Isoscalar Giant Dipole Resonance Research Articles

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.

Particle-vibration coupling for giant resonances beyond the diagonal approximation

A self-consistent particle-vibration coupling (PVC) model without diagonal approximation is presented. The diagonal approximation, that neglects completely the interaction between the doorway states, has been removed by taking into account the interaction between the two particle-holes inside the doorway states. As applications, isoscalar giant monopole, dipole, and quadrupole resonances in 16O are investigated based on the use of Skyrme functionals. The diagonal approximation is found to clearly impact the strength distribution of the giant quadrupole resonance, and the description of the experimental data is improved without this approximation. The impact of the diagonal approximation is analyzed in detail, especially its effect on the eigenenergies and the induced coupling between neutron and proton particle-hole configurations. The latter is a direct and physically sound effect of the improvement on our formalism. The importance of using self-consistently the full effective interaction in the PVC vertex, and the effect of its renormalization via the subtraction method, are also discussed. For completeness, we also analyze the dependence of our results on the Skyrme parametrization.

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.

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 giant monopole, dipole, and quadrupole resonances inZr90,92andMo92

The isoscalar giant monopole, dipole, and quadrupole strength distributions have been deduced in $^{90, 92}$Zr, and $^{92}$Mo from "background-free" spectra of inelastic $\alpha$-particle scattering at a beam energy of 385 MeV at extremely forward angles, including 0$^{\circ}$. These strength distributions were extracted by a multipole-decomposition analysis based on the expected angular distributions of the respective multipoles. All these strength distributions for the three nuclei practically coincide with each other, affirming that giant resonances, being collective phenomena, are not influenced by nuclear shell structure near $A\sim$90, contrary to the claim in a recent measurement.

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.

Deformation effects on isoscalar giant resonances inMg24

Strength distributions for isoscalar giant resonances with multipolarity $L\ensuremath{\le}2$ have been determined in $^{24}\mathrm{Mg}$ from ``instrumental background-free'' inelastic scattering of 386-MeV $\ensuremath{\alpha}$ particles at extreme forward angles, including ${0}^{\ensuremath{\circ}}$. The isoscalar $E0, E1$, and $E2$ strengths are observed to be $57\ifmmode\pm\else\textpm\fi{}7%, 111.{1}_{\ensuremath{-}7.2}^{+10.9}%$, and $148.6\ifmmode\pm\else\textpm\fi{}7.3%$, respectively, of their energy-weighted sum rules in the excitation energy range of 6 to 35 MeV. The isoscalar giant monopole (ISGMR) and quadrupole (ISGQR) resonances exhibit a prominent $K$ splitting which is consistent with microscopic theory for a prolate-deformed ground state of $^{24}\mathrm{Mg}$. For the ISGQR it is due to splitting of the three $K$ components, whereas for the ISGMR it is due to its coupling to the $K=0$ component of the ISGQR. Deformation effects on the isoscalar giant dipole resonance are less pronounced, however.

Observation of isoscalar multipole strengths in exotic doubly-magic 56Ni in inelastic α scattering in inverse kinematics

The Isoscalar Giant Monopole Resonance (ISGMR) and the Isoscalar Giant Dipole Resonance (ISGDR) compression modes have been studied in the doubly-magic unstable nucleus 56Ni. They were measured by inelastic α-particle scattering in inverse kinematics at 50 MeV/u with the MAYA active target at the GANIL facility. The centroid of the ISGMR has been obtained at Ex=19.1±0.5 MeV. Evidence for the low-lying part of the ISGDR has been found at Ex=17.4±0.7 MeV. The strength distribution for the dipole mode shows similarity with the prediction from the Hartree–Fock (HF) based random-phase approximation (RPA) [1]. These measurements confirm inelastic α-particle scattering as a suitable probe for exciting the ISGMR and the ISGDR modes in radioactive isotopes in inverse kinematics.

Isoscalar and isovector dipole strength distributions in nuclei and the Schiff moment

It was pointed out that the isoscalar dipole strength distribution in nuclei contributes to the Schiff moment. The nuclear Schiff moment is essential in the mechanism that induces parity and time-reversal violations in the atom. In this paper, we explore, theoretically, the properties and systematics of the isoscalar dipole in nuclei with an 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 large neutron excess in exotic nuclei is examined. The centroid energies of the isoscalar giant dipole resonance and the overtone of the isovector giant dipole resonance are given for a wide range of nuclei.

Toroidal, compression, and vortical dipole strengths in 144-154Sm: Skyrme-RPA exploration of the deformation effect

A comparative analysis of toroidal, compressional and vortical dipole strengths in the spherical $^{144}$Sm and the deformed $^{154}$Sm is performed within the random-phase-approximation using a set of different Skyrme forces. Isoscalar (T=0), isovector (T=1), and electromagnetic excitation channels are considered. The role of the nuclear convection $j_{\text{con}}$ and magnetization $j_{\text{mag}}$ currents is inspected. It is shown that the deformation leads to an appreciable redistribution of the strengths and causes a spectacular deformation splitting (exceeding 5 MeV) of the isoscalar compressional mode. In $^{154}$Sm, the $\mu$=0 and $\mu$=1 branches of the mode form well separated resonances. When stepping from $^{144}$Sm to $^{154}$Sm, we observe an increase of the toroidal, compression and vortical contributions in the low-energy region (often called pygmy resonance). The strength in this region seems to be an overlap of various excitation modes. The energy centroids of the strengths depend significantly on the isoscalar effective mass $m_0$. Skyrme forces with a large $m_0$ (typically $m_0/m \approx 0.8 - 1$) seem to be more suitable for description of experimental data for the isoscalar giant dipole resonance.

The Nuclear Incompressibility and Isoscalar Giant Dipole Resonance in Relativistic Continuum Random Phase Approximation

The isoscalar giant dipole resonance (ISGDR) in nuclei is studied in the framework of a fully self-consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function technique. We employ different type interactions (NL1, NL3, NL3*, NL4, TM1, NLSH and PK1) corresponding to incompressibilities in the range 200–360 MeV. The results are discussed in comparison with the existing experimental data. It is found that the term can remove spurious components from the admixture of the center of mass state perfectly. The ISGDR distribution has two components, the lower-energy component and the higher-energy component. There is a large amount of very sharp peaks in the lower-energy region in RCRPA calculations. Only the higher-energy component is sensitive to the value of nuclear incompressibility employed in the calculations; the position of the lower-energy component is completely independent of the nuclear incompressibility Knm.

Charge-exchange and charge-conserving reactions on Mg, Ar, Zr, and Sn isotopes

We investigate charge-exchange reactions (CEXRs) and charge-conserving reactions (CCORs) on Mg, Ar, Zr, and Sn isotopes by comparing our theoretical results to relevant experimental data on stable nuclei. As for CEXRs, first, we discuss nuclear beta decay because it may give more convincing input data on the network calculations for successive capture reactions by protons and neutrons. Second, we address the importance of the Gamow Teller (GT) states that are low-lying excited states well known in the conventional nuclear physics while high-lying excited states still remain to be studied. The third topic, which is viable through the CCORs, is the symmetry energy associated with the equation of state of nuclear matter. By using the CCORs, we can study the isoscalar giant dipole resonance (ISGDR) and the pigmy dipole resonance (PDR). We discuss theoretical results regarding these CEXRs and CCORs on 26Mg, 40Ar, 90,92Zr, and 112∼124Sn and compare them with available experimental data. Our calculations are carried out by using the proton-neutron quasi-particle random phase approximation (pnQRPA), the QRPA, the deformed QRPA (DQRPA), the shell model and a hybrid model. Our results are shown to agree with the data available. These nuclear reactions considered in this report will complement capture reactions by protons and neutrons which are of vital importance for understanding the element abundances in the cosmos.

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.

Investigation of the Giant Monopole Resonance in the Cd and Pb Isotopes: The Asymmetry Term in Nuclear Incompressibility and the MEM Effect

The giant monopole resonance (GMR) has been investigated in the even-A Cd and Pb isotopes 112−124 Cd, and 204−208 Pb, with the aim of obtaining a confirmatory value for the asymmetry term in nuclear incompressibility, Kτ , and to test the Mutual Enhancement Magicity (MEM) effect in nuclear incompressibilities. The latter was advanced as a possible explanation of the puzzling softness of the Sn and Cd nuclei, as evidenced by their low GMR energies as compared to theoretical predictions. The GMR results in the Cd isotopes give a value Kτ = �490± 100 MeV, in close agreement with the value obtained previously from the Sn isotopes. Our results rule out the MEM effect as an explanation of the aforementioned softness observed for the Sn and Cd nuclei. The asymmetry term of nuclear incompressibility, Kτ , associated with the neutron-excess (NZ), is crucial in obtaining the radii of neutron stars in the equation of state (EOS) calculations. 1)-4) It has been suggested that the radius of a neutron star whose mass is between about 1.0 and 1.5 solar masses (M� )i s mostly determined by the density dependence of the symmetry-energy term. 5),6) In recent measurements on the giant monopole resonance (GMR) in the even- A Sn isotopes (A = 112 � 124), we had obtained an value for this term, Kτ = �550 ± 100 MeV. 7),8) This number is in agreement with the value Kτ = �500 +125100 MeV, obtained by Centelles et al. 9) from constraints put by neutron- skin data from anti-protonic atoms across the mass table; Kτ = �500 ± 50 MeV obtained by Sagawa et al. 10) by comparing our Sn GMR data with calculations using different Skyrme Hamiltonians and RMF Lagrangians; and, Kτ = �370 ± 120 MeV obtained from an analysis of the isotopic transport ratios in medium- energy heavy-ion reactions. 11) Combined with the value of K∞ = 240 ± 10 MeV extracted from data on GMR and the other compression-mode, the isoscalar giant dipole resonance (ISGDR), 12),13) this value for Kτ may provide a means of selecting the most appropriate of the interactions commonly used in nuclear structure and EOS calculations. To confirm the value of Kτ obtained from the GMR in the Sn isotopes, we have investigated the GMR in the another series of isotopes, viz. 106,110,112,114,116 Cd using inelastic scattering of 400-MeV α particles at extremely forward angles, including 0 ◦ . The measurements were performed at the Research Center for Nuclear Physics (RCNP) at Osaka University, Japan, using the Grand Raiden spectrometer. The experimental techniques and data analysis procedures were identical to those in the measurements described previously for the Sn isotopes. 7),8)

10.1007/s11496-008-2005-2

Accurate assessment of the value of the incompressibility coefficient, K ∞, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K ∞ as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei by employing the microscopic theory based on the Random Phase Approximation (RPA). The importance of full self-consistent calculations is emphasized. In recent years, a comparision between RPA calculations based on either non-relativistic effective interactions or relativistic Lagrangians has been pursued in great detail. It has been pointed out that these two types of models embed different ansatz for the density dependence of the symmetry energy. This fact has consequences on the extraction of the nuclear incompressibility, as it is discussed. The comparison with other ways of extracting K ∞ from experimental data is highlighted.

Proton decay from the isoscalar giant dipole resonance inNi58

Proton decay from the $3\ensuremath{\hbar}\ensuremath{\omega}$ isoscalar giant dipole resonance (ISGDR) in $^{58}\mathrm{Ni}$ has been measured using the ($\ensuremath{\alpha},{\ensuremath{\alpha}}^{'}p$) reaction at a bombarding energy of 386 MeV to investigate its decay properties. We have extracted the ISGDR strength under the coincidence condition between inelastically scattered $\ensuremath{\alpha}$ particles at forward angles and decay protons emitted at backward angles. Branching ratios for proton decay to low-lying states of $^{57}\mathrm{Co}$ have been determined, and the results compared with predictions of recent continuum-RPA calculations. The final-state spectra of protons decaying to the low-lying states in $^{57}\mathrm{Co}$ were analyzed for a more detailed understanding of the structure of the ISGDR. It is found that there are differences in the structure of the ISGDR as a function of excitation energy.

Direct proton decay of the isoscalar giant dipole resonance in 208Pb

The excitation and subsequent proton decay of the isoscalar giant dipole resonance (ISGDR) in 208Pb have been investigated via the Pb208(α,α′p)Tl207 reaction at 400 MeV. Excitation of the ISGDR has been identified by the difference-of-spectra method. The enhancement of the ISGDR strength at high excitation energies observed in the multipole-decomposition-analysis of the singles Pb208(α,α′) spectra is not present in the excitation energy spectrum obtained in coincidence measurement. The partial branching ratios for direct proton decay of ISGDR to low-lying states of 207Tl have been determined and the results are compared with predictions of continuum random-phase-approximation (CRPA) calculations.

Giant Resonance Overtones: Compression Modes of the Nucleus

Giant resonances are high-frequency collective excitations of atomic nuclei, the occurrence of which is a typical phenomenon in many-body quantum systems confined in a potential well [1]. In hydrodynamic models, giant resonances can be described as density and shape oscillations around the ground-state density distribution and shape. Such collective excitations of a nucleus may, similarly to other media with given boundary conditions, exhibit standing wave oscillations with a discrete series of frequencies as solutions of the applied wave equations. In this simple picture, most of the giant resonances studied extensively so far can be associated with the lowest energy, leading-order solutions (main tone). Giant resonances corresponding to higher-order solutions (overtones) have not been identified, except for the special cases of the isoscalar giant monopole (ISGMR) and isoscalar giant dipole (ISGDR) resonances, where excitation of the main-tone components is physically forbidden. Strong evidence for the overtone mode of the isoscalar giant quadrupole resonance, which is denoted as ISGQR2, has been found in our experiments [2,3], which is highly supported by predictions of recent RPA calculations [4]. Moreover, the microscopic structures of high-energy isoscalar giant resonances have been studied through measurements of direct particle decay, and in the case of the ISGDR for the first time in our measurements of such branching ratios.

The compression modes in atomic nuclei and their relevance for the nuclear equation of state

Accurate assessment of the value of the incompressibility coefficient, K∞, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K∞ as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei by employing the microscopic theory based on the Random Phase Approximation (RPA). The importance of full self-consistent calculations is emphasized. In recent years, a comparision between RPA calculations based on either non-relativistic effective interactions or relativistic Lagrangians has been pursued in great detail. It has been pointed out that these two types of models embed different ansatz for the density dependence of the symmetry energy. This fact has consequences on the extraction of the nuclear incompressibility, as it is discussed. The comparison with other ways of extracting K∞ from experimental data is highlighted.

Direct neutron decay of the isoscalar giant dipole resonance

The direct and statistical neutron decay of the isoscalar giant dipole resonance has been studied in 90Zr, 116Sn, and 208Pb using the (α, α’ n) reaction at a bombarding energy of 200 MeV. The spectra of fast decay neutrons populating valence hole states of the Z, N − 1 nuclei were analyzed, and estimates for the branching ratios were determined. The observation of the nucleon-direct-decay channels helped to select giant-resonance strengths and suppress the underlying background and continuum, which led to an indication of the existence of a new mode with L = 2 character, presumably the overtone of the isoscalar giant quadrupole resonance.