Isovector Giant Dipole Resonance Research Articles

Isovector giant dipole resonance mode with an improved propagation approach in the framework of EQMD model

Isovector giant dipole resonance mode with an improved propagation approach in the framework of EQMD model

What can we learn from giant resonances in light nuclei?

Extensive experimental investigations into understanding the fine structure of giant resonances in nuclei across the periodic table have been carried out in recent years using the state-of-the-art K600 magnetic spectrometer of iThemba LABS, Cape Town, South Africa. Based on the established results in comparison to various theoretical calculations, it has been found that the fine structure observed in different giant resonances, namely Isoscalar Giant Quadrupole Resonance (ISGQR), Isovector Giant Dipole Resonance (IVGDR) and Isoscalar Giant Monopole Resonance (ISGMR), in light nuclei such as 40Ca, 28Si and 27Al is dominated by Landau damping although signatures for the role of the spreading width are also found. In this report, characteristic energy scales extracted in light nuclei are compared with the state-of-the-art theoretical calculations, while the fine structures results obtained are compared using semblance analysis to search for possible signatures of common fragmentation patterns induced by Landau damping and coupling to 2p-2h states obtained from different giant resonances.

Nuclear-structure experiments at iThemba LABS to investigate discrepancies between (p, p′) and (γ, xn) data

The iThemba Laboratory for Accelerator Based Sciences (iThemba LABS) is a centre of expertise and innovation in the field of nuclear-structure physics and is a leader in several high-impact studies. One of the highlights of these nuclear-structure experiments is the study of the broad structure of the IsoVector Giant Dipole Resonance (IVGDR) in the rare-earth region. Proton inelastic scattering experiments with Ep = 200 MeV were performed on the even-even Nd isotope chain and 152Sm at very forward scattering angles including zero degrees with the K600 magnetic spectrometer. The evolution of the shape of the IVGDR in the transition from spherical to deformed nuclei was investigated. One of the goals of this highlighted study was to confirm the K-splitting observed in previous photo-absorption measurements from Saclay. Significant discrepancies were found between the direct (γ, xn) data obtained at Saclay and the equivalent photo-absorption cross sections obtained using (p, p′) data from the K600. Furthermore, discrepancies exist for several nuclei between photo-absorption data taken at the Saclay and Livermore laboratories. These discrepancies, possible reasons for them and future investigations will be presented and discussed.

Measurement of the photoabsorption cross section of 24Mg.

Accurate nuclear data is a key factor in determining the suitability and reliability of many theoretical nuclear models and large-scale calculations. One of the main ingredients of these calculations is how nuclei respond to an electromagnetic field. The excitation of the isovector giant dipole resonance (GDR) is of particular importance in both nuclear structure studies as well as being the main mode of interaction of ultra-high-energy cosmic rays with the extra-galactic medium. This study investigates the photoabsorption cross section in the region of the GDR in 24Mg through the use of proton inelastic scattering and the equivalent virtual photon method. The K600 spectrometer at the iThemba LABS facility was used to obtain high resolution, low background 24Mg(p,p’)24Mg* inelastic scattering data. The virtual photon absorption method is described and the result of applying the method is presented and compared to a previous real photon absorption cross section.

Investigation of giant dipole resonance in Mo isotopes within TDHF theory

The isovector giant dipole resonance (IVGDR) in the chain of even-even Mo isotopes is investigated within the time-dependent Hartree-Fock (TDHF) using the Skyrme force Sly6. The GDR calculated in Mo92−108 are presented, and compared with the available experimental data. An overall agreement between them is obtained. Moreover, the dipole strength in Mo102−108 is predicted. Shape phase transition from spherical to oblate as well as shape coexistence (A ∼ 100) in Mo isotopes are also investigated in this work. In addition, the correlation between the deformation splitting ΔE and the quadrupole deformation parameter β2 is studied. The results confirm that ΔE is proportional to the deformation of nucleus. We also discuss the dependence of GDR strength on some nuclear properties of Skyrme forces, such as the asymmetry energy as. We find that as=32 MeV, corresponding to SLy6, is quite consistent with experimental data.

Finite-temperature calculation of the isovector giant dipole resonance in Sn120 using self-consistent inputs

Background: Although microscopic models are frequently used to investigate giant resonances built on the ground state of a nucleus, similar calculations at nonzero temperature are limited. Approaches based on the classical thermal shape-fluctuation model (TSFM) are often utilized to analyze the properties of giant dipole resonance at finite temperature. However, TSFM fails to predict the correct trend of resonance width over a wide range of temperature starting from zero.Purpose: To study the isovector giant dipole resonance (IVGDR) at finite temperature, we present an improved version of TSFM, where driving potential and IVGDR centroid energies are obtained self-consistently using the nuclear energy density functional formalism. The temperature dependence of IVGDR width in $^{120}\mathrm{Sn}$ is calculated to benchmark the proposed method.Method: Nuclear free energy surfaces and entropy surfaces are simulated at different temperatures for two different parametrizations of Skyrme energy density functionals. Moreover, IVGDR centroid energies are calculated by incorporating nuclear deformations extracted from the corresponding self-consistent densities. Subsequently, IVGDR widths are obtained within TSFM. Also, we demonstrate the role of pairing fluctuation in improving the low temperature behavior of IVGDR width.Result: We found good overall agreement of our results with the measured IVGDR widths. Specifically, except at a very low temperature, unprecedented accuracy has been achieved in TSFM. Calculated IVGDR widths are shown to be robust against the choices of driving potential and Skyrme parametrization.Conclusion: The present paper provides guidance on using TSFM based calculations in predicting the IVGDR width over a broad range of temperature. For a more consistent calculation, pairing fluctuations are required to be included as additional degrees of freedom.

Damping of the isovector giant dipole resonance in 40,48Ca

The fine structure of the IsoVector Giant Dipole Resonance (IVGDR) in the doubly-magic nuclei 40,48Ca observed in inelastic proton scattering experiments under 0∘ is used to investigate the role of different mechanisms contributing to the IVGDR decay width. Characteristic energy scales are extracted from the fine structure by means of wavelet analysis. The experimental scales are compared to different theoretical approaches allowing for the inclusion of complex configurations beyond the mean-field level. Calculations are performed in the framework of RPA and beyond-RPA in a relativistic approach based on an effective meson-exchange interaction, with the UCOM effective interaction and, for the first time, with realistic two- plus three-nucleon interactions from chiral effective field theory employing the in-medium similarity renormalization group. All models highlight the role of Landau fragmentation for the damping of the IVGDR, while the differences in the coupling strength between one particle-one hole (1p-1h) and two particle-two hole (2p-2h) correlated (relativistic) and non-correlated (non-relativistic) configurations lead to very different pictures of the importance of the spreading width resulting in wavelet scales being a sensitive measure of their interplay. The relativistic approach with particle-vibration coupling, in particular, shows impressive agreement with the number and absolute values of the scales extracted from the experimental data.

Pygmy and isovector giant dipole resonance in $$^{175}$$Lu

Pygmy and isovector giant dipole resonance in $$^{175}$$Lu

Bayesian inference of finite-nuclei observables based on the KIDS model

Bayesian analyses on both isoscalar and isovector nuclear interaction parameters are carried out based on the Korea-IBS-Daegu-SKKU (KIDS) model under the constraints of nuclear structure data of $^{208}$Pb and $^{120}$Sn. Under the constraint of the neutron-skin thickness, it is found that incorporating the curvature parameter $K_{sym}$ of nuclear symmetry energy as an independent variable significantly broadens the posterior probability distribution function (PDF) of the slope parameter $L$, and affects the related correlations. Typically, the anticorrelation between $L$ and the symmetry energy at saturation density disappears, while a positive correlation between $L$ and $K_{sym}$ is observed. Under the constraint of the isoscalar giant monopole resonance (ISGMR), incorporating the skewness parameter as an independent variable also significantly broadens the posterior PDF of the nuclear matter incompressibility $K_0$. Even with the broad uncertainties of higher-order parameters of the equation of state (EOS), robust constraints of $L<90$ MeV and $K_0<270$ MeV are obtained. Our study quantifies the consistency between the constraints on $L$ from the neutron-skin data of PREXII and isovector giant dipole resonance (IVGDR) data, and the constraints on $K_0$ from the data of ISGMR in $^{208}$Pb and $^{120}$Sn.

Effects of ground-state correlations on the damping of giant dipole resonances in LS closed-shell nuclei

Abstract The effects of ground-state correlations on the damping of isovector giant dipole resonances in the LS closed-shell nuclei 16O and 40Ca are studied using extended random phase approximation (RPA) approaches derived from the time-dependent density matrix theory. It is pointed out that unconventional two-body amplitudes of one-particle–three-hole and three-particle–one-hole types that are neglected in most extended RPA theories play an important role in the fragmentation of isovector dipole strength.

Bayesian uncertainty quantification for nuclear matter incompressibility

Within a Bayesian statistical framework using the standard Skyrme-Hartree-Fock model, the maximum {\it a posteriori} (MAP) values and uncertainties of nuclear matter incompressibility and isovector interaction parameters are inferred from the experimental data of giant resonances and neutron-skin thicknesses of typical heavy nuclei. With the uncertainties of the isovector interaction parameters constrained by the data of the isovector giant dipole resonance and the neutron-skin thickness, we have obtained $K_0 = 223_{-8}^{+7}$ MeV at 68% confidence level using the data of the isoscalar giant monopole resonance in $^{208}$Pb measured at the Research Center for Nuclear Physics (RCNP), Japan, and at the Texas A&M University (TAMU), USA. Although the corresponding $^{120}$Sn data gives a MAP value for $K_0$ about 5 MeV smaller than the $^{208}$Pb data, there are significant overlaps in their posterior probability distribution functions.

Isovector giant monopole and quadrupole resonances in a Skyrme energy density functional approach with axial symmetry

[Background] Giant resonance (GR) is a typical collective mode of vibration. The deformation splitting of the isovector (IV) giant dipole resonance is well established. However, the splitting of GRs with other multipolarities is not well understood. [Purpose] I explore the IV monopole and quadrupole excitations and attempt to obtain the generic features of IV giant resonances in deformed nuclei by investigating the neutral and charge-exchange channels simultaneously. [Method] I employ a nuclear energy-density functional (EDF) method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random-phase approximation are used to describe the ground state and the transition to excited states. [Results] I find the concentration of the monopole strengths in the energy region of the isobaric analog or Gamow-Teller resonance irrespective of nuclear deformation, and the appearance of a high-energy giant resonance composed of the particle-hole configurations of $2\hbar \omega_0$ excitation. Splitting of the distribution of the strength occurs in the giant monopole and quadrupole resonances due to deformation. The lower $K$ states of quadrupole resonances appear lower in energy and possess the enhanced strengths in the prolate configuration, and vice versa in the oblate configuration, while the energy ordering depending on $K$ is not clear for the $J=1$ and $J=2$ spin-quadrupole resonances. [Conclusions] The deformation splitting occurs generously in the giant monopole and quadrupole resonances. The $K$-dependence of the quadrupole transition strengths is largely understood by the anisotropy of density distribution.

Bayesian inference on isospin splitting of nucleon effective mass from giant resonances in 208Pb * *Supported in part by the National Natural Science Foundation of China (11905302, 11625521) and National SKA Program of China (2020SKA0120300)

From a Bayesian analysis of the electric dipole polarizability, the constrained energy of isovector giant dipole resonance, the peak energy of isocalar giant quadrupole resonance, and the constrained energy of isocalar giant monopole resonance in 208Pb, we extract the isoscalar and isovector effective masses in nuclear matter at saturation density as and , respectively, at 90% confidence level. The constraints obtained on and lead to a positive isospin splitting of nucleon effective mass in asymmetric nuclear matter of isospin asymmetry at as . In addition, the symmetry energy at the subsaturation density is determined to be MeV at 90% confidence level.

Constraining Isovector Nuclear Interactions with Giant Dipole Resonance and Neutron Skin in 208Pb from a Bayesian ApproachSupported by the National Natural Science Foundation of China (Grant No. 11922514).

The remaining uncertainties in relation to isovector nuclear interactions call for reliable experimental measurements of isovector probes in finite nuclei. Based on the Bayesian analysis, although neutron-skin thickness data or isovector giant dipole resonance data in 208Pb can constrain only one isovector interaction parameter, correlations among other parameters can also be built. Using combined data for both the neutron-skin thickness and the isovector giant dipole resonance helps to significantly constrain all isovector interaction parameters; as such, it serves as a useful methodology for future research.

Isoscalar and isovector giant resonances in 44Ca, 54Fe, 64,68Zn and 56,58,60,68Ni

We have studied the uncharacteristic behavior of the measured values of the isoscalar and isovector centroid energies, ECEN, of nuclear giant resonances of multipolarity from L = 0 to L = 3 in 44Ca, 54Fe, 64,68Zn and 56,58,60,68Ni. For this purpose, we carried out calculations of ECEN within the spherical Hartree-Fock (HF)-based random phase approximation (RPA) theory with 33 distinct Skyrme-like effective nucleon-nucleon interactions. We have also determined the Pearson linear correlation coefficients between centroid energies, obtained from the HF-RPA, and the various properties of nuclear matter (NM) of each interaction and determined the sensitivity of ECEN to NM properties. We compared the theoretical values of ECEN obtained from the HF-RPA calculations with experimental data and discuss the results, pointing out significant disagreements between theoretical and experimental values. We note in particular, that we obtain good agreement for the theoretical ECEN of the isovector giant dipole resonance and the available experimental data.

Isovector giant dipole resonances in proton-rich Ar and Ca isotopes * *This work is partly Supported by the National Natural Science Foundation of China (11975096, 11775014) and the Fundamental Research Funds for the Central Universities (2020NTST06)

The isovector giant dipole resonances (IVGDR) in proton-rich Ar and Ca isotopes have been systematically investigated using the resonant continuum Hartree-Fock+BCS (HF+BCS) and quasiparticle random phase approximation (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 increasing mass number in each isotopic chain. The transition densities of the PDR states show that motions of protons 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.

Giant dipole resonance in Sm isotopes within TDHF method

In this work, we have studied the isovector giant dipole resonance (IVGDR) in even-even Sm isotopes within time-dependent Hartree–Fock (TDHF) with four Skyrme forces SLy6, SVbas, SLy5 and UNEDF1. The approach we have followed is somewhat similar to the one we did in our previous work in the region of neodymium (Nd, \(Z=60\)) [Physica Scripta (2020)]. We have calculated the dipole strength of \( ^{128-164}\text {Sm}\) and compared with the available experimental data. An overall agreement between them is obtained. The dipole strength in neutron-deficient \( ^{128-142}\text {Sm}\) and in neutron-rich \(^{156-164}\text {Sm}\) isotopes is predicted. Shape phase transition and shape coexistence in Sm isotopes are also investigated in the light of IVGDR. In addition, the correlation between the quadrupole deformation parameter \(\beta _{2}\) and the splitting \(\Delta E/ \bar{E}_{m}\) of the giant dipole resonance spectra is studied. The results confirm that \(\Delta E/ \bar{E}_{m}\) is proportional to quadrupole deformation \(\beta _{2}\).

Fine structure of the isovector giant dipole resonance in Nd142–150 and Sm152

Background: Inelastic proton scattering at energies of a few hundred MeV and very-forward angles including $0^\circ$ has been established as a tool to study electric-dipole strength distributions in nuclei. The present work reports a systematic investigation of the chain of stable even-mass Nd isotopes representing a transition from spherical to quadrupole-deformed nuclei. Purpose: Extraction of the equivalent photo-absorption cross sections and analysis of their fine structure in the energy region of the IsoVector Giant Dipole Resonance (IVGDR). Method: Proton inelastic scattering reactions of 200 MeV protons were measured at iThemba LABS in Cape Town, South Africa. The scattering products were momentum-analysed by the K600 magnetic spectrometer positioned at $\theta_{\mathrm{Lab}}=0^\circ$. Using dispersion-matching techniques, energy resolutions of $\Delta E \approx 40 - 50$ keV were obtained. After subtraction of background and contributions from other multipoles, the spectra were converted to photo-absorption cross sections using the equivalent virtual-photon method. Results: Wavelet-analysis techniques are used to extract characteristic energy scales of the fine structure of the IVGDR from the experimental data. Comparisons with the Quasiparticle-Phonon Model (QPM) and Skyrme Separable Random Phase Approximation (SSRPA) predictions provide insight into the role of different giant resonance damping mechanisms. Conclusions: Fine structure is observed even for the most deformed nuclei studied. Fragmentation of the one particle-one hole ($1p1h$) strength seems to be the main source of fine structure in both spherical and deformed nuclei. Some impact of the spreading due to coupling of the two particle-two hole ($2p2h$) states to the $1p1h$ doorway states is seen in the spherical/transitional nuclei, where calculations beyond the $1p1h$ level are available.

Nuclear Collective Dynamics in Transport Model With the Lattice Hamiltonian Method

We review the recent progress on studying the nuclear collective dynamics by solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation with the lattice Hamiltonian method treating the collision term by the full-ensemble stochastic collision approach. This lattice BUU (LBUU) method has recently been developed and implemented in a GPU parallel computing technique, and achieves a rather stable nuclear ground-state evolution and high accuracy in evaluating the nucleon-nucleon (NN) collision term. This new LBUU method has been applied to investigate the nuclear isoscalar giant monopole resonances and isovector giant dipole resonances. While the calculations with the LBUU method without the NN collision term (i.e., the lattice Hamiltonian Vlasov method) describe reasonably the excitation energies of nuclear giant resonances, the full LBUU calculations can well reproduce the width of the giant dipole resonance of $^{208}$Pb by including a collisional damping from NN scattering. The observed strong correlation between the width of nuclear giant dipole resonance and the NN elastic cross section suggests that the NN elastic scattering plays an important role in nuclear collective dynamics, and the width of nuclear giant dipole resonance provides a good probe of the in-medium NN elastic cross section.

Constraining isovector nuclear interactions with giant resonances within a Bayesian approach

We put a stringent constraint on the isovector nuclear interactions in the Skyrme-Hartree-Fock model from the centroid energy E−1 of the isovector giant dipole resonance in 208Pb as well as its electric polarizability αD. Using the Bayesian analysis method, E−1 and αD are found to be mostly determined by the nuclear symmetry energy Esym at about ρ⋆=0.05 fm−3 and the isovector nucleon effective mass mv⋆ at the saturation density. At 90% confidence level, we obtain Esym(ρ⋆)=16.4−0.9+1.0 MeV and mv⋆/m=0.79−0.06+0.06.