Isoscalar Giant Resonance Research Articles

Semimicroscopic description of isoscalar giant multipole resonances in medium-mass closed-shell nuclei

Semimicroscopic description of isoscalar giant multipole resonances in medium-mass closed-shell nuclei

ISOSCALAR DIPOLE RESPONSE IN 92Mo AND 100Mo ISOTOPES

In this work, the Isoscalar (IS) Giant Dipole Resonance (GDR) and Pygmy Dipole Resonance (PDR) of 92Mo and 100Mo Isotopes were calculated in the farmwork of the self-consistent quasi-particle random phase approximation (QRPA) based on the results of Hartree-Fock-Bardeen, Cooper and Schrieffer (HF-BCS) using 10 Skyrme-type interactions: KDE0v1, eMSL08, SKX, SGOI, v080, SKP, SIV, SIII, SKIII, and SGI. The strength distributions of isoscalar dipole response were compared with the available experimental data. Also, we discussed the statistical relation between the centroid energy and the nuclear matter incompressibility KNM.

Isoscalar Giant Octupole Resonance ISGOR of 116Cd using Self-Consistent Skyrme QRPA

Collective models based on the random phase approximation (RPA) are widely used to accurately depict collective modes of response. They can quickly calculate the strength function for the entire nuclear mass range. The quasi-particle random phase approximation (QRPA), which considers the pairing effect, is an enhanced RPA model. It is anticipated that this effect will be significant for open-shell nuclei. In this work, the self-consistent Skyrme Hartree-Fock-Bardeen, Cooper, and Schrieffer (HF-BCS) and QRPA models have been used to study the isoscalar giant octupole resonance (ISGOR) in the 116Cd isotope. Ten Skyrme-type parameters are utilized in the computations since they may be identified by different values of the incompressibility modulus KMN in nuclear matter. The calculated strength distributions and centroid energy are compared with available experimental data. We saw that the strength distributions varied depending on the type of Skyrme-interaction, and we also observed a definite impact of the KNM values on the centroid energy.

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 $^{86}\mathrm{Ge}$.

Nuclear giant quadruple resonance within a transport approach and its constraint on the nucleon effective mass

We study the nuclear iso-scalar giant quadruple resonance~(ISGQR) based on the Boltzmann-Uehling-Uhlenbeck~(BUU) transport equation. The mean-field part of the BUU equation is described by the Skyrme nucleon-nucleon effective interaction, and its collision term, which embodies the two-particle-two-hole ($2$p-$2$h) correlation, is implemented through the stochastic approach. We find that the width of ISGQR for heavy nuclei is exhausted dominated by collisional damping, which is incorporated into the BUU equation through its collision term, and it can be well reproduced through employing a proper in-medium nucleon-nucleon cross section. Based on further Vlasov and BUU calculations with a number of representative Skyrme interactions, the iso-scalar nucleon effective mass at saturation density is extracted respectively as $m^{*}_{s,0}/m$ $=$ $0.83\pm0.04$ and $m^{*}_{s,0}/m$ $=$ $0.82\pm0.03$ from the measured excitation energy $E_x$ of the ISGQR of $\isotope[208]{Pb}$. The small discrepancy between the two constraints indicates the negligible role of $2$p-$2$h correlation in constraining $m_{s,0}^*$ with the ISGQR excitation energy.

Properties of isoscalar giant multipole resonances in medium-heavy closed-shell nuclei: A semimicroscopic description

The semimicroscopic particle-hole dispersive optical model (PHDOM) is implemented to describe main properties of Isoscalar Giant Multipole Resonances (up to L=3) in medium-heavy closed-shell nuclei. The main properties are characterized by the strength distribution, transition density, partial and total probabilities of direct one-nucleon decay. Calculation results obtained for the 208Pb nucleus are compared with available experimental data.

Nucleus giant resonances from an improved isospin-dependent Boltzmann-Uehling-Uhlenbeck transport approach

We have studied the isoscalar giant quadruple resonance (ISGQR) and the isovector giant dipole resonance (IVGDR) in $^{208}$Pb based on an improved isospin-dependent Boltzmann-Uehling-Uhlenbeck transport approach using an improved isospin- and momentum-dependent interaction. With the isoscalar nucleon effective mass and the nucleon-nucleon cross section which reproduces respectively the excitation energy and the width of the ISGQR strength function, the slope parameter of the symmetry energy and the neutron-proton effective mass splitting are constrained respectively within $36<L<62$ MeV and $0.08\delta<(m_{n0}^*-m_{p0}^*)/m<0.42\delta$, by comparing the resulting centroid energy of the IVGDR and the electric dipole polarizability with the experimental data. It is found that nucleon-nucleon collisions have considerable effects on the resulting electric dipole polarizability, which needs to be measured more accurately in order to pin down isovector nuclear interactions.

Isoscalar and Isovector Giant Resonances in Closed Shells Nuclei and Bulk Properties of Nuclear Matter

Centroid energies, $$E_{\textrm{CEN}}$$ , of the isoscalar ( $$T=0$$ ) and isovector ( $$T=1$$ ) giant resonances of multipolarities $$L_{m}=0$$ –3 in $${}^{\mathrm{40,48}}$$ Ca, $${}^{\mathrm{68}}$$ Ni, $${}^{\mathrm{90}}$$ Zr, $${}^{\mathrm{116}}$$ Sn, $${}^{\mathrm{144}}$$ Sm, and $${}^{\mathrm{208}}$$ Pb, were calculated within the fully self-consistent spherical Hartree–Fock (HF)-based random-phase approximation (RPA) theory, using 33 different energy density functionals associated with Skyrme-type effective nucleon–nucleon interactions of the standard form commonly employed in the literature. We also calculate the Pearson linear correlation coefficients between each $$E_{\mathrm{CEN}}$$ and each bulk property of nuclear matter (NM), associated with the Skyrme interactions used in the calculations, and determine the sensitivity of $$E_{\mathrm{CEN}}$$ to bulk properties of NM. By comparing the calculated values of $$E_{\textrm{CEN}}$$ to the experimental data, we constrain the values of the bulk NM properties. We find that interactions associated with the values of the NM effective mass, $$m^{\ast}/m=0.70$$ –0.90, incompressibility coefficient, $$K_{\textrm{NM}}=210$$ –240 MeV, and the enhancement coefficient of the energy-weighted sum rule of the isovector giant dipole resonance, $$\kappa=0.25$$ –0.70, best reproduce the experimental data.

Reexamination of isoscalar giant resonances inC12andNb93throughLi6scattering

Inelastic ${}^{6}$Li scattering at 100 MeV/u on ${}^{12}$C and ${}^{93}$Nb have been measured with the high-resolution magnetic spectrometer Grand Raiden. The magnetic-rigidity settings of the spectrometer covered excitation energies from 10 to 40 MeV and scattering angles in the range $0^\circ < \theta_{\text{lab.}}< 2^\circ$. The isoscalar giant monopole resonance was selectively excited in the present data. Measurements free of instrumental background and the very favorable resonance-to-continuum ratio of ${}^{6}$Li scattering allowed for precise determination of the $E0$ strengths in ${}^{12}$C and ${}^{93}$Nb. It was found that the monopole strength in ${}^{12}$C exhausts $52 \pm 3^\text{(stat.)} \pm 8 ^\text{(sys.)}$\% of the energy-weighted sum rule (EWSR), which is considerably higher than results from previous $\alpha$-scattering experiments. The monopole strength in ${}^{93}$Nb exhausts $92 \pm 4^\text{(stat.)} \pm 10 ^\text{(sys.)}$\% of the EWSR, and it is consistent with measurements of nuclei with mass number of $A\approx90$. Such comparison indicates that the isoscalar giant monopole resonance distributions in these nuclei are very similar, and no influence due to nuclear structure was observed.

Semimicroscopic Description of Isoscalar Giant Multipole Resonances in the $${}^{\mathbf{208}}$$Pb Nucleus

An approach to describing main properties of isoscalar giant multipole resonances in medium-heavy closed-shell nuclei is proposed within the particle–hole dispersive optical model formulated recently. The description includes the energy-averaged strength function, projected transition density, and partial branching ratios for direct single-nucleon decay. The results obtained within this approach for the $${}^{208}$$ Pb nucleus are compared with available experimental data.

Nuclear Structure of Zirconium Isotopes 90,96,106Zr Using Skyrme HF-RPA

The ground state properties of the closed-shell 90Zr and closed-subshell 96,106Zr isotopes were investigated using a self-consistent spherical Hartree-Fock HF method and Random Phase Approximation RPA with five different Skyrme type effective nucleon-nucleon interaction: KDE0v1, BsK1, SIII, SVII and SGOI. Having a large number of Skyrme-force parameterizations requires a continuous search for the best for describing the experimental data. The presented approach attempts to accurately describe the structure of the Zirconium isotopes 90, 96, 106Zr. The calculated binding energies, root-mean squares, charge distributions, single particle energies were compared with the experimental data. Moreover, the transition strength function S(E) of the isoscalar giant monopole resonance (ISGMR), Jπ = 0+, T=0, the isoscalar giant dipole resonance (ISGDR), Jπ = 1-, T=0, isoscalar giant quadrupole resonance (ISGQR), Jπ = 2+, T=0, and isoscalar giant octupole resonance (ISGOR), Jπ = 3-, T=0 were calculated for the investigated isotopes and compared with the available experimental data.

Where we stand on structure dependence of ISGMR in the Zr-Mo region: Implications on K∞

Isoscalar giant resonances, being the archetypal forms of collective nuclear behavior, have been studied extensively for decades with the goal of constraining bulk nuclear properties of the equation of state, as well as for modeling dynamical behaviors within stellar environments. An important such mode is the isoscalar electric giant monopole resonance (ISGMR) that can be understood as a radially symmetric density vibration within the saturated nuclear volume. The field has a few key open questions, which have been proposed and remain unresolved. One of the more provocative questions is the extra high-energy strength in the $A\approx 90$ region, which manifested in large percentages of the $E0$ sum rule in $^{92}$Zr and $^{92}$Mo above the main ISGMR peak. The purpose of this article is to introduce these questions within the context of experimental investigations into the phenomena in the zirconium and molybdenum isotopic chains, and to address, via a discussion of previously published and preliminary results, the implications of recent experimental efforts on extraction of the nuclear incompressibility from this data.

Isoscalar and isovector giant resonances in 92,94,96,98,100Mo and 90,92,94Zr

The response functions, S(E), and centroid energies, ECEN, of the isoscalar and isovector giant resonances of multipolarity L = 0–3 in 92,94,96,98,100Mo and 90,92,94Zr have been calculated employing the spherical Hartree-Fock (HF) based random phase approximation (RPA) method, using the Skyrme-type effective nucleon-nucleon interaction. In particular, we investigate the recent experimental results of the uncharacteristic behavior of ECEN for the isoscalar giant resonances, by extending our HF-based RPA calculations with only the KDE0v1 interaction to 32 additional Skyrme interactions. The main result of our investigation is that we find significant disagreements between the theoretical and the experimental values of ECEN for isoscalar giant monopole and dipole resonance of some nuclei. For the isoscalar giant octupole resonance we find the theoretical values of the ECEN to be well above the experimental results. We also study the sensitivity of ECEN to nuclear matter (NM) properties, including the effective mass, the incompressibility coefficient and the symmetry energy at saturation density, by determining the Pearson linear correlation coefficient between the calculated values of ECEN and the various nuclear matter properties of each Skyrme parametrization. For the isovector giant dipole resonance we find good agreement between the experimental and theoretical values of ECEN for Skyrme interactions with values of the enhancement coefficient of the energy weighted sum rule, κ, in the range between 0.25–0.70.

Isoscalar E0, E1 , and E2 strength in Ca44

Isoscalar giant resonances in $^{44}\mathrm{Ca}$ have been studied with inelastic scattering of 240 MeV \ensuremath{\alpha} particles at small angles including ${0}^{\ensuremath{\circ}}$. A majority of the energy weighted sum rule was identified for $E0$ and $E2$ ($\ensuremath{\approx}70%$), and nearly half was identified for $E1$. The strength distributions are compared with the predictions from Hartree-Fock based random phase approximation calculations with the KDE0v1 Skyrme-type interaction. The giant monopole resonance energy moments for $^{40,44,48}\mathrm{Ca}$ increase with mass, contrary to what would be expected with a negative symmetry energy, ${K}_{\ensuremath{\tau}}$.

Pairing and deformation effects in nuclear excitation spectra

We investigate effects of pairing and of quadrupole deformation on two sorts of nuclear excitations,$\gamma$-vibrational $K^{\pi}=2^+$ states and dipole resonances (isovector dipole, pygmy, compression, toroidal). The analysis is performed within the quasiparticle random-phase approximation (QRPA) based on the Skyrme energy functional using the Skyrme parametrization SLy6. Particular attention is paid to i) the role of the particle-particle (pp) channel in the residual interaction of QRPA, ii) comparison of volume pairing (VP) and surface pairing (SP), iii) peculiarities of deformation splitting in the various resonances. We find that the impact of the pp-channel on the considered excitations is negligible. This conclusion applies also to any other excitation except for the $K^{\pi}=0^+$ states. Furthermore, the difference between VP and SP is found small (with exception of peak height in the toroidal mode). In the low-energy isovector dipole (pygmy) and isoscalar toroidal modes, the branch $K^{\pi}=1^-$ is shown to dominate over $K^{\pi}=0^-$ one in the range of excitation energy $E <$ 8--10 MeV. The effect becomes impressive for the toroidal resonance whose low-energy part is concentrated in a high peak of almost pure $K^{\pi}=1^-$ nature. This peculiarity may be used as a fingerprint of the toroidal mode in future experiments. The interplay between pygmy, toroidal and compression resonances is discussed, the interpretation of the observed isoscalar giant dipole resonance is partly revised.

Constraining simultaneously nuclear symmetry energy and neutron-proton effective mass splitting with nucleus giant resonances using a dynamical approach

With a newly improved isospin- and momentum-dependent interaction and an isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, we have investigated the effects of the slope parameter $L$ of the nuclear symmetry energy and the isospin splitting of the nucleon effective mass $m_{n-p}^*=(m_n^*-m_p^*)/m$ on the centroid energy of the isovector giant dipole resonance and the electric dipole polarizability in $^{208}$Pb. With the isoscalar nucleon effective mass $m_s^*=0.7m$ constrained by the empirical optical potential, we obtain a constraint of $L=64.29\pm11.84 (\rm MeV)$ and $m_{n-p}^*= (-0.019 \pm 0.090)\delta$, with $\delta$ being the isospin asymmetry of nuclear medium. With the isoscalar nucleon effective mass $m_s^*=0.84m$ extracted from the excitation energy of the isoscalar giant quadruple resonance in $^{208}$Pb, we obtain a constraint of $L=53.85\pm10.29 (\rm MeV)$ and $m_{n-p}^*= (0.216 \pm 0.114)\delta$.

First measurement of isoscalar giant resonances in a stored-beam experiment

Abstract A new technique developed for measuring nuclear reactions at low momentum transfer with stored beams in inverse kinematics was successfully used to study isoscalar giant resonances. The experiment was carried out at the experimental heavy-ion storage ring (ESR) at the GSI facility using a stored 58 Ni beam at 100 MeV/u and an internal helium gas-jet target. In these measurements, inelastically scattered α -recoils at very forward center-of-mass angles ( θ cm ≤ 1.5 ° ) were detected with a dedicated setup, including ultra-high vacuum compatible detectors. Experimental results indicate a dominant contribution of the isoscalar giant monopole resonance at this very forward angular range. It was found that the monopole contribution exhausts 79 − 11 + 12 % of the energy-weighted sum rule (EWSR), which agrees with measurements performed in normal kinematics. This opens up the opportunity to investigate the giant resonances in a large domain of unstable and exotic nuclei in the near future. It is a fundamental milestone towards new nuclear reaction studies with stored ion beams.

IsoscalarE0,E1,E2, andE3strength inMo94

Isoscalar giant resonances in $^{94}\mathrm{Mo}$ have been studied with inelastic scattering of 240 MeV \ensuremath{\alpha} particles at small angles including 0\ifmmode^\circ\else\textdegree\fi{}. All of the expected energy-weighted sum rule (EWSR) for the isoscalar $E0$ resonance was found (112%). A significant portion of the EWSR was found for the isoscalar $E1$ (83%), $E2$ (61%), and the high-energy octupole $E3$ (46%) resonances. The strength distributions are compared with the predictions from Hartree-Fock random-phase-approximation calculations with the KDE0v1 Skyrme-type interaction.

Investigation of the energy-averaged double transition density of isoscalar monopole excitations in medium-heavy mass spherical nuclei

The particle–hole dispersive optical model, developed recently, is applied to study properties of high-energy isoscalar monopole excitations in medium-heavy mass spherical nuclei. The energy-averaged strength functions of the isoscalar giant monopole resonance and its overtone in 208Pb are analyzed. In particular, we analyze the energy-averaged isoscalar monopole double transition density, the key quantity in the description of the hadron–nucleus inelastic scattering, and studied the validity of the factorization approximation using semi classical and microscopic one body transition densities, respectively, in calculating the cross sections for the excitation of isoscalar giant resonances by inelastic alpha scattering.

Electric Dipole States and Time Reversal Violation in Nuclei.

The nuclear Schiff moment is essential in the mechanism that induces a parity and time reversal violation in the atom. In this presentation we explore theoretically the properties and systematics of the isoscalar dipole in nuclei with the emphasis on the low-energy strength and the inverse energy weighted sum which determines the Schiff moment. We also study the influence of the isovector dipole strength distribution on the Schiff moment. The influence of a large neutron excess in nuclei is examined. The centroid energies of the isoscalar giant resonance (ISGDR) and the overtone of the isovector giant dipole resonance (OIVGDR) are given for a range of nuclei.