The electric dipole response of $^{140}$Ce is investigated using the fully consistent relativistic quasiparticle random phase approximation. By analyzing the isospin structure of the E1 response, it is shown that the low-energy (pygmy) strength separates into two segments with different isospin character. The more pronounced pygmy structure at lower energy is composed of predominantly isoscalar states with surface-peaked transition densities. At somewhat higher energy the calculated E1 strength is primarily of isovector character, as expected for the low-energy tail of the giant dipole resonance. The results are in qualitative agreement with those obtained in recent $(γ,γ')$ and $(α,α'γ)$ experiments, and provide a simple explanation for the splitting of low-energy E1 strength into two groups of states with different isospin structure and radial dependence of the corresponding transition densities.
The vibrational structure of the Pygmy Dipole Resonance (PDR) is investigated within a quantum many-body treatment with extended separable interactions able to encode the dependence of nuclear symmetry energy on density. A new picture of PDR is unveiled in terms of a combined dynamics of the neutron skin and of the core isovector polarization, which determines the isoscalar features of PDR while reproducing the isovector properties of Giant Dipole Resonance. The key role played by the variation with density of the symmetry energy on shaping the low-lying dipole response and its isoscalar-isove…
Inelastic $α$-scattering excitation cross sections are calculated for electric dipole excitations in $^{124}$Sn based on the transition densities obtained from the relativistic quasiparticle time-blocking approximation (RQTBA) in the framework of a semiclassical model. The calculation provides the missing link to directly compare the results from the microscopic RQTBA calculations to recent experimental data measured via the $(α,α'γ)$ reaction, which show a structural splitting of the low-lying E1 strength often denoted as pygmy dipole resonance (PDR). The experimentally observed splitting is …
The structure of the isovector dipole resonance in neutron-rich calcium isotope, $^{60}Ca$, has been investigated by implementing a careful treatment of the differences of neutron and proton radii in the continuum random phase approximation ($RPA$). The calculations have taken into account the current estimates of the neutron skin. The estimates of the escape widths for direct neutron decay from the pygmy dipole resonance ($PDR$) were shown rather wide, implicating a strong coupling to the continuum. The width of the giant dipole resonance ($GDR$) was evaluated, bringing on a detailed discussi…
The isotopic dependence of the isovector Pygmy dipole response in tin is studied within the framework of the relativistic random phase approximation. Regarded as an oscillation of the neutron skin against the isospin-symmetric core, the pygmy dipole resonance may place important constraints on the neutron skin of heavy nuclei and, as a result, on the equation of state of neutron-rich matter. The present study centers around two questions. First, is there a strong correlation between the development of a neutron skin and the emergence of low-energy isovector dipole strength? Second, could one u…
Stable and unstable nuclei with neutron excess ($N>Z$) show - in the isovector dipole transition strength distribution - a small hump around the neutron emission threshold energy known as Pygmy Dipole Resonance (PDR). One of its main features is the isospin mixing allowing the experimental studies with both isovector and isoscalar probes. Different theoretical approaches and methodologies are used to deduce the characteristics of the PDR. In this Chapter, the various mean-field theories and their extensions, devoted to understand and reproduce the strength distribution of these low-lying dipol…
The interplay between isoscalar and isovector correlations in the 1$^{-}$ states in neutron-rich (N$\neq$Z) even-even nuclei is studied, taking examples of the nuclei, $^{22}_{8}$O$_{14}$ and $^{24}_{8}$O$_{16}$. The excitation modes explored are isovector dipole and isoscalar compression dipole modes. The self-consistent Hartree-Fock plus the random-phase approximation with the Skyrme interaction, SLy4, is solved in coordinate space so as to take properly into account the continuum effect. The isovector peak induced by isoscalar correlation, the isoscalar peak induced by isovector correlation…
Isoscalar density is a sum of neutron and proton densities and isovector is a normalized difference. Here, we report on the experimental evidence for the displacement of the isovector and isoscalar surfaces in nuclei, by $\sim$$0.9 \, \text{fm}$ from each other. We analyze data on quasielastic (QE) charge exchange (p,n) reactions, concurrently with proton and neutron elastic scattering data for the same target nuclei, following the concepts of the isoscalar and isovector potentials combined into Lane optical potential. The elastic data largely probe the geometry of the isoscalar potential and …
Neutron-proton (np-) pairing is expected to play an important role in the N Z nuclei. In general, it can have isovector and isoscalar character. The existence of isovector np-pairing is well established. On the contrary, it is still debated whether there is an isoscalar np-pairing. The review of the situation with these two types of pairing with special emphasis on the isoscalar one is presented. It is concluded that there are no substantial evidences for the existence of isoscalar np-pairing.
In calculations of isoscalar magnetic moments of odd-odd N=Z nuclei it was found that for medium to heavy mass nuclei large scale shell model calculations yielded results which were very close to much simpler single j shell ones. To understand this we compare isoscalar and isovector configuration mixing in first order perturbation theory using a spin dependant delata interaction.The isoscalar corrections are much smaller
Isoscalar (T=0,J=1) and isovector (T=1,J=0) pairing correlations in the ground state of self-conjugate nuclei are treated in terms of alpha-like quartets built by two protons and two neutrons coupled to total isospin T=0 and total angular momentum J=0. Quartets are constructed dynamically via an iterative variational procedure and the ground state is represented as a product of such quartets. It is shown that the quartet formalism describes accurately the ground state energies of realistic isovector plus isoscalar pairing Hamiltonians in nuclei with valence particles outside the 16O, 40Ca and …
The pygmy dipole resonance in neutron-rich nuclei is studied within the framework of the Vlasov equation which is solved numerically. The interaction used in the Thomas-Fermi ground state and in the Vlasov equation is derived from an energy functional which correctly describes the equation of state of nuclear matter and neutron matter. It is found that the pygmy resonance appears in the electric dipole response of all nuclei with strong neutron excess, the energies and transition probabilities being in reasonable agreement with experimental results. Since the Vlasov equation does not account f…
We show that the correlations generated in the ground state of $N=Z$ nuclei by the isovector and isoscalar pairing forces can be treated with high precision as a condensate of alpha-like quartets. To treat these correlations, the quartet condensation model (QCM) is extended to the treatment of spherically symmetric isovector $(T=1,J=0)$ and isoscalar $(T=0,J=1)$ pairing forces . Within QCM we discuss the competition between $T=1$ and $T=0$ pairing correlations in the case of a two-level model and for $N=Z$ nuclei with nucleons moving in the open shells above $^{16}$O, $^{40}$Ca and $^{100}$Sn.…
A strong isoscalar dipole resonance is known to be excited in a variety of nuclei, including isospin symmetric ones, at approximately 6-7 MeV. A series of theoretical studies and accumulating experimental evidence support an interpretation of the above dipole resonance as an elementary surface vibration. Obviously, such a mode is potentially as interesting as any collective excitation for a variety of reasons. In addition, though, it is found to account for the observed isoscalar segment of pygmy dipole strength. As discussed here, this has important implications for pygmy-strength interpretat…
The isovector dipole response in $^{208}$Pb is described in the framework of a fully self-consistent relativistic random phase approximation. The NL3 parameter set for the effective mean-field Lagrangian with nonlinear meson self-interaction terms, used in the present calculations, reproduces ground state properties as well as the excitation energies of giant resonances in nuclei. In addition to the isovector dipole resonance in $^{208}$Pb, the present analysis predicts the occurrence of low-lying E1 peaks in the energy region between 7 and 11 MeV. In particular, a collective state has been id…
We probe nuclear multipole resonances in the framework of the random-phase approximation by using the interaction obtained from the chiral effective field theory. The three-nucleon force is included in a form of the in-medium two-nucleon interaction which was derived from the chiral three-nucleon force. The isoscalar monopole, isoscalar dipole, isovector dipole and isoscalar quadrupole resonances of the closed-shell $^{56,68,78}$Ni have been investigated. The calculations reasonably reproduce the experimental multipole resonances of $^{56,68}$Ni, and well describe the pygmy dipole resonance an…
We use shell model techniques in the complete pf shell to study pair correlations in nuclei. Particular attention is paid to the competition of isoscalar and isovector proton-neutron pairing modes which is investigated in the odd-odd N=Z nucleus 46V and in the chain of even Fe-isotopes. We confirm the dominance of isovector pairing in the ground states. An inspection of the level density and pair correlation strength in 46V, however, shows the increasing relative importance of isoscalar correlations with increasing excitation energy. In the Fe-isotopes we find the expected strong dependence of…
Working on the framework of Relativistic Mean Field theory, we exposed the effect of nonlinear isoscalar-isovector coupling on G2 parameter set on the density dependence of nuclear symmetry energy in infinite nuclear matter. The observables like symmetric energy and few related coefficients are studied systematically. We presented the results of stiff symmetry energy at sub-saturation densities and a soft variation at normal densities. Correlation between the symmetric energy and the isoscalar-isovector coupling parameter fully demonstrated for wide range of density. The work further extended …
The subtle interplay between the two nuclear superfluids, isovector T=1 and isoscalar T=0 phases, are investigated in an exactly soluble model. It is shown that T=1 and T=0 pair-modes decouple in the exact calculations with the T=1 pair-energy being independent of the T=0 pair-strength and vice-versa. In the rotating-field, the isoscalar correlations remain constant in contrast to the well known quenching of isovector pairing. An increase of the isoscalar (J=1, T=0) pair-field results in a delay of the bandcrossing frequency. This behaviour is shown to be present only near the N=Z line and its…
We investigate the phase coherence of isoscalar pairs from the $B({\rm GT};0^+_1\,T\!=\!1 \to 1^+_1\,T\!=\!0)$ values in two-particle configurations of $A=6$, 18, and 42 nuclei and two-hole configurations of $A=14$ and 38 ones. We find that these Gamow-Teller (GT) matrix elements are always constructive and thus enlarged under isovector- and isoscalar-pairing Hamiltonians, whereas the observed GT strengths are strongly hindered for the two-hole configurations, including the famous $^{14}$C dating $β$ decay. This indicates that the actual isoscalar pair, unlike the isovector pair, has no defini…
The isoscalar-isovector ($ρ-ω$) interferences in the exclusive reactions $π^- p \to n e^+ e^-$ and $π^+ n \to p e^+ e^-$ near the $ω$ threshold leads to a distinct difference of the dielectron invariant mass distributions depending on beam energy. The strength of this effect is determined by the coupling of resonances to the nucleon vector-meson channels and other resonance properties. Therefore, a combined analysis of these reactions can be used as a tool for determining the baryon resonance dynamics.
The isoscalar proton-neutron pairing and isovector pairing, including both isovector proton-neutron pairing and like-particle pairing, are treated in a formalism which conserves exactly the particle number and the isospin. The formalism is designed for self-conjugate (N=Z) systems of nucleons moving in axially deformed mean fields and interacting through the most general isovector and isoscalar pairing interactions. The ground state of these systems is described by a superposition of two types of condensates, i.e., condensates of isovector quartets, built by two isovector pairs coupled to the …
We investigate the problem of the extraction of the isovector and isoscalar spectral functions from data on $e^+e^-\to hadrons$, in the presence of non-zero isospin breaking. It is shown that the conventional approach to extracting the isovector spectral function in the $ρ$ resonance region, in which only the isoscalar contribution associated with $ω\to ππ$ is subtracted, fails to fully remove the effects of the isoscalar component of the electromagnetic current. The additional subtractions required to extract the pure isovector and isoscalar spectral functions are estimated using results from…
The quartet condensation model (QCM) is extended for the treatment of isovector and isoscalar pairing in odd-odd N=Z nuclei. In the extended QCM approach the lowest states of isospin T=1 and T=0 in odd-odd nuclei are described variationally by trial functions composed by a proton-neutron pair appended to a condensate of 4-body operators. The latter are taken as a linear superposition of an isovector quartet, built by two isovector pairs coupled to the total isospin T=0, and two collective isoscalar pairs. In all pairs the nucleons are distributed in time-reversed single-particle states of axia…
The systematic study of isoscalar (IS) and isovector (IV) giant quadrupole responses (GQR) in normal and superfluid nuclei presented in [G. Scamps and D. Lacroix, Phys. Rev. 88, 044310 (2013)] is extended to the case of axially deformed and triaxial nuclei. The static and dynamical energy density functional based on Skyrme effective interaction are used to study static properties and dynamical response functions over the whole nuclear chart. Among the 749 nuclei that are considered, 301 and 65 are respectively found to be prolate and oblate while 54 do not present any symmetry axis. For these …
We study the isoscalar (T=0) and isovector (T=1) pairing correlations in N=Z nuclei. They are estimated from the double difference of binding energies for odd-odd N=Z nuclei and the odd-even mass difference for the neighboring odd-mass nuclei, respectively. The empirical and BCS calculations based on a T=0 and T=1 pairing model reproduce well the almost degeneracy of the lowest T=0 and T=1 states over a wide range of even-even and odd-odd N=Z nuclei. It is shown that this degeneracy is attributed to competition between the isoscalar and isovector pairing correlations in N=Z nuclei. The calcula…
The self-consistent random phase approximation (RPA), based on the framework of relativistic energy density functionals, is employed in the study of isovector and isoscalar dipole response in $^{68}$Ni, $^{132}$Sn, and $^{208}$Pb. The evolution of pygmy dipole states (PDS) in the region of low excitation energies is analyzed as a function of the density-dependence of the symmetry energy for a set of relativistic effective interactions. The occurrence of PDS is predicted in the response to both the isovector and isoscalar dipole operators, and its strength is enhanced with the increase of the s…
A very important open question related to the pygmy dipole resonance is about its quite elusive collective nature. In this paper, within a harmonic oscillator shell model, generalizing an approach introduced by Brink, we first identify the dipole normal modes in neutron rich nuclei and derive the energy weighted sum rule exhausted by the pygmy dipole resonance. Then solving numerically the self-consistent Landau-Vlasov kinetic equations for neutrons and protons with specific initial conditions, we explore the structure of the different dipole vibrations in the $^{132}Sn$ system and investigate…
We propose a particle number conserving formalism for the treatment of isovector-isoscalar pairing in nuclei with $N>Z$. The ground state of the pairing Hamiltonian is described by a quartet condensate to which is appended a pair condensate formed by the neutrons in excess. The quartets are built by two isovector pairs coupled to the total isospin $T=0$ and two collective isoscalar proton-neutron pairs. To probe this ansatz for the ground state we performed calculations for $N>Z$ nuclei with the valence nucleons moving above the cores $^{16}$O, $^{40}$Ca and $^{100}$Sn. The calculations are do…
The pygmy dipole resonance has been studied in the proton-magic nucleus 124Sn with the (a,a'g) coincidence method at E=136 MeV. The comparison with results of photon-scattering experiments reveals a splitting into two components with different structure: one group of states which is excited in (a,a'g) as well as in (g,g') reactions and a group of states at higher energies which is only excited in (g,g') reactions. Calculations with the self-consistent relativistic quasiparticle time-blocking approximation and the quasiparticle phonon model are in qualitative agreement with the experimental res…
Recent improvements in the experimental determination of properties of the Isovector Giant Quadrupole Resonance (IVGQR), as demonstrated in the A=208 mass region, may be instrumental for characterizing the isovector channel of the effective nuclear interaction. We analyze properties of the IVGQR in 208Pb, using both macroscopic and microscopic approaches. The microscopic method is based on families of non-relativistic and covariant Energy Density Functionals (EDF), characterized by a systematic variation of isoscalar and isovector properties of the corresponding nuclear matter equations of sta…
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
We review a recent progress in investigation of the isoscalar toroidal dipole resonance (TDR). A possible relation of the TDR and low-energy dipole strength (also called a pygmy resonance) is analyzed. It is shown that the dipole strength in the pygmy region can by understood as a local manifestation of the collective vortical toroidal motion at the nuclear surface. Application of the TDR as a measure of the nuclear dipole vorticity is discussed. Finally, an anomalous splitting of the TDR in deformed nuclei is scrutinized.
We have studied the uncharacteristic behavior of the measured values of the isoscalar and isovector centroid energies, ECEN, of giant resonances with multipolarity L=0-3 in 44Ca, 54Fe, 64,68Zn and 56,58,60,68Ni. For this purpose, we carried out calculations of ECEN within the spherical Hartree-Fock (HF)-based random phase approximation (RPA) theory with 33 different Skyrme-type effective nucleon-nucleon interactions. We have also determined the Pearson linear correlation coefficients between the calculated centroid energies and the various nuclear matter (NM) properties associated with each in…
We study the nature of the low-lying dipole strength in neutron-rich nuclei, often associated to the Pygmy Dipole Resonance. The states are described within the Hartree-Fock plus RPA formalism, using different parametrizations of the Skyrme interaction. We show how the information from combined reactions processes involving the Coulomb and different mixtures of isoscalar and isovector nuclear interactions can provide a clue to reveal the characteristic features of these states.
We study the correlation between the neutron skin development and the low-energy dipole response associated with the pygmy dipole resonance (PDR) in connection with the properties of symmetry energy. We perform our investigation within a microscopic transport model based on the Landau-Vlasov kinetic equation by employing three different equations of state in the isovector sector. Together with the giant dipole resonance (GDR) for all studied systems, we identify a PDR collective mode whose energy centroid is very well described by the parametrization E_{PDR}=41 A^{-1/3}. A linear correlation b…
Using the relativistic mean-field model with nonlinear couplings between the isoscalar and isovector mesons, we study the properties of isospin-asymmetric nuclear matter. Not only the vector mixing, $ω_μω^μ\mathbfρ_ν\mathbfρ^ν$, but also the quartic interaction due to the scalar mesons, $σ^{2}\mathbfδ^{2}$, is taken into account to investigate the density dependence of nuclear symmetry energy, $E_{\rm sym}$, and the neutron-star properties. It is found that the $δ$ meson increases $E_{\rm sym}$ at high densities, whereas the $σ$-$δ$ mixing makes $E_{\rm sym}$ soft above the saturation density.…
This study revisits the issue of the extraction of estimates for the masses and for the partial decay widths to two pions of the scalar-isoscalar $I^G\,(J^{PC}) = 0^+\,(0^{++})$ and vector-isovector $I^G\,(J^{PC}) = 1^+\,(1^{--})$ mesons below $2$ GeV, from the data contained in the recent compilation by the Particle Data Group.
The spin magnetic dipole transitions and the neutron-proton spin-spin correlations in $sd-$shell even-even nuclei with $N=Z$ are investigated using shell model wave functions taking into accout enhanced isoscalar (IS) spin-triplet pairing as well as the effective spin operators. It was shown that the IS pairing and the effective spin operators gives a large quenching effect on the IV spin transitions to be consistent with observed data by $(p,p')$ experiments. On the other hand, the observed IS spin strength show much smaller quenching effect than expected by the calculated results. The IS pai…
The long standing problem of proton-neutron pairing and, in particular, the limitations imposed on the solutions by the available symmetries, is revisited. We look for solutions with non-vanishing expectation values of the proton, the neutron and the isoscalar gaps. For an equal number of protons and neutrons we find two solutions where the absolute values of proton and neutrons gaps are equal but have the same or opposite sign. The behavior and structure of these solutions differ for spin saturated (single l-shell) and spin unsaturared systems (single j-shell). In the former case the BCS resu…
The isospin character, the collective or single-particle nature, and the sensitivity to the slope of the nuclear symmetry energy of the low-energy isovector dipole response (known as pygmy dipole resonance) are nowadays under debate. In the present work we study, within the fully self-consistent non-relativistic mean field (MF) approach based on Skyrme Hartree-Fock plus Random Phase Approximation (RPA), the measured even-even nuclei ${}^{68}$Ni, ${}^{132}$Sn and ${}^{208}$Pb. To analyze the model dependence in the predictions of the pygmy dipole strength, we employ three different Skyrme param…
The nature of E1 low-energy strength (LES), often denoted as a "pygmy dipole resonance", is analyzed within the random-phase-approximation (RPA) in $^{208}$Pb using Skyrme forces in fully self-consistent manner. A first overview is given by the strength functions for the dipole, compressional and toroidal operators. More detailed insight is gained by averaged transition densities and currents where the latter provide very illustrative flow pattern. The analysis reveals clear isoscalar toroidal flow in the low-energy bin 6.0-8.8 MeV of the LES and a mixed isoscalar/isovector toroidal/compressio…
A compact approach based on the folding model is suggested for the determination of the isoscalar and isovector transition strengths of the low-lying ($ΔS=ΔT=0$) excitations induced by inelastic proton scattering measured with exotic beams. Our analysis of the recently measured inelastic $^{18,20}$O+p scattering data at $E_{\rm lab}=30$ and 43 MeV/nucleon has given for the first time an accurate estimate of the isoscalar $β_0$ and isovector $β_1$ deformation parameters (which cannot be determined from the (p,p') data alone by standard methods) for 2$^+_1$ and $3^-_1$ excited states in $^{18,20…
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.
The role of the isoscalar hyperon Lambda in probing the density dependence of the nuclear symmetry energy is studied in multi-Lambda hypernuclei, hyperon-rich matter and neutron stars in relativistic models. Relationships between the properties of three types of objects and the neutron thickness in 208Pb are established with respect to the isoscalar-isovector coupling that modifies the density dependence of the symmetry energy. The exotic isotopes far from the neutron drip line can be stabilized by filling in considerable Lambda hyperons. The difference of the binding energy of multi-Lambda hy…
We investigate the microscopic structure of the low-lying isovector-dipole excitation mode in neutron-rich $^{36,38,40}$Mg close to the drip line by means of the deformed quasiparticle-random-phase-approximation employing the Skyrme and the local pairing energy-density functionals. It is found that the low-lying bump structure above the neutron emission-threshold energy develops when the drip line is approached, and that the isovector dipole strength at $E_{x} < 10$ MeV exhausts about $6.0 %$ of the classical Thomas-Reiche-Kuhn dipole sum rule in $^{40}$Mg. We obtained the collective dipole mo…
We calculate the imaginary parts of the isoscalar scalar and isovector electromagnetic form factors of the nucleon up to two-loop order in chiral perturbation theory. Particular attention is paid on the correct behavior of Im $σ_N(t)$ and Im $G_{E,M}^V(t)$ at the two-pion threshold $t_0=4 m_π^2$ in connection with the non-relativistic 1/M-expansion. We recover the well-known strong enhancement near threshold originating from the nearby anomalous singularity at $t_c = 4m_π^2-m_π^4/M^2 = 3.98 m_π^2$. In the case of the scalar spectral function Im $σ_N(t)$ one finds a significant improvement in c…
The low-lying spectra of $^{24,25,26}{\rm Ne}$ and the structure of the pygmy dipole resonance (PDR) in $^{26}{\rm Ne}$ have been theoretically studied by the antisymmetrized molecular dynamics (AMD) and its extended version called shifted-basis AMD. The calculated energy and strength of the PDR reasonably agree with the observation, and the analysis of the wave function shows that the PDR is dominated by neutron excitation coupled to the quadrupole excited core nucleus $^{25}{\rm Ne}$, which explains the observed unexpected decay of PDR to the excited states of $^{25}{\rm Ne}$. The large isos…
In order to explore the nature of collective modes in weakly bound nuclei, we have investigated deformation effects and surface flow patterns of isovector dipole modes in a shape-coexisting nucleus $^{40}$Mg. The calculations were done in a fully self-consistent continuum finite-amplitude Quasiparticle Random Phase Approximation (QRPA) in a large deformed spatial mesh. An unexpected result of pygmy and giant dipole modes having disproportionate deformation splittings in strength functions was obtained. Furthermore, the transition current densities demonstrate that the long-sought core-halo osc…
We perform a systematic study of Gamow-Teller (GT) transitions in the 2p1f shell, using the nuclear shell model with two schematic Hamiltonians. The use of the shell model provides flexibility to analyze the role of different proton-neutron pairing modes in the presence of nuclear deformation. The schematic Hamiltonians that are used contain a quadrupole-quadrupole interaction as well as isoscalar (T=0) and isovector (T=1) pairing interactions, but differ in the single particle energies. The objective of the work is to observe the behavior of GT transitions in different isoscalar and isovector…
The nuclear isovector-dipole strength structure is analyzed in terms of the main and satellite (pygmy) peaks within the Fermi-liquid droplet model. Such a structure is sensitive to the value of the surface symmetry-energy constant obtained analytically for different Skyrme forces in the leptodermous effective surface approximation. Energies, sum rules and transition densities of the main and satellite peaks for specific Skyrme forces are qualitatively in agreement with the experimental data and other theoretical calculations.
The electric dipole excitation of various nuclei is calculated with a Random Phase Approximation phenomenological approach. The evolution of the strength distribution in various groups of isotopes, oxygen, calcium, zirconium and tin, is studied. The neutron excess produces $E1$ strength in the low energy region. Indexes to measure the collectivity of the excitation are defined. We studied the behavior of proton and neutron transition densities to determine the isoscalar or isovector nature of the excitation. We observed that in medium-heavy nuclei the low-energy $E1$ excitation has characteris…
The short-range nuclear attraction is stronger in the isoscalar channel than in the isovector channel, as evidenced by the existence of the deuteron and not the dineutron. Nevertheless, apart from light N=Z nuclei, pairing is only seen in the isovector channel. This is explained by the effect of the strong spin-orbit splitting on the single-particle energies. A semiquantitative argument is presented treating the high-j orbitals at the Fermi surface as plane waves on a two-dimensional sheet.
Isovector and isoscalar dipole excitations in $^9$Be and $^{10}$Be are investigated in the framework of antisymmetrized molecular dynamics, in which angular-momentum and parity projections are performed. In the present method, 1p-1h excitations on the ground state and large amplitude $α$-cluster mode are incorporated. The isovector giant dipole resonance (GDR) in $E>20$ MeV shows the two peak structure which is understood by the dipole excitation in the 2$α$ core part with the prolate deformation. Because of valence neutron modes against the $2α$ core, low-energy E1 resonances appear in $E<20$…
Based on the accurately calibrated interaction FSUGold, we show that including isovector scalar $δ$ meson and its coupling to isoscalar scalar $σ$ meson in the relativistic mean field (RMF) model can soften the symmetry energy $E_{\rm{sym}}(n)$ at intermediate densities while stiffen the $E_{\rm{sym}}(n)$ at high densities. We find this new RMF model can be simultaneously compatible with (1) the constraints on the equation of state of symmetric nuclear matter at suprasaturation densities from flow data in heavy-ion collisions, (2) the neutron skin thickness of $^{208}$Pb from the PREX-II exper…
The isoscalar (IS) and isovector (IV) quadrupole responses of nuclei are systematically investigated using the time-dependent Skyrme Energy Density Functional including pairing in the BCS approximation. Using two different Skyrme functionals, Sly4 and SkM*, respectively 263 and 304 nuclei have been found to be spherical along the nuclear charts. The time-dependent evolution of these nuclei has been systematically performed giving access to their quadrupole responses. It is shown that the mean-energy of the collective high energy state globally reproduces the experimental IS and IV collective e…
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…
