (BCP) functional \cite{Baldo.08}, it is the purpose of this paper to still improve on it. It is, for instance, shown that the number of open parameters can be reduced from 4-5 to 2-3, i.e. by practically a factor of two. One parameter is tightly fixed by a fine-tuning of the bulk, a second by the surface energy. The third is the strength of the spin-orbit potential on which the final result does not depend within the scatter of the values used in Skyrme and Gogny like functionals. An energy rms value of 1.58 MeV is obtained from a fit of these three parameters to the 579 measured masses reported in the Audi and Waspra 2003 compilation. This rms value compares favorably with the one obtained using other successful mean field theories. Charge radii are also well reproduced when compared with experiment. The energies of some excited states, mostly the isoscalar giant monopole resonances, are studied within this model as well.

Feasibility of the finite-amplitude method in covariant density functional theory

The self-consistent relativistic random-phase approximation (RPA) in the radial coordinate representation is established by using the finite-amplitude method (FAM). Taking the isoscalar giant monopole resonance in spherical nuclei as example, the feasibility of the FAM for the covariant density functionals is demonstrated, and the newly developed methods are verified by the conventional RPA calculations. In the present relativistic RPA calculations, the effects of the Dirac sea can be automatically taken into account in the coordinate-space representation. The rearrangement terms due to the density-dependent couplings can be implicitly calculated without extra computational costs in both iterative and matrix FAM schemes.

Microscopic study of the isoscalar giant monopole resonance in Cd, Sn, and Pb isotopes

The isoscalar giant monopole resonance (ISGMR) in Cd, Sn and Pb isotopes has been studied within the self-consistent Skyrme Hartree-Fock+BCS and quasi-particle random phase approximation (QRPA). Three Skyrme parameter sets are used in the calculations, i.e., SLy5, SkM* and SkP, since they are characterized by different values of the compression modulus in symmetric nuclear matter, namely K=230, 217, and 202 MeV, respectively. We also investigate the effect of different types of pairing forces on the ISGMR in Cd, Sn and Pb isotopes. The calculated peak energies and the strength distributions of ISGMR are compared with available experimental data. We find that SkP fails completely to describe the ISGMR strength distribution for all isotopes due to its low value of the nuclear matter incompressibility, namely K=202 MeV. On the other hand, the SLy5 parameter set, supplemented by an appropriate pairing interaction, gives a reasonable description of the ISGMR in Cd and Pb isotopes. A better description of ISGMR in Sn isotopes is achieved by the SkM* interaction, that has a somewhat softer value of the nuclear incompressibility.

Fully Self-Consistency in Relativistic Random Phase Approximation

Fully self-consistent relativistic random phase approximation (RRPA) is built on the relativistic mean field ground state with a non-linear relativistic Lagrangian. The consistency requires that the same effective interaction is adopted to simultaneously describe both the ground states and the excited states of the nucleus. Reliable and accurate numerical results of the nuclear giant resonances obtained in the RRPA require fully consistent calculations. In some excitation modes they are extremely sensitive to consistent treatment, e.g., such as isoscalar giant monopole and dipole resonances (ISGMR and ISGDR). In this work we perform the numerical calculations in the case of ISGDR for 208Pb and check the consistency. The spurious state in the ISGDR vanishes once the full self-consistency is achieved.

Giant monopole resonance in even-A Cd isotopes, the asymmetry term in nuclear incompressibility, and the “softness” of Sn and Cd nuclei

The isoscalar giant monopole resonance (ISGMR) in even-A Cd isotopes has been studied by inelastic α-scattering at 100 MeV/u and at extremely forward angles, including 0°. The asymmetry term in the nuclear incompressibility extracted from the ISGMR in Cd isotopes is found to be Kτ=−555±75 MeV, confirming the value previously obtained from the Sn isotopes. ISGMR strength has been computed in relativistic RPA using NL3 and FSUGold effective interactions. Both models significantly overestimate the centroids of the ISGMR strength in the Cd isotopes. Combined with other recent theoretical effort, the question of the “softness” of the open-shell nuclei in the tin region remains open still.

Measurement of Giant Monopole Resonance in unstable nuclei and the determination of the nuclear matter incompressibility

The role of superfluidity in incompressibility is studied in nuclear matter and finite nuclei. Pairing has a weak effect on nuclear matter incompressibility at saturation density, but the effects are strong at lower densities. The pairing effect on the centroid energy of the isoscalar Giant Monopole Resonance (GMR) is also evaluated by using a microscopic constrained-Hartree–Fock Bogoliubov approach. The measurement of the GMR in isotopic chains including unstable nuclei is useful for the determination of nuclear incompressibility.

Optimization of relativistic mean field model for finite nuclei to neutron star matter

We have optimized the parameters of extended relativistic mean-field model using a selected set of global observables which includes binding energies and charge radii for nuclei along several isotopic and isotonic chains and the iso-scalar giant monopole resonance energies for the $^{90}$Zr and $^{208}$Pb nuclei. The model parameters are further constrained by the available informations on the energy per neutron for the dilute neutron matter and bounds on the equations of state of the symmetric and asymmetric nuclear matter at supra-nuclear densities. Two new parameter sets BSP and IUFSU* are obtained, later one being the variant of recently proposed IUFSU parameter set. The BSP parametrization uses the contributions from the quartic order cross-coupling between $\omega$ and $\sigma$ mesons to model the high density behaviour of the equation of state instead of the $\omega$ meson self-coupling as in the case of IUFSU* or IUFSU. Our parameter sets yield appreciable improvements in the binding energy systematics and the equation of state for the dilute neutron matter. The importance of the quartic order $\omega-\sigma$ cross coupling term of the extended RMF model, as often ignored, is realized.