The isoscalar giant monopole resonance (ISGMR) in Cd, Sn and Pb isotopes has been studied within the self-consistent Skyrme Hartree-Fock+BCS and quasi-particle random phase approximation (QRPA). Three Skyrme parameter sets are used in the calculations, i.e., SLy5, SkM* and SkP, since they are characterized by different values of the compression modulus in symmetric nuclear matter, namely K=230, 217, and 202 MeV, respectively. We also investigate the effect of different types of pairing forces on the ISGMR in Cd, Sn and Pb isotopes. The calculated peak energies and the strength distributions of ISGMR are compared with available experimental data. We find that SkP fails completely to describe the ISGMR strength distribution for all isotopes due to its low value of the nuclear matter incompressibility, namely K=202 MeV. On the other hand, the SLy5 parameter set, supplemented by an appropriate pairing interaction, gives a reasonable description of the ISGMR in Cd and Pb isotopes. A better description of ISGMR in Sn isotopes is achieved by the SkM* interaction, that has a somewhat softer value of the nuclear incompressibility.
A semi-microscopic approach, based on the continuum-random-phase Approximation (CRPA) method, is applied to describe the main properties (strength function, transition density, direct-nucleon-decay branching ratios) of the overtone of the isoscalar giant monopole resonance. Results of the calculation are presented for 208Pb in comparison with those obtained for the isoscalar monopole and dipole giant resonances within the same approach.
The particle-hole dispersive optical model, developed recently, is applied to describe properties of high-energy isoscalar monopole excitations in medium-heavy mass spherical nuclei. We consider, in particular, the double transition density averaged over the energy of the isoscalar monopole excitations in $^{208}$Pb in a wide energy interval, which includes the isoscalar giant monopole resonance and its overtone. The energy-averaged strength functions of these resonances are also analyzed. Possibilities for using the mentioned transition density to description of inelastic $α$-scattering are d…
The isoscalar giant resonances for $^{86}\textrm{Ge}$ 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 triaxially deformed nucleus $^{86}\textrm{Ge}$, 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 s…
In this contribution we review and clarify the arguments which might allow the interpretation of the isoscalar monopole resonance of $^4$He as a collective breathing mode.
We investigate structure of the excited $0^+$ states of $^{24}$Mg populated by isoscalar monopole transition from the ground state on the basis of antisymmetrized molecular dynamics calculation with Gogny D1S interaction. The calculated isoscalar monopole strength function shows reasonable agreement with experiment and is consistent with other theoretical calculation. The structure of the excited $0^+$ states with pronounced isoscalar monopole transitions are analyzed. It is found that the $0^+_2$, $0^+_3$ and $0^+_5$ states have mixed nature of mean-field and cluster, and that the $0^+_8$ sta…
The strength distributions of the isoscalar giant monopole resonance have been calculated in $^{16}$O, $^{40}$Ca, $^{90}$Zr, $^{112-124}$Sn, $^{144}$Sm, and $^{208}$Pb nuclei within the self-consistent random phase approximation and its extensions which include pairing correlations and quasiparticle-phonon coupling. The results are compared with the available experimental data. The problem of the nuclear matter incompressibility is discussed.
We motivate and summarise some recent results in the application of formally exact boundary conditions in nuclear time-dependent Hartree-Fock calculations, making use of Laplace transformations to calculate the values of the wave functions at the boundaries. We have realised the method in the case of giant monopole resonances of spherically-symmetric nuclei, and present strength functions of O-16 and Ca-40 using a simplified version of the Skyrme force, showing that no artefacts from discretisation occur as contaminants
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 ar…
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…
We study the isoscalar giant monopole resonance for drip-lines and super heavy nuclei in the frame work of a relativistic mean field theory with scaling approach. The well known extended Thomas-Fermi approximation in the non-linear $σ$-$ω$ model is used to estimate the giant monopole excitation energy for some selected light spherical nuclei starting from the region of proton to neutron drip-lines. The application is extended to super heavy region for Z=114 and 120, which are predicted by several models as the next proton magic number beyond Z=82. We compared the excitation energy obtained by …
Using the density-dependent Hartree-Fock approximation and Skyrme forces together with the scaling method and constrained Hartree-Fock calculations, we obtain the average energies of the isoscalar giant monopole resonance. The calculations are done along several isotopic chains from the proton to the neutron drip lines. It is found that while approaching the neutron drip line, the scaled and the constrained energies decrease and the resonance width increases. Similar but smaller effects arise near the proton drip line, although only for the lighter isotopic chains. A qualitatively good agreeme…
The isoscalar giant monopole resonance (ISGMR) in Sn isotopes and other nuclei is investigated in the framework of the isospin-dependent quantum molecular dynamics (IQMD) model. The spectrum of GMR is calculated by taking the root-mean-square (RMS) radius of a nucleus as its monopole moment. The peak energy, the full width at half maximum (FWHM), and the strength of GMR extracted by a Gaussian fit to the spectrum have been studied. The GMR peak energies for Sn isotopes from the calculations using a mass-number dependent Gaussian wave-packet width $σ_r$ for nucleons are found to be overestimate…
To identify the 3alpha BEC state with the excess neutron, we have investigated the monopole strength of the excited states of 13C by using the theoretical framework of the real-time evolution method. The calculations have revealed several candidates of the Hoyle-analog states in a highly excited region.
A fully consistent relativistic RPA calculation is performed for the monopole and dipole compression modes in nuclei. The emphasis is put on the effects of Dirac sea states which are generally neglected in relativistic RPA calculations. It is found that these effects can be quite important for the isoscalar monopole mode. The main contributions from the pairs of Fermi to Dirac sea states are through the exchange of the scalar meson, while the vector mesons play a negligible role. Numerical results of relativistic RPA are checked with the constrained relativistic mean field model in the monopol…
We study theoretically the electric dipole transitions of even Ni isotopes at low energies, using the self-consistent quasi-particle random-phase approximation (RPA) with the D1S Gogny interaction and a continuum-RPA model with the SLy4 Skyrme force. We analyze isoscalar states, isovector states, and the dipole polarizability. We define a reference value for the polarizability, to remove a trivial dependence on the mass number. We compare our results with data and other calculations, with a focus on collective states, shell effects, and threshold transitions. Our results support the presence o…
We calculate the transition density for the overtone of the isosclar giant monopole resonance (ISGMR) from the response to an appropriate external field $\hat{f}_ξ(r)$ obtained using the seemiclassical fluid dynamic approximation and the Hartree-Fock (HF) based random phase approximation (RPA). We determine the mixing parameter $ξ$ by maximizing the ratio of the energy weighted sum for the overtone mode to the total energy weighted sum rule and derive a simple expression for the microscopic transition density associated with the overtone mode. This macroscopic transition density agrees well wi…
Very recent inelastic $α$-scattering data on the isoscalar monopole and dipole strength distributions in $^{56}$Fe, $^{58}$Ni, and $^{60}$Ni are analyzed in the relativistic quasiparticle random-phase approximation (RQRPA) with the DD-ME2 effective nuclear interaction (nuclear matter compression modulus K$_{nm}= 251$ MeV). In all three nuclei the calculation nicely reproduces the observed asymmetric shapes of the monopole strength, and the bimodal structure of the dipole strength distributions. The calculated centroid and mean energies are in very good qualitative agreement with the experiment…
"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 isoscaler giant monopole resonances (ISGMR) are computed using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory (Cb-TDHFB) with five kinds of Skyrme parameter sets (SGII, SkM$^*$, SLy4, SkT3 and SkI3). To extract the nuclear matter property from finite system, ISGMRs of $N$=$Z$ ($Z$=20 - 50), isobar even-even nuclide for $A$=100, 132 and Sn isotopes are analysed systematically. The magnitude relation of nuclear incompressibility-parameter ($K_\infty$) among Skyrme parameter sets, can be corresponded to the peak positions of GMR in spherical isotopes over $A$=80. The parame…
A numerical method to integrate the time-dependent Hartree-Fock Bogoliubov (TDHFB) equations with Gogny interaction is proposed. The feasibility of the TDHFB code is illustrated by the conservation of the energy, particle numbers, and center-of-mass in the small amplitude vibrations of oxygen 20. The TDHFB code is applied to the isoscalar quadrupole and/or isovector dipole vibrations in the linear (small amplitude) region in oxygen isotopes (masses A = 18,20,22 and 24), titanium isotopes (A = 44,50,52 and 54), neon isotope (A = 26), and magnesium isotopes (A = 24 and 34). The isoscalar quadrup…
The extraction of the nuclear incompressibility from the isoscalar giant monopole resonance (GMR) measurements is analysed. Both pairing and mutually enhanced magicity (MEM) effects play a role in the shift of the GMR energy between the doubly closed shell $^{208}$Pb nucleus and other Pb isotopes. Pairing effects are microscopically predicted whereas the MEM effect is phenomenologically evaluated. Accurate measurements of the GMR in open-shell Pb isotopes are called for.
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 to us to describe a gross s…
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 $K_\infty$ and the coupling between IS0 and isoscalar quadrupole (IS2) strength. Objective: This study aims to investigate the two-peaked structure …
Monopole shift in the proton states in odd neutron rich F isotopes has been studied with neutron number changing from N = 10 to 20 for three different interactions. The variation of monopole shift point out towards appearance of shell closure at N = 14 and N = 16 and its disappearance at N = 20. Low lying states of odd F isotopes have also been calculated in the limited configuration space of {\it sd} shells for these interactions.
The recent RCNP $(α, α')$ data on the Isoscalar Giant Monopole Resonance (ISGMR) and Isoscalar Giant Quadrupole Resonance (ISGQR) in $^{92,94,96,98,100}$Mo are analyzed within a fully self-consistent Quasiparticle Random Phase Approximation (QRPA) approach with Skyrme interactions, in which pairing correlations and possible axial deformations are taken into account. The Skyrme sets SkM*, SLy6, SVbas and SkP$^δ$, that explore a diversity of nuclear matter properties, are used. We discuss the connection between the line shape of the monopole strength ISGMR and the deformation-induced coupling be…
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
We present an ab-initio study of the isoscalar monopole excitations of 4He using different realistic nuclear interactions, including modern effective field theory potentials. In particular we concentrate on the transition form factor $F_{\cal M}$ to the narrow $0^+$ resonance close to threshold. F_M exhibits a strong potential model dependence, and can serve as a kind of prism to distinguish among different nuclear force models. Comparing to the measurements obtained from inelastic electron scattering off 4He, one finds that the state-of-the-art theoretical transition form factors are at varia…
The correspondence between the isoscalar monopole (IS0) transition strengths and $α$ inelastic cross sections, the $B({\rm IS0})$-$(α,α')$ correspondence, is investigated for $^{24}$Mg($α,α'$) at 130 and 386 MeV. We adopt a microscopic coupled-channel reaction framework to link structural inputs, diagonal and transition densities, for $^{24}$Mg obtained with antisymmetrized molecular dynamics to the ($α,α'$) cross sections. We aim at clarifying how the $B({\rm IS0})$-$(α,α')$ correspondence is affected by the nuclear distortion, the in-medium modification to the nucleon-nucleon effective inter…
The longstanding problem of characterization of the $0^+_2$ states in Gd isotopes is revisited by adopting the Nilsson$+$BCS mean field and the random-phase approximation. The interband electric quadrupole transition strengths varying almost two orders of magnitude are nicely reproduced at the same time as other observables. These results indicate that the $0^+_2$ states, in particular, those in lighter isotopes are well described as $β$ vibrations excited on top of deformed ground states without recourse to the shape-coexistence picture.
We derive analytical expressions for the excitation energy of the isoscalar giant monopole and quadrupole resonances in finite nuclei, by using the scaling method and the extended Thomas-Fermi approach to relativistic mean field theory. We study the ability of several non-linear sigma-omega parameter sets of common use in reproducing the experimental data. For monopole oscillations the calculations agree better with experiment when the nuclear matter incompressibility of the relativistic interaction lies in the range 220-260 MeV. The breathing-mode energies of the scaling method compare satisf…
The strong deformation splitting of the isoscalar giant monopole resonance (ISGMR), recently observed in ($α,α'$) reaction in prolate $^{24}$Mg, is analyzed in the framework of the Skyrme quasiparticle random-phase-approximation (QRPA) approach with the Skyrme forces SkM*, SVbas and SkP$^δ$. The calculations with these forces give close results and confirm that the low-energy E0-peak is caused by the deformation-induced coupling of ISGMR with the K=0 branch of the isoscalar giant quadrupole resonance.
[Background] Various cluster states of astrophysical interest are expected to exist in the excited states of $^{28}{\rm Si}$. However, they have not been identified firmly, because of the experimental and theoretical difficulties. [Purpose] To establish the $^{24}$Mg+$α$, $^{16}$O+$^{12}$C and $^{20}$Ne+2$α$ cluster bands, we theoretically search for the negative-parity cluster bands that are paired with the positive-parity bands to constitute the inversion doublets. We also offer the isoscalar monopole and dipole transitions as a promising probe for the clustering. We numerically show that th…
Isoscalar (IS) monopole and dipole excitations in $^{16}$O were investigated by the method of shifted basis antisymmetrized molecular dynamics combined with the generator coordinate method. Significant strengths of the IS monopole and dipole transitions were obtained in the low-energy region below the giant resonances. In addition to the compressive mode, which mainly contributes to the high-energy strengths for the IS dipole giant resonance, we obtained a variety of low-energy dipole modes such as the vortical dipole mode in the $1^-_1$ state of the vibrating tetrahedral $4α$ and the $^{12}$C…
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 $α$-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 influence…
Isoscalar monopole strength function in $^{16}$O up to $E_{x}\simeq40$ MeV is discussed. We found that the fine structures at the low energy region up to $E_{x} \simeq 16$ MeV in the experimental monopole strength function obtained by the $^{16}$O$(α,α^{\prime})$ reaction can be rather satisfactorily reproduced within the framework of the $4α$ cluster model, while the gross three bump structures observed at the higher energy region ($16 \lesssim E_{x} \lesssim 40$ MeV) look likely to be approximately reconciled by the mean-field calculations such as RPA and QRPA. In this paper, it is emphasize…
The isoscalar monopole(ISM) and dipole(ISD) excitations in $^{12}$C are theoretically investigated with the shifted antisymmetrized molecular dynamics(AMD) plus $3α$-cluster generator coordinate method(GCM). The small amplitude vibration modes are described by coherent one-particle one-hole excitations expressed by small shift of single-nucleon Gaussian wave functions within the AMD framework, whereas the large amplitude cluster modes are incorporated by superposing $3α$-cluster wave functions in the GCM. The coupling of the excitations in the intrinsic frame with the rotation and parity trans…
The decay of the Isoscalar Giant Monopole Resonance (ISGMR) in nuclei is studied by means of a nonlinear classical model consisting of several noninteracting nucleons (particles) moving in a potential well with an oscillating nuclear surface (wall). The motion of the nuclear surface is described by means of a collective variable which appears explicitly in the Hamiltonian as an additional degree of freedom. The total energy of the system is therefore conserved. Although the particles do not directly interact with each other, their motions are indirectly coupled by means of their interaction wi…
The properties of the alpha+28Si and 16O+16O molecular states which are embedded in the excited states of 32S and can have an impact on the stellar reactions are investigated using the antisymmetrized molecular dynamics. From the analysis of the cluster spectroscopic factors, the candidates of alpha+28Si and 16O+16O molecular states are identified close to and above the cluster threshold energies. The calculated properties of the alpha+28Si molecular states are consistent with those reported by the alpha+28Siresonant scattering experiments. On the other hand, the 16O+16O molecular state, which…
The RPA monopole strength as well as the unperturbed particle-hole excitation strength is studied, in which the strength in the continuum is properly treated without discretizing unbound particle spectra. The model is the sef-consistent Hartree-Fock calculation and the RPA Green's function method with Skyrme interactions. Numerical examples are the Ni-isotopes, especially $^{68}_{28}$Ni$_{40}$, in which an experimental observation of low-lying socalled "pigmy resonance" with an appreciable amount of monopole strength at 12.9 $\pm$ 1.0 MeV was recently reported. In the present study it is concl…
We analyze the relation between isoscalar toroidal modes and so-called pygmy dipole resonance (PDR) which both appear in the same region of low-energy dipole excitations. To this end, we use a theoretical description within the fully self-consistent Skyrme quasiparticle random-phase approximation (QRPA). Test cases are spherical nuclei $^{40,48}$Ca, $^{58,72}$Ni, $^{90,100}$Zr, and $^{100,120,132}$Sn which cover four different elements and for each element at least two isotopes with different neutron excess, one small and another large. The structure of the modes is investigated in terms of st…
A self-consistent Quasiparticle-Random-Phase-Approximation (QRPA) model which employs the canonical Hartree-Fock-Bogoliubov (HFB) basis and an energy-density functional with a Skyrme mean field part and a density-dependent pairing, is used to study the monopole collective excitations of spherical even-even nuclei. The influence of the spurious state on the strength function of the isoscalar monopole excitations is clearly assessed. We compare the effect of different kinds of pairing forces (volume pairing, surface pairing and mixed pairing) on the monopole excitation strength function. The ene…
We study microscopic structures of monopole pair vibrational modes and associated two-neutron transfer amplitudes in neutron-rich Sn isotopes by means of the linear response formalism of the quasiparticle random phase approximation(QRPA). For this purpose we introduce a method to decompose the transfer amplitudes with respect to two-quasiparticle components of the QRPA eigen mode. It is found that pair-addition ibrational modes in neutron-rich $^{132-140}$Sn and the pair rotational modes in $^{142-150}$Sn are commonly characterized by coherent contributions of quasaiparticle states having high…
We present results of microscopic calculations of the strength function, S(E), and alpha-particle excitation cross sections sigma(E) for the isoscalar giant dipole resonance (ISGDR). An accurate and a general method to eliminate the contributions of spurious state mixing is presented and used in the calculations. Our results provide a resolution to the long standing problem that the nuclear matter incompressibility coefficient, K, deduced from sigma(E) data for the ISGDR is significantly smaller than that deduced from data for the isoscalar giant monopole resonance (ISGMR).
We study boron, carbon, nitrogen and oxygen isotopes with a newly constructed shell-model Hamiltonian developed from monopole-based-universal interaction ($V_{MU}$). The present Hamiltonian can reproduce well the ground-state energies, energy levels, electric quadrupole properties and spin properties of these nuclei in full psd model space including $(0-3)\hbarω$ excitations. Especially, it correctly describes the drip lines of carbon and oxygen isotopes and the spins of the ground states of $^{10}$B and $^{18}$N while some former interactions such as WBP and WBT fail. We point out that the in…
We have calculated the strength distributions of the giant monopole resonance in the even-A tin isotopes (A = 112-124) which were recently measured in inelastic $α$-scattering. The calculations were performed within two microscopic models: the quasiparticle random phase approximation (QRPA) and the quasiparticle time blocking approximation which is an extension of the QRPA including quasiparticle-phonon coupling. We used a self-consistent calculational scheme based on the HF+BCS approximation. The single-particle continuum was exactly included on the RPA level. The self-consistent mean field a…
For the recently developed particle-hole dispersive optical model, weak violations of unitarity due to a phenomenological description of the spreading effect are considered. Methods for unitarity restoration are proposed and implemented for the 208Pb nucleus in the description of the energy-averaged isoscalar monopole double transition density and strength functions in a wide excitation energy interval that includes the isoscalar giant monopole resonance and its overtone. To illustrate abilities of the model, direct neutron decay of the mentioned giant resonance is also considered.
Nuclei in the $sd$-shell demonstrate a remarkable interplay of cluster and mean-field phenomena. The $N=Z$ nuclei, such as $^{24}$Mg and $^{28}$Si, have been the focus of the theoretical study of both these phenomena in the past. The cluster and vortical mean-field phenomena can be probed by excitation of isoscalar monopole and dipole states in scattering of isoscalar particles such as deuterons or $α$ particles. Inelastically scattered $α$ particles were momentum-analysed in the K600 magnetic spectrometer at iThemba LABS, Cape Town, South Africa. The scattered particles were detected in two m…
We study the couplings between collective vibrations such as the isovector giant dipole and isoscalar giant quadrupole resonances in tin isotopes in the framework of the time-dependent Hartree-Fock theory with a Skyrme energy density functional. These couplings are a source of anharmonicity in the multiphonon spectrum. In particular, the residual interaction is known to couple the isovector giant dipole resonance with the isoscalar giant quadrupole resonance built on top of it, inducing a nonlinear evolution of the quadrupole moment after a dipole boost. This coupling also affects the dipole m…
A semi-microscopic approach based on both the continum-random-phase-approximation (CRPA) method and a phenomenological treatment of the spreading effect is extended and applied to describe the main properties (particle-hole strength distribution, energy-dependent transition density, partial direct-nucleon-decay branching ratios) of the isoscalar giant dipole, second monopole, and second quadrupole resonances. Abilities of the approach are checked by description of gross properties of the main-tone resonances. Calculation results obtained for the resonances in a few singly- and doubly-closed-sh…
We perform Time Dependent Hartree-Fock (TDHF) calculations to investigate the small amplitude dipole response of selected neutron-rich nuclei and Sn isotopes. A detailed comparison with the dipole strength predicted by Random-Phase Approximation (RPA) calculations is presented for the first time. TDHF results are also confronted to Vlasov calculations, to explore up to which extent a semi-classical picture can explain the properties of the nuclear response. The focus is on the low-energy response, below the Giant Dipole Resonance region, where different modes of non negligible strength are ide…
Low-energy strength is predicted for the isoscalar monopole response of neutron-rich Ni isotopes, in calculations performed using the microscopic Skyrme HF+RPA and relativistic RHB+RQRPA models. Both models, although based on different energy density functionals, predict the occurrence of pronounced monopole states in the energy region between 10 MeV and 15 MeV, well separated from the isoscalar GMR. The analysis of transition densities and corresponding particle-hole configurations shows that these states represent almost pure neutron single hole-particle excitations. Even though their locati…
The isoscalar giant monopole resonance (GMR) in spherical nuclei $^{100-132}$Sn, $^{144}$Sm, and $^{208}$Pb is investigated within the Skyrme random-phase-approximation (RPA) for a variety of Skyrme forces and different pairing options. The calculated GMR strength functions are directly compared to the available experimental distributions. It is shown that, in accordance to results of other groups, description of GMR in Sn and heavier Sm/Pb nuclei needs different values of the nuclear incompressibilty, $K \approx$ 200 or 230 MeV, respectively. Thus none from the used Skyrme forces is able to d…
We present recent investigations on dipole and quadrupole excitations in spherical skin nuclei, particular exploring their connection to the thickness of the neutron skin. Our theoretical method relies on density functional theory, which provides us with a proper link between nuclear many-body theory of the nuclear ground state and its phenomenological description. For the calculation of the nuclear excited states we apply QPM theory. A new quadrupole mode related to pygmy quadrupole resonance (PQR) in tin isotopes is suggested.
We investigate the roles of deformation on the giant monopole resonance (GMR), particularly the mixing of the giant quadrupole resonance (GQR) and the effects of the neutron excess in the well-deformed nuclei around $^{110}$Zr and in the drip-line nuclei around $^{140}$Zr by means of the deformed quasiparticle-random-phase-approximation employing the Skyrme and the local pairing energy-density functionals. It is found that the isoscalar (IS) GMR has a two-peak structure, the lower peak of which is associated with the mixing between the ISGMR and the $K^π=0^{+}$ component of the ISGQR. The tran…
Within the frame-work of relativistic Thomas-Fermi and relativistic extended Thomas-Fermi approximations, we calculate the giant monopole resonance (GMR) excitation energies for Sn and related nuclei. A large number of non-linear relativistic force parameters are used in this calculations. We find that a parameter set is capable to reproduce the experimental monopole energy of Sn isotopes, when its nuclear matter compressibility lies within $210-230$ MeV, however fails to reproduce the GMR energy of other related nuclei. That means, simultaneously a parameter set can not reproduce the GMR valu…
The recently-proposed effective shell-model interaction, the pairing-plus-multipole Hamiltonian with the monopole interaction obtained by empirical fits starting from the monopole-based universal force (PMMU), is systematically applied to nuclei of the pf5/2g9/2 shell region. It is demonstrated that the calculation describes reasonably well a wide range of experimental data, including not only the low-lying and high-excitation spectra, E2 transitions, quadrupole moments, and magnetic moments, but also the binding energies, for Ni, Cu, Zn, Ga, Ge, As, and Se isotopes with A=64-80. In particular…
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 $0^\circ < θ_{\text{lab.}}< 2^\circ$. 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…
The description of the of nuclei energy spectra of 0^{+} states has been done involving the degree of their collectivity as a systematics parameter. Within the framework of this approach the parameter of the collectivity is mainly determined by pairs of particles placed on single ''effective'' level and coupled to monopole bosons. Holshtein-Primakoff transformation of these monopole bosons leads to clear physical explanation of the structure of 0^{+} states in terms of ''ideal bosons''. The results may be helpful both for experimentalists and theorists in their investigations of low- lying sta…
