Isoscalar Giant Monopole Resonance Research Articles

Effect of ground-state deformation on the isoscalar giant monopole resonance and the first observation of overtones of the isoscalar giant quadrupole resonance in rare-Earth Nd isotopes

The strength distributions of the Isoscalar Giant Monopole Resonance (ISGMR) and Isoscalar Giant Quadrupole Resonance (ISGQR) in 142,146−150Nd have been determined via inelastic α-particle scattering with the Grand Raiden (GR) Spectrometer at the Research Center for Nuclear Physics (RCNP), Japan. In the deformed nuclei 146−150Nd, the ISGMR strength distributions exhibit a splitting into two components, while the nearly spherical nucleus 142Nd displays a single peak in the ISGMR strength distribution. A noteworthy achievement in this study is the first-time detection of overtones in the Isoscalar Giant Quadrupole Resonance (ISGQR) strength distributions within Nd isotopes at an excitation energy around 25 MeV obtained through Multipole Decomposition Analysis (MDA).

Ab initio description of monopole resonances in light- and medium-mass nuclei

Giant resonances (GRs) are a striking manifestation of collective motions in mesoscopic systems such as atomic nuclei. Until recently, theoretical investigations have essentially relied on the (quasiparticle) random phase approximation ((Q)RPA), and extensions of it, based on phenomenological energy density functionals (EDFs). As part of a current effort to describe GRs within an ab initio theoretical scheme, the present work promotes the use of the projected generator coordinate method (PGCM). This method, which can handle anharmonic effects while satisfying symmetries of the nuclear Hamiltonian, displays a favorable (i.e. mean-field-like) scaling with system’s size. Presently focusing on the isoscalar giant monopole resonance (GMR) of light- and medium-mass nuclei, PGCM’s potential to deliver wide-range ab initio studies of GRs in closed- and open-shell nuclei encompassing pairing, deformation, and shape coexistence effects is demonstrated. The comparison with consistent QRPA calculations highlights PGCM’s unique attributes and sheds light on the intricate interplay of nuclear collective excitations. The present paper is the first in a series of four and focuses on technical aspects and uncertainty quantification of ab initio PGCM calculations of GMR using the doubly open-shell 46\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{46}$$\\end{document}Ti as an illustrative example. The second paper displays results for a set of nuclei of physical interest and proceeds to the comparison with consistent (deformed) ab initio QRPA calculations. While the third paper analyzes useful moments of the monopolar strength function and different ways to access them within PGCM calculations, the fourth paper focuses on the effect of the symmetry restoration on the monopole strength function.

Probing isoscalar giant monopole resonance in axially and triaxially deformed zirconium isotopes

Probing isoscalar giant monopole resonance in axially and triaxially deformed zirconium isotopes

Isoscalar giant resonances of <inline-formula><tex-math id="M1">\begin{document}$^{{\bf{18}}}_{{\boldsymbol{\Lambda\Lambda}}}{\bf{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M1.png"/></alternatives></inline-formula> in relativistic approach

The interactions between hyperon-nucleon and hyperon-hyperon have been an important topic in strangeness nuclear physics, which play an important role in understanding the properties of hypernuclei and equation of state of strangeness nuclear matter. It is very difficult to perform a direct scattering experiment of the nucleon and hyperon because the short lifetime of the hyperon. Therefore, the hyperon-nucleon interaction and the hyperon-hyperon interaction have been mainly investigated experimentally by <inline-formula><tex-math id="M4">\begin{document}$\gamma$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M4.png"/></alternatives></inline-formula> spectroscopy of single-<inline-formula><tex-math id="M5">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M5.png"/></alternatives></inline-formula> hypernuclei or double-<inline-formula><tex-math id="M6">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M6.png"/></alternatives></inline-formula> hypernuclei. There are also many theoretical methods developed to describe the properties of hypernuclei. Most of these models focus mostly on the ground state properties of hypernuclei, and have given exciting results in producing the banding energy, the energy of single-particle levels, deformations, and other properties of hypernuclei. Only a few researches adopting Skyrme energy density functionals is devoted to the study of the collective excitation properties of hypernuclei. In present work, we have extended the relativistic mean field and relativistic random phase approximation theories to study the collective excitation properties of hypernuclei, and use the methods to study the isoscalar collective excited state properties of double <inline-formula><tex-math id="M7">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M7.png"/></alternatives></inline-formula> hypernuclei. First, the effect of <inline-formula><tex-math id="M8">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M8.png"/></alternatives></inline-formula> hyperons on the single-particle energy of <sup>16</sup>O and <inline-formula><tex-math id="M9">\begin{document}$^{18}_{\Lambda\Lambda}{\rm{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M9.png"/></alternatives></inline-formula> are discussed in the relativistic mean field theory, the calculations are performed within TM1 parameter set and related hyperon-nucleon interaction, and hyperon-hyperon interaction. We find that it gives a larger attractive effect on the <inline-formula><tex-math id="M10">\begin{document}${{\mathrm{s}}}_{1/2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M10.png"/></alternatives></inline-formula> state of proton and neutron, while gives a weaker attractive effect on the state around Fermi surface. The self-consistent relativistic random phase approximation is used to study the collectively excited state properties of hypernucleus <inline-formula><tex-math id="M11">\begin{document}$^{18}_{\Lambda\Lambda}{\rm{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M11.png"/></alternatives></inline-formula>. The isoscalar giant monopole resonance and quadrupole resonance are calculated and analysed in detail, we pay more attention to the effect of the inclusion of <inline-formula><tex-math id="M12">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M12.png"/></alternatives></inline-formula> hyperons on the properties of giant resonances. Comparing with the strength distributions of <sup>16</sup>O, changes of response function of <inline-formula><tex-math id="M13">\begin{document}$^{18}_{\Lambda\Lambda}{\rm{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M13.png"/></alternatives></inline-formula> are evidently found both on the isoscalar giant monopole resonance and quadrupole resonance. It is shown that the difference comes mainly from the change of Hartree energy of particle-hole configuration and the contribution of the excitations of <inline-formula><tex-math id="M14">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M14.png"/></alternatives></inline-formula> hyperons. We find that the hyperon-hyperon residual interactions have small effect on the monopole resonance function and quadrupole response function in the low-energy region, and have almost no effect on the response functions in the high-energy region.

Isoscalar monopole response in the neutron-rich molybdenum isotopes using self-consistent QRPA

The isoscalar giant monopole resonance (ISGMR) of even molybdenum isotopes 92,94,96,98,100Mo has been studied within the Skyrme self-consistent Hartree - Fock - Bardeen, Cooper, and Schrieffer and quasi-particle random phase approximation. Ten sets of Skyrme-type interactions of different values of the nuclear matter incompressibility coefficient KNM are used in the calculations. The calculated strength distributions, centroid energies Ecen, scaled energies Es and constrained energies Econ of ISGMR are compared with available experimental data. Due to the appropriate value of the nuclear matter incompressibility KNM, several types of Skyrme interactions were successful in describing the ISGMR strength distribution in the 92,94,96,98,100Mo isotopes. As a result, high correlations between Ecen and KNM were found.

A multi-shell extension of the interacting boson model

A multi-shell extension of the simplest formulation of the interacting boson model that appends parity-conserving (2ħω) energy excitations to the non-extended theory is proffered. From a physical perspective this extension links the system's low-lying configurations to higher-lying multiple one-particle-one-hole (1p-1h) excitation modes that are in part tethered to the system's isoscalar giant monopole and quadrupole resonances. An application of the theory to low-lying energy levels and known B(E0) and B(E2) values of 152Sm shows that the results obtained with the extension are better than those without the extension.

Excitation of the isoscalar giant monopole resonance and incompressibility of nuclear matter: resolution of a long-standing puzzle

Excitation of the isoscalar giant monopole resonance and incompressibility of nuclear matter: resolution of a long-standing puzzle

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.

Isoscalar giant monopole resonance in 40,48Ca

Starting from the Skyrme energy-density functional, the microscopic model is developed for the monopole excitations. We take into account the coupling between one-, two-, and three-phonon terms in the wave functions of excited 0+ states. As an example, the properties of the isoscalar giant monopole resonance (ISGMR) for the doubly magic nuclei 40,48Ca are discussed. The inclusion of complex configurations leads to a fragmentation of the ISGMR strength to lower energy 0+ states and also higher energy tail.

Toward a Unified Description of Isoscalar Giant Monopole Resonances in a Self-Consistent Quasiparticle-Vibration Coupling Approach.

The nuclear incompressibility is a key parameter of the nuclear equation of state that can be extracted from the measurements of the so-called "breathing mode" of finite nuclei. The most serious discrepancy so far is between values extracted from Pb and Sn, that has provoked the longstanding question "Why is tin so soft?". To solve this puzzle, a fully self-consistent quasiparticle random-phase approximation plus quasiparticle-vibration coupling approach based on Skyrme-Hartree-Fock-Bogoliubov is developed. We show that the many-body correlations introduced by quasiparticle-vibration coupling, which shift the isoscalar giant monopole resonance energy in Sn isotopes by about 0.4MeV more than the energy in ^{208}Pb, play a crucial role in providing a unified description of the isoscalar giant monopole resonance in Sn and Pb isotopes. The best description of the experimental strength functions is given by SV-K226 and KDE0, which are characterized by incompressibility values K_{∞}=226 MeV and 229MeV, respectively, at mean field level.

Relativistic approach to the nuclear breathing mode

Microscopic theory of the nuclear response based on the relativistic meson-nucleon Lagrangian is applied to the description of the isoscalar giant monopole resonance (ISGMR) in a variety of nuclear systems. It is shown that the parameter-free inclusion of beyond-mean-field correlations of the quasiparticle-vibration coupling (qPVC) type in the leading approximation allows for a simultaneous realistic description of the ISGMR in nuclei of lead, tin, zirconium, and nickel mass regions, which is difficult on the mean-field level. The calculations employ the finite-range effective meson-nucleon interaction, which, in combination with the qPVC, has consistently demonstrated the ability to reliably describe many other nuclear structure phenomena. Systematic calculations of the isoscalar monopole response for nickel isotopes help reveal the central role of the coupling between the ISGMR and the low-energy quadrupole states in the placement of the ISGMR centroids.

Isoscalar giant monopole strength in Ni58, Zr90, Sn120 , and Pb208

Background: Inelastic $\ensuremath{\alpha}$-particle scattering at energies of a few hundred MeV and very-forward scattering angles including 0\ifmmode^\circ\else\textdegree\fi{} has been established as a tool for the study of the isoscalar giant monopole (IS0) strength distributions in nuclei. This compressional mode of nuclear excitation can be used to derive the incompressibility of nuclear matter.Purpose: An independent investigation of the IS0 strength in nuclei across a wide mass range was performed using the ${0}^{\ensuremath{\circ}}$ facility at iThemba Laboratory for Accelerator Based Sciences (iThemba LABS), South Africa, to understand differences observed between IS0 strength distributions in previous experiments performed at the Texas A University (TAMU) Cyclotron Institute, USA and the Research Center for Nuclear Physics (RCNP), Japan.Methods: The isoscalar giant monopole resonance (ISGMR) was excited in $^{58}\mathrm{Ni}, ^{90}\mathrm{Zr}, ^{120}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ using $\ensuremath{\alpha}$-particle inelastic scattering with a 196 MeV $\ensuremath{\alpha}$ beam and scattering angles ${\ensuremath{\theta}}_{\text{Lab}}={0}^{\ensuremath{\circ}}$ and ${4}^{\ensuremath{\circ}}$. The K600 magnetic spectrometer at iThemba LABS was used to detect and momentum analyze the inelastically scattered $\ensuremath{\alpha}$ particles. The IS0 strength distributions in the nuclei studied were deduced with the difference-of-spectra (DoS) technique including a correction factor for the ${4}^{\ensuremath{\circ}}$ data based on the decomposition of $L0$ cross sections in previous experiments.Results: IS0 strength distributions for $^{58}\mathrm{Ni}, ^{90}\mathrm{Zr}, ^{120}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ are extracted in the excitation-energy region ${E}_{\mathrm{x}}=9--25$ MeV. Using correction factors extracted from the RCNP experiments, there is a fair agreement with their published IS0 results. Good agreement for IS0 strength in $^{58}\mathrm{Ni}$ is also obtained with correction factors deduced from the TAMU results, while marked differences are found for $^{90}\mathrm{Zr}$ and $^{208}\mathrm{Pb}$.Conclusions: Previous measurements show significant differences in the IS0 strength distributions of $^{90}\mathrm{Zr}$ and $^{208}\mathrm{Pb}$. This work demonstrates clear structural differences in the energy region of the main resonance peaks with possible impact on the determination of the nuclear matter incompressibility presently based on the IS0 centroid energies of these two nuclei. The results also suggest that, for an improved determination of the incompressibility, theoretical approaches should aim at a description of the full strength distributions rather than the centroid energy only.

Isoscalar Giant Monopole Resonance in Spherical Nuclei as a Nuclear Matter Incompressibility Indicator

The incompressibility of both nuclear matter and finite nuclei is estimated by the monopole compression modes in nuclei in the framework of a nonrelativistic Hartree–Fock–Bogoliyubov method and the coherent density fluctuation model. The monopole states originate from vibrations of the nuclear density. The calculations in the model for the incompressibility in finite nuclei are based on the Brueckner energy–density functional for nuclear matter. Results for the energies of the breathing vibrational states and finite nuclei incompressibilities are obtained for various nuclei and their values are compared with recent experimental data. The evolution of the isoscalar giant monopole resonance (ISGMR) along Ni, Sn, and Pb isotopic chains is discussed. This approach can be applied to analyses of neutron stars properties, such as incompressibility, symmetry energy, slope parameter, and other astrophysical quantities, as well as for modelling dynamical behaviors within stellar environments.

Microscopic Description of Isoscalar Giant Monopole Resonance in $${}^{{48}}$$Ca

The properties of the isoscalar giant monopole resonance (ISGMR) for the double magic $${}^{48}$$ Ca are analyzed in the framework of a microscopic model based on Skyrme-type interactions. A method for simultaneously taking into account the coupling between one-, two- and three-phonon terms in the wave functions of $$0^{+}$$ states has been developed. The inclusion of three-phonon configurations leads to a substantial redistribution of the ISGMR strength to lower energy $$0^{+}$$ states and also higher energy tail. Our results demonstrate that the developed approach enables us to describe a gross structure of the ISGMR spreading width.

Triaxiality-induced monopole-quadrupole-hexadecupole coupling in the isoscalar giant resonances ofGe86

The isoscalar giant resonances for $^{86}\mathrm{Ge}$ are studied by the quasiparticle finite amplitude method based on the covariant density functional theory. In addition to the well-known monopole-quadrupole coupling that splits the isoscalar giant monopole resonance in axially deformed nuclei, a monopole-quadrupole-hexadecupole coupling is identified in the neutron-rich triaxially deformed nucleus $^{86}\mathrm{Ge}$, leading to the emergence of a distinct resonance peak at the low energy side of the isoscalar monopole strength function. The transition density of the triaxiality-induced resonance peak shows a strong interplay among monopole, quadrupole, and hexadecupole vibrations. The resonance peak responds to monopole, quadrupole, and hexadecupole perturbations simultaneously, which could be regarded as a fingerprint of the triaxiality in $^{86}\mathrm{Ge}$.

Evolution of the isoscalar giant monopole resonance in the Ca isotope chain

Background: Two recent studies of the evolution of the isoscalar giant monopole resonance (ISGMR) within the calcium isotope chain report conflicting results. One study suggests that the monopole resonance energy, and thus the incompressibility of the nucleus, KA, increase with mass, which implies that Kτ, the asymmetry term in the nuclear incompressibility, has a positive value. The other study reports a weak decreasing trend of the energy moments, resulting in a generally accepted negative value for Kτ. Differences in the observed trends have been attributed to the use of different techniques to account for instrumental background and the physical continuum. Purpose: An independent measurement of the ISGMR in the Ca isotope chain is provided to gain a better understanding of the origin of possible systematic trends. Methods: Inelastically scattering of 196 MeV α particles were observed at small scattering angles, including 0∘, for a range of calcium targets (40,42,44,48Ca). The scattered α particles were momentum analyzed in the K600 magnetic spectrometer at iThemba LABS, South Africa. Monopole strengths spanning an excitation-energy range between 9.5 and 25.5 MeV were obtained using the difference-of-spectra (DoS) technique, adjusted to allow corrections for the variation of the angular shape of the sum of the L>0 multipoles as a function of excitation energy, and compared with previous results that employed the multipole-decomposition analysis (MDA) techniques. Results: The structure of the E0 strength distributions of Ca40,42,44 agrees well with the results from the previous measurement that support a weak decreasing trend of the energy moments, while no two datasets agree in the case of Ca48. Despite the variation in the structural character of E0 strength distribution from different studies, we find for all datasets that the moment ratios, calculated from the ISGMR strength in the excitation-energy range that covers the resonance peak, display at best only a weak systematic sensitivity to a mass increase. Conclusion: Different trends observed in the nuclear incompressibility are caused by contributions to the E0 strength outside of the region covering the resonance peak, and in particular for high excitation energies. While procedures exist to identify and subtract instrumental background, more work is required to characterize and subtract continuum background contributions at high excitation energies.4 MoreReceived 30 January 2022Accepted 16 May 2022DOI:https://doi.org/10.1103/PhysRevC.105.054319©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsH & He induced nuclear reactionsNucleon-nucleon interactionsResonance reactionsProperties39 ≤ A ≤ 58Nuclear Physics

Finite amplitude method on the deformed relativistic Hartree-Bogoliubov theory in continuum: The isoscalar giant monopole resonance in exotic nuclei

Finite amplitude method based on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc-FAM) is developed and applied to study isoscalar giant monopole resonance in exotic nuclei. Validation of the numerical implementation is examined for $^{208}\textrm{Pb}$. The isoscalar giant monopole resonances for even-even calcium isotopes from $^{40}\textrm{Ca}$ to the last bound neutron-rich nucleus $^{80}\textrm{Ca}$ are calculated, and a good agreement with the available experimental centroid energies is obtained for $^{40-48}\textrm{Ca}$. For the exotic calcium isotopes, e.g., $^{68}\textrm{Ca}$ and $^{80}\textrm{Ca}$, the DRHBc-FAM calculated results are closer to the energy weighted sum rule than the calculations on the harmonic oscillator basis, which highlights the advantages of DRHBc-FAM in describing giant resonances for exotic nuclei. In order to explore the soft monopole mode in the exotic nuclei, the giant monopole resonance for the deformed exotic nucleus $^{200}\textrm{Nd}$ is investigated, where the prolate shape and the oblate shape coexist. A soft monopole mode near 6.0 MeV is found in the prolate case, and another one near 4.5 MeV is found in the oblate case. The transition density of the soft monopole mode shows in phase or out-of-phase vibrations near the surface region, which is generated by quadrupole vibrations.

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.

Isoscalar giant monopole resonance inMg24andSi28: Effect of coupling between the isoscalar monopole and quadrupole strength

Background: In highly deformed nuclei, there is a noticeable coupling of the isoscalar giant monopole resonance (ISGMR) and the K=0 component of the isoscalar giant quadrupole resonance (ISGQR), which results in a double peak structure of the isoscalar monopole (IS0) strength (a narrow low-energy deformation-induced peak and a main broad ISGMR part). The energy of the narrow low-lying IS0 peak is sensitive to both the incompressibility modulus K∞ and the coupling between IS0 and isoscalar quadrupole (IS2) strength. Purpose: This study aims to investigate the two-peaked structure of the ISGMR in the prolate Mg24 and oblate Si28 nuclei and identify among a variety of energy density functionals based on Skyrme parametrizations the one which best describes the experimental data. This will allow for conclusions regarding the nuclear incompressibility. Because of the strong IS0/IS2 coupling, the deformation splitting of the ISGQR will also be analyzed. Methods: The ISGMR was excited in Mg24 and Si28 using α-particle inelastic scattering measurements acquired with an Eα=196 MeV beam at scattering angles θLab=0∘ and 4∘. The K600 magnetic spectrometer at iThemba LABS was used to detect and momentum analyze the inelastically scattered α particles. An experimental energy resolution of ≈70 keV (FWHM) was attained, revealing fine structure in the excitation-energy region of the ISGMR. The IS0 strength distributions in the nuclei studied were obtained with the difference-of-spectra (DoS) technique. The theoretical comparison is based on the quasiparticle random-phase approximation (QRPA) with a representative set of Skyrme forces. Results: IS0 strength distributions for Mg24 and Si28 are extracted and compared to previously published results from experiments with a lower energy resolution. With some exceptions, a reasonable agreement is obtained. The IS0 strength is found to be separated into a narrow structure at about 13–14 MeV in Mg24, 17–19 MeV in Si28, and a broad structure at 19–26 MeV in both nuclei. The data are compared with QRPA results. The results of the calculated characteristics of IS0 states demonstrate the strong IS0/IS2 coupling in strongly prolate Mg24 and oblate Si28. The narrow IS0 peaks are shown to arise due to the deformation-induced IS0/IS2 coupling and strong collective effects. The cluster features of the narrow IS0 peak at 13.87MeV in Mg24 are also discussed. The best description of the IS0 data is obtained using the Skyrme force SkPδ with an associated low nuclear incompressibility K∞=202MeV allowing for both the energy of the peak and integral IS0 strength in Mg24 and Si28 to be reproduced. The features of the ISGQR in these nuclei are also investigated. An anomalous deformation splitting of the ISGQR in oblate Si28 is found. The observed structure of ISGQR in Mg24 is described. Conclusions: The ISGMR and ISGQR in light deformed nuclei are coupled and thus need to be described simultaneously. Only such a description is relevant and consistent. The deformation-induced narrow IS0 peaks can serve as an additional sensitive measure of the nuclear incompressibility.8 MoreReceived 13 November 2021Revised 20 December 2021Accepted 25 January 2022DOI:https://doi.org/10.1103/PhysRevC.105.024311©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsNuclear forcesNuclear many-body theoryNuclear spin & parityNuclear structure & decaysNucleon induced nuclear reactionsNucleon-nucleon interactionsResonance reactionsProperties20 ≤ A ≤ 38Accelerators & BeamsNuclear Physics

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.