Isovector Dipole Modes Research Articles

Insights into the possible existence of a soft dipole mode inHe8

With an extreme neutron-to-proton ratio of N/Z=3, 8He provides an ideal laboratory for the study of a variety of exotic phenomena, such as the emergence of a soft dipole mode that is dominated by transitions into the continuum. In this contribution, a covariant density functional theory (DFT) framework is used to compute ground-state properties and the dipole response of 8He. Although 8He is admittedly too light for DFT to be applicable, the great merit of the approach is that the spurious contamination associated with the center-of-mass motion is guaranteed to decouple from the physical response. Given that a strong mixing between the isoscalar and isovector dipole modes is expected for a system with such a large neutron-proton asymmetry as 8He, the narrow structures that emerged at low energies in the isovector dipole response are attributed to the shift of the spurious strength to zero (or near zero) excitation energy. Thus, the theoretical framework implemented here disfavors the emergence of a soft dipole mode in 8He.

Dynamics of one-dimensional correlated nuclear systems within non-equilibrium Green’s function theory

Theory of non-equilibrium Green’s function (NGF) provides a practical framework for studying quantum many-body systems out of equilibrium. Extending the previous mean field approach developed for nuclear systems in one dimension with NGF, we introduce isospin degrees of freedom to the Green’s functions and incorporate short-range two-body interactions in the second-order self-consistent approximation to correlations, which represents the scattering of momentum orbitals in the Born approximation. We discuss the preparation of a finite nuclear system and examine the impact of correlations on the ground state. We also excite a finite symmetric nuclear system to oscillate in an isovector dipole mode and explore the dissipation effects in the oscillation. Finally, we demonstrate how to boost a slab to a constant and stable motion in a box, based on Galilean covariance of the theory. The studies in this paper lay the ground for the future exploration of collisions of correlated nuclear systems in one dimension.

Interplay between low-lying isoscalar and isovector dipole modes: A comparative analysis between semiclassical and quantum approaches

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 identified. We show that the relative weight of these excitations evolves with nuclear global features, such as density profile and neutron skin, which in turn reflect impor tant properties of the nuclear effective interaction. A thorough analysis of the associated transition densities turns out to be quite useful to better characterize the mixed isoscalar(IS)/isovector(IV) nature of the different modes and their surface/volume components. In particular, we show that the dipole response in the so-called Pygmy Dipole Resonance region corresponds to isoscalar-like surface oscillations, of larger strength in nuclei with a more diffuse surface. The ratio between the IV and IS Energy Weighted Sum Rule fractions exhausted in this region is shown to almost linearly increase with the neutron skin thickness in Sn isotopes.

Interplay between isoscalar and isovector correlations in neutron-rich nuclei

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, and the possible collective states made by both isoscalar and isovector correlations, ("iS-iV pigmy resonance"), are shown. The strong neutron-proton interaction in nuclei can be responsible for controlling the isospin structure of normal modes. It is explicitly shown that in the scattering by isoscalar (isovector) particles on N$\neq$Z even-even nuclei isovector (isoscalar) strength in addition to isoscalar (isovector) strength may be populated.

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.

Probing surface quantum flows in deformed pygmy dipole modes

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 oscillation in pygmy resonances is collective and compressional, corresponding to the lowest excitation energy and the simplest quantum flow topology. Our calculations show that surface flow patterns become more complicated as excitation energies increase.

Pygmy dipole mode in deformed neutron-rich Mg isotopes close to the drip line

We investigate the microscopic structure of the low-lying isovector-dipole excitation mode in neutron-rich $^{36,38,40}\mathrm{Mg}$ 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 ${E}_{x}l10$ MeV exhausts about $6.0%$ of the classical Thomas-Reiche-Kuhn dipole sum rule in $^{40}\mathrm{Mg}$. We obtained the collective dipole modes at around $8\text{\ensuremath{-}}10$ MeV in Mg isotopes, that consist of many two-quasiparticle excitations of the neutron. The transition density clearly shows an oscillation of the neutron skin against the isoscalar core. We found significant coupling effects between the dipole and octupole excitation modes due to the nuclear deformation. It is also found that the responses for the compressional dipole and isoscalar octupole excitations are much enhanced in the lower energy region.

Low-energy monopole and dipole response in nuclei at finite temperature

The multipole response of nuclei at temperatures T=0–2 MeV is studied using a self-consistent finite-temperature RPA (random phase approximation) based on relativistic energy density functionals. Illustrative calculations are performed for the isoscalar monopole and isovector dipole modes and, in particular, the evolution of low-energy excitations with temperature is analyzed, including the modification of pygmy structures. Both for the monopole and dipole modes, in the temperature range T=1–2 MeV additional transition strength appears at low energies due to thermal unblocking of single-particle orbitals close to the Fermi level. A concentration of dipole strength around 10 MeV excitation energy is predicted in 60,62Ni. The principal effect of finite temperature on low-energy strength that is already present at zero temperature, e.g. in 68Ni and 132Sn, is the spreading of this structure to even lower energy and the appearance of states that correspond to thermally unblocked transitions.

Dynamical effects on the way to fusion of very heavy nuclei

The central collision of 40Ar and 208Pb is studied considering the ellipsoidal deformations and isovector dipole mode of motion in the approaching phase. The collective energy dissipation is suggested to originate from the Fermi surface deformation which is treated as a kinematically independent mode of motion within the canonical Lagrange-Rayleigh dynamics. The possible extensions of the approach are discussed. The potential energy surface, calculated using the generalized (folded) surface potential, is studied. The saddle point in the potential energy surface lying at the border of strongly deformed compact configurations is located. The potential energy at this point is about 10MeV smaller than that of the ions touching each other in the spherical shape. The examination of trajectories followed by the system in its evolution shows that the inertia forces strongly hinder the motion of ions along the potential energy valley. The collective energy dissipated during the approach is found to be smaller than the difference in the potential energies at saddle point and at the touching configuration of unpolarized ions.

Splitting of the isovector giant dipole resonance in neutron-rich spherical nuclei

The well-known splitting of the isovector giant dipole resonance is traditionally explained as a phenomenon of the nuclear isospin asymmetry (isospin splitting model) or the nuclear deformation. We suggest a new mechanism of the splitting of the giant multipole resonances in spherical neutron-rich nuclei resulting from the interplay of the isovector and isoscalar sounds with different velocities. Our approach is based on the collisional Landau kinetic theory and can be used for description of the splitting phenomena for both the isoscalar and the isovector modes in a wide region of nuclear masses $A~40\text{\ensuremath{-}}240$. For the isovector dipole modes, the evaluated values of the splitting energy, the relative strength of the main and satellite resonance peaks, and the contribution to the energy-weighted sum rule are in agreement with experimental data.

Low-lying dipole modes inNe26,28in the quasiparticle relativistic random phase approximation

The low-lying isovector dipole strengths in neutron rich nuclei $^{26}$Ne and $^{28}$Ne are investigated in the quasiparticle relativistic random phase approximation. Nuclear ground state properties are calculated in an extended relativistic mean-field theory plus BCS method where the contribution of the resonant continuum to pairing correlations is properly treated. Numerical calculations are tested in the case of isovector dipole and isoscalar quadrupole modes in the neutron rich nucleus $^{22}$O. It is found that in present calculation low-lying isovector dipole strengths at $E_x < 10$ MeV in nuclei $^{26}$Ne and $^{28}$Ne exhaust about 4.9% and 5.8% of the Thomas-Reiche-Kuhn dipole sum rule, respectively. The centroid energy of the low-lying dipole excitation is located at 8.3 MeV in $^{26}$Ne and 7.9 MeV in $^{28}$Ne.

Collective excitations of the element Z = 120

The low-lying vibrational excitations of superheavy even-even nuclei around Z=120 and N=172, predicted to be spherical by the relativistic mean-field (RMF) model, are studied within a phenomenological collective approach. In the framework of the macroscopic model for giant resonances, we compute the transition densities of the isoscalar monopole, quadrupole, and octupole and isovector dipole modes for the superheavy nucleus 292120, whose ground-state density is determined from the RMF model. The results are also compared to those for208Pb.

Properties of some collective excitations in spherical nuclei from the superheavy island

We study the β-vibrational spectrum of the putative double magic superheavy nucleus 292120, as predicted by the relativistic mean-field (RMF) model in a phenomenological collective approach and compare it with the one of the well-known double magic heavy nuclei 208Pb. Results are also presented for the elements 300120 and 298114. We use a selection of different mean-field forces and discuss their different predictions and the consequences for the collective modes.In the framework of the macroscopic model for giant resonances we compute the transition densities of the isoscalar monopole, quadrupole and octupole, and isovector dipole modes for the superheavy element 292120, whose ground state density is determined from the RMF model. The results are also compared to those of 208Pb.

Collectivity of the low-lying dipole strength in relativistic random phase approximation

The relativistic random phase approximation is applied in the analysis of the evolution of the isovector dipole response in nuclei with a large neutron excess. The self-consistent framework of relativistic mean-field theory, which has been very successfully applied in the description of ground-state properties of nuclei far from the valley of β-stability, is extended to study the possible onset of low-energy collective isovector dipole modes in nuclei with extreme isospin values.

Soft Giant Dipole Modes in Ca Isotopes in the Relativistic RPA**The project supported by National Natural Science Foundation of China under Grant Nos 19847002, 19835010, 10075080 and Major State Basic Research Development Program under contract No. G200077407

The isovector giant dipole resonance in Ca isotopes is investigated in the framework of the fully consistent relativistic random phase approximation. The calculations are performed in an effective Lagrangian with a parameter set , which was proposed for satisfactorily describing nuclear ground state properties. It is found that a soft isovector dipole mode for Ca isotopes near drip lines exists at energy around . The soft dipole states are mainly due to the excitation of the weakly bound and pure neutron (proton) states near Fermi surface as well as the correlation of isoscalar and isovector operators. For nuclei with the extreme value of , the contributions of isoscalar mesons in the isovector mode play a non-negligible role.

GIANT RESONANCE PROPERTIES IN β STABLEAND UNSTABLE NUCLEI

We study the giant resonances of stable and unstable nuclei in the framework of the consistent relativistic random phase approximation built on the nonlinear relativistic mean field (RMF) ground states. The isoscalar and isovector modes of giant resonances for stable nuclei, such as 208Pb,144Sm,116Sn,90Zr,40Ca,16O and Ca isotope chains are investigated. The contribution to the giant resonances from the Dirac sea states and the currents of vector mesons are examined. The results show that the effects of the Dirac sea states on the isoscalar giant modes are pronounced, but become weaker for light nuclei, while the contributions of the isovector modes are negligible. The few sets of parameterizations of nonlinear RMF model, which are commonly used to give a good description of ground-state properties of finite nuclei, could also well describe the nuclear dynamic properties-giant resonances. For nuclei with the extreme value of N/Z, low-lying collective excitations are found in isovector dipole modes, which are mainly due to the ph excitation of the weakly bound states near Fermi surface and the isospin mixture effect.

Zero- to first-sound transition for the Giant Dipole propagation in hot nuclei

We discuss the transition to first sound propagation of the isovector dipole mode in heated nuclear matter. The presence of a damping of the isovector current leads to new features of the transition: i) the attenuation keeps a T 2 dependence, although with a change in the slope; ii) for large n- p friction the dipole mode can be fully damped before reaching the transition point. From a realistic estimation of relevant relaxation times we predict a transition around T = 3 MeV in medium-heavy nuclei with detectable effects on the GDR γ- yield in the direction of a better agreement with experiments.

Isoscalar and isovector dipole mode in drip line nuclei in comparison with β-stable nuclei

The isoscalar and the isovector dipole mode of drip line and \ensuremath{\beta}-stable nuclei are investigated, using the self-consistent Hartree-Fock plus the random-phase approximation with Skyrme interactions. Including simultaneously both the isoscalar and the isovector correlation, the RPA response function is estimated in the coordinate space so as to take into account properly the continuum effect. The spurious component is carefully taken away from the calculated strength. In \ensuremath{\beta}-stable nuclei such as ${}^{208}\mathrm{Pb}$ the frequency of the isovector giant dipole resonance (IVGDR) is lower than that of the isoscalar giant dipole resonance (compression mode). In contrast, in lighter drip line nuclei a major part of the isoscalar compression dipole strength lies at an energy much lower than the energy of the IVGDR.

Finite rank approximation for random phase approximation calculations with Skyrme interactions: An application to Ar isotopes

Starting from an effective interaction of Skyrme type, a finite rank separable approximation is proposed for the residual particle-hole interaction with the aim to allow one to perform structure calculations in very large particle-hole spaces. The approximation is checked on a specific example by calculating isoscalar quadrupole and isovector dipole modes in a finite nucleus using the random phase approximation. It is found that the finite rank approximation is very accurate in the isoscalar channel and it reproduces reasonably well the isovector channel. The use of the finite rank interaction is illustrated by calculating the evolution of the dipole strength distribution along the Ar isotope chain, from $A=32$ to $A=52.$

Excitation of isovector modes in very neutron-rich nuclei via heavy-ion isoscalar probes

The existence of a neutron skin in neutron-rich nuclei is discussed in connection with the excitation of isovector dipole and quadrupole giant modes via isoscalar nuclear probes. In the case of large neutron excess, important contributions are obtained from the nuclear excitation, which may even become predominant according to proper kinematical conditions. At variance with the usual situation encountered in inelastic processes, constructive interference can be found between nuclear and Coulomb contributions.