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![The centroid of the Gaussian fit to the high energy peak in the ISGDR distributions for each of the Zr (this work) and Mo [48] isotopes is plotted vs mass number (A) in the lower panel (a), while the strength in the upper peak is plotted in the upper panel (b). The error bars indicate the uncertainty obtained using the errors shown in Figs. 5, 6, 7.](profile/Yiu-Wing-Lui/publication/283959650/figure/fig12/AS:317672190431257@1452750360869/The-centroid-of-the-Gaussian-fit-to-the-high-energy-peak-in-the-ISGDR-distributions-for.png)
The centroid of the Gaussian fit to the high energy peak in the ISGDR distributions for each of the Zr (this work) and Mo [48] isotopes is plotted vs mass number (A) in the lower panel (a), while the strength in the upper peak is plotted in the upper panel (b). The error bars indicate the uncertainty obtained using the errors shown in Figs. 5, 6, 7.
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Isoscalar giant resonances in Zr90,92,94 have been studied with inelastic scattering of 240 MeV α particles at small angles including 0. A significant fraction of the energy-weighted sum rule (EWSR) was found for isoscalar E0 (106%,103%,106%), E1 (64%,53%,96%), E2 (92%,93%,67%) and high energy octupole E3 (59%,69%,58%) resonances in Zr90,92,94 resp...
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Citations
... IS0 strength distributions obtained with correction factors derived from Refs. [19] and [72] are shown in the top and third rows, respectively. The two-dimensional plots of the wavelet coefficients are displayed in the second and fourth panels on the right-hand side of Fig. 4. The intermittent appearance of blue (red) regions indicating negative (positive) values, result from the oscillatory structure of the mother wavelet [Eq. ...
Background: Over the past two decades high energy-resolution inelastic proton scattering studies were used to gain an understanding of the origin of fine structure observed in the isoscalar giant quadrupole resonance (ISGQR) and the isovector giant dipole resonance (IVGDR). Recently, the isoscalar giant monopole resonance (ISGMR) in Ni58, Zr90, Sn120, and Pb208 was studied at the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS) by means of inelastic α-particle scattering at very forward scattering angles (including 0∘). The good energy resolution of the measurement revealed significant fine structure of the ISGMR.
... The E3 response is split into two branches, the 1ħω component has been referred to as the low energy octupole resonance, which is firstly observe by Moss et al. in 1976 utilizing inelastic scattering of alpha particles, while the higher (3ħω) component is referred to as the high energy octupole resonance [7]. ...
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.
... In 208 Pb, the ISGMR was measured in the Research Center for Nuclear Physics (RCNP) by means of inelastic αscattering [6,7] and inelastic deuteron scattering [8], and in Texas A&M University (TAMU) by means of inelastic αscattering [9,10]. These measurements, together with those performed in 90 Zr [7,11,12], hint to a value K ∞ = 240 ± 20 MeV for the nuclear incompressibility [3]. However, it was found that in even-even stable tin isotopes, 112−124 Sn, the IS-GMR centroid energy is overestimated (by about 1 MeV) by the same models which reproduce the ISGMR centroid energy well in 208 Pb [13,14]. ...
"Why is the EoS for tin so soft?" is a longstanding question, which prevents us from determining the nuclear incompressibility $K_\infty$ accurately. To solve this puzzle, a fully self-consistent quasiparticle random phase approximation (QRPA) plus quasiparticle-vibration coupling (QPVC) approach based on Skyrme-Hartree-Fock-Bogoliubov is developed. We show that the many-body correlations introduced by QPVC, which shift the ISGMR energy in Sn isotopes by about 0.4 MeV more than the energy in $^{208}$Pb, play a crucial role in providing a unified description of the ISGMR 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 $K_\infty=$ 226 MeV and 229 MeV, respectively, at mean field level.
... So far, the ISGQR has been measured systematically over the nuclear mass range by using inelastic electron-* sujun3@mail.sysu.edu.cn scattering and light-ion-scattering experiments [21][22][23][24][25][26][27][28][29][30][31]. Because of the difficulty to produce targets of radioactivity nuclei, those measurements are limited to stable nuclei. ...
... Experimental data are taken from Refs. [21][22][23][24][25][26][27][28][29][30][31][32]. The data are divided into two groups: Group O includes those measured before the year 2000 and is shown as solid circles. ...
Background: Previous theoretical work has found that the effective mass of the nucleon influences the excitation energy of the isoscalar giant quadrupole resonance (ISGQR).
... In the cases of 94,96 Mo, although a second peak was included in the modeling of the data, the extracted EWSR for the low-energy peak is Fig. 1.5 from Refs. [16,62,122,123] (black and green triangles), juxtaposed with the finite nuclear incompressibilities K A (blue squares) measured for 90,92 Zr, 92 Mo [41,42,50] and 94−100 Mo within these works. Shown clearly is a consistent scaling-model nuclear incompressibility for the nuclei in this mass region. ...
Giant resonances are collective nuclear vibrations which provide a unique laboratory setting to probe the bulk properties of the nuclear force. One of the isoscalar compressional modes -- the isoscalar giant monopole resonance (ISGMR) -- is useful in constraining the equation of state (EoS) of nuclear matter. For example, the nuclear incompressibility, $K_\infty$, is a fundamental quantity in the EoS and is directly correlated with the energies of the ISGMR in finite nuclei. Previous work has shown that interactions with $K_\infty$ which reproduce the energies of the ISGMR in $^{208}$Pb and $^{90}$Zr well, overestimate those of the tin and cadmium nuclei. To further investigate where this "softness" appears in moving away from the doubly-closed nucleus $^{90}$Zr, and how this effect develops, the first portion of this thesis consists of measurements of the ISGMR in the molybdenum isotopes. Comparison of the ISGMR strengths with Random Phase Approximation calculations shows that these nuclei have ISGMR energies which are overestimated to a similar degree as seen in the tin and cadmium nuclei, while the strength of $^{208}$Pb is precisely reproduced. This suggests clearly that the molybdenum nuclei exhibit the same open-shell softness which has been documented previously. The ISGMR in isotopes encompassing a broad range of proton-neutron asymmetries constrains the dependence of the nuclear incompressibility on the isospin asymmetry, as quantified by the asymmetry term, $K_\tau$. To reconcile previously-published and highly concerning conclusions that $K_\tau = + 582$ MeV, the second portion of this thesis is focused upon independently studying this claim. A simultaneous measurement of the ISGMR in $^{40,42,44,48}$Ca has excluded the possibility of a positive value for $K_\tau$, and found consistency with previous data, placing $K_\tau$ at $-510 \pm 115$ MeV.
... The predictive power of the DD-PCX interaction is also tested on the nuclear excitations of nuclei. Table IV shows the constrained ISGMR energies for 90 Zr, 120 Sn, 208 Pb calculated using various relativistic interactions, and compared to the experimental results [34,35,[42][43][44]. In this part, we should mention that the DD-ME2 calculations are performed using the finite-range Gogny interaction D1S in the particle-particle TABLE III. ...
We introduce a new relativistic energy density functional constrained by the ground state properties of atomic nuclei along with the isoscalar giant monopole resonance energy and dipole polarizability in Pb208. A unified framework of the relativistic Hartree-Bogoliubov model and random phase approximation based on the relativistic density-dependent point coupling interaction is established in order to determine the DD-PCX parametrization by χ2 minimization. This procedure is supplemented with the covariance analysis in order to estimate statistical uncertainties in the model parameters and observables. The effective interaction DD-PCX accurately describes the nuclear ground state properties including the neutron-skin thickness, as well as the isoscalar giant monopole resonance excitation energies and dipole polarizabilities. The implementation of the experimental data on nuclear excitations allows constraining the symmetry energy close to the saturation density, and the incompressibility of nuclear matter by using genuine observables on finite nuclei in the χ2 minimization protocol, rather than using pseudo-observables on the nuclear matter, or by relying on the ground state properties only, as it has been customary in the previous studies.
... MeV, Ŵ γ = 5.0 MeV, and σ γ = 2mb [40]. The current result is compatible with the fraction of GQR in 94 Zr, which is 67(11)% obtained in the scattering measurement [41]. The theoretical calculations with Cb-TDHFB and HFB+QRPA are shown by the red dashed and green dot-dashed curves in Fig. 4(a). ...
Coulomb breakup reactions of 93,94 Zr have been studied in inverse kinematics at incident beam energies of about 200 MeV/nucleon in order to evaluate neutron capture reaction methods. The 93 Zr(n,γ) 94 Zr reaction is particularly important as a candidate nuclear transmutation reaction for the long-lived fission product 93 Zr in nuclear power plants. One- and two-neutron removal cross sections on Pb and C targets were measured to deduce the inclusive Coulomb breakup cross sections, 375 ± 29 (stat.) ± 30 (syst.) and 403 ± 26 (stat.) ± 31 (syst.) mb for 93 Zr and 94 Zr, respectively. The results are compared with estimates using the standard Lorentzian model and microscopic calculations. The results reveal a possible contribution of the pygmy dipole resonance or giant quadrupole resonance in the Coulomb breakup reactions of 94 Zr.
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.
