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 between the energy weighted sum rule (EWSR) associated to PDR and the neutron skin thickness is evidenced. An increase of 15 MeVfm^2 of EWSR, in correspondence to a change of 0.1fm of the neutron skin size, is obtained. We conjecture that different nuclei having close neutron skin sizes will exhaust the same EWSR in the pygmy region. This suggests that a precise experimental estimate of the total EWSR exhausted by the PDR allows the determination of the neutron skin size, constraining the slope parameter of the symmetry energy.
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…
Motivated by a recent experiment, the distribution of electric dipole strength in the neutron-rich 68Ni isotope was computed using a relativistic random phase approximation with a set of effective interactions that - although well calibrated - predict significantly different values for the neutron-skin thickness in 208Pb. The emergence of low-energy "Pygmy" strength that exhausts about 5-8% of the energy weighted sum rule (EWSR) is clearly identified. In addition to the EWSR, special emphasis is placed on the dipole polarizability. In particular, our results suggest a strong correlation betwee…
The electric quadrupole response is investigated theoretically by HFB and QPM calculations along the Sn isotopic chain with special emphasis on excitations above the first collective state and below the particle threshold. Depending on the asymmetry, additional strength clustering as a group of states similar to the known PDR mode is found. The spectral distributions and electric response functions are discussed. The transition densities of these Pygmy Quadrupole Resonances (PQR) states are closely related to the neutron excess and showing special features being compatible with an oscillation …
Correlations between the behavior of the nuclear symmetry energy, the neutron skins, and the percentage of energy-weighted sum rule (EWSR) exhausted by the Pygmy Dipole Resonance (PDR) in 68Ni and 132Sn have been investigated by using different Random Phase Approximation (RPA) models for the dipole response, based on a representative set of Skyrme effective forces plus meson-exchange effective Lagrangians. A comparison with the experimental data has allowed us to constrain the value of the derivative of the symmetry energy at saturation. The neutron skin radius is deduced under this constraint…
The information on pygmy resonances reveals new aspects on the isospin dynamics of the nucleus with important astrophysical consequences. In this connection, the precise knowledge of nuclear response functions plays a key role in the determination of photonuclear reactions cross sections which are of importance for the synthesis of heavy neutron-rich elements. For that purpose, a theoretical method based on density functional theory and multi-phonon approach is applied for investigations of nuclear excitations with different multipolarities and energies in stable and exotic nuclei. The possibl…
The pygmy dipole resonances (PDR) for even-even nuclei in 8=<Z=<40 are studied performing a systematic calculation of the random-phase approximation with the Skyrme functional of SkM*. The calculation is fully self-consistent and does not assume any symmetry in the nuclear shape of the ground state. In every isotopic chain, the PDR emerges by showing a peak of the E1 strength at energies less than 10 MeV. The E1 strength of the PDR strongly depends on the position of the Fermi level and shows a clear correlation with the occupation of the orbits with the orbital angular momenta less than 3\hba…
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…
The accurate characterization of the nuclear symmetry energy and its density dependence is one of the outstanding open problems in nuclear physics. A promising nuclear observable in order to constrain the density dependence of the symmetry energy at saturation is the neutron skin thickness of medium and heavy nuclei. Recently, a low-energy peak in the isovector dipole response of neutron-rich nuclei has been discovered that may be correlated with the neutron skin thickness. The existence of this correlation is currently under debate due to our limited experimental knowledge on the microscopic …
The evolution of the low-energy electromagnetic dipole response with the neutron excess is investigated along the Sn isotopic chain within an approach incorporating Hartree-Fock-Bogoljubov (HFB) and multi-phonon Quasiparticle-Phonon-Model (QPM) theory. General aspects of the relationship of nuclear skins and dipole sum rules are discussed. Neutron and proton transition densities serve to identify the Pygmy Dipole Resonance (PDR) as a generic mode of excitation. The PDR is distinct from the GDR by its own characteristic pattern given by a mixture of isoscalar and isovector components. Results f…
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…
The evolution of the PDR strength with the neutron excess is investigated in Sn isotopic and N=82 isotonic chains with regard to its possible connection with the neutron skin thickness. For this purpose a recently proposed method incorporating both HFB and multi-phonon QPM theory is applied. Analysis of the corresponding neutron and proton dipole transition densities is presented.
A high-resolution study of the electromagnetic response of $^{206}$Pb below the neutron separation energy is performed using a ($\vecγ$,$γ'$) experiment at the HI$\vecγ$S facility. Nuclear resonance fluorescence with 100% linearly polarized photon beams is used to measure spins, parities, branching ratios, and decay widths of excited states in $^{206}$Pb from $4.9$ to $8.1$MeV. The extracted $Σ$$B$(E1)$\uparrow$ and $Σ$$B$(M1)$\uparrow$ values for the total electric and magnetic dipole strength below the neutron separation energy are 0.9$\pm$0.2e$^2$fm$^2$ and 8.3$\pm$2.0$μ_{N}^2$, respectivel…
I present a brief summary of the first three decades of studies of pygmy resonances in nuclei and their relation to the symmetry energy of nuclear matter. I discuss the first experiments and theories dedicated to study the electromagnetic response in halo nuclei and how a low energy peak was initially identified as a candidate for the pygmy resonance. This is followed by the description of a collective state in medium heavy and heavy nuclei which was definitely identified as a pygmy resonance. The role of the slope parameter of the symmetry energy in determining the properties of neutron stars…
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…
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 isotopic dependence of the excitation energies of the pygmy dipole resonance (PDR) is analyzed in the framework of the self-consistent relativistic Hartree-Bogoliubov (RHB) model and the relativistic quasiparticle random-phase approximation (RQRPA). The DD-ME1 density-dependent meson-exchange interaction is used in the effective mean-field Lagrangian, and pairing correlations are described by the pairing part of the finite-range Gogny interaction D1S. Model calculations reproduce available experimental data on charge radii, the neutron skin, neutron separation energies, and excitation ener…
The electric quadrupole response in $^{112,114}$Sn isotopes is investigated by energy-density functional (EDF) and three-phonon quasiparticle-phonon model (QPM) theory with special emphasis on 2$^+$ excitations located above the first collective quadrupole state and below 5 MeV. Additional quadrupole strength clustering as a sequence of states similar to the recently observed pygmy quadrupole resonance in $^{124}$Sn is found. The spectral distributions and transition densities of these 2$^+$ states show special features being compatible with oscillations of a neutron skin against the isospin-s…
Nuclear collective motion provides valuable constraint on the size of neutron-skin thickness and the properties of nuclear matter symmetry energy. By employing relativistic nuclear energy density functional (RNEDF) and covariance analysis related to $χ^2$ fitting of the model parameters, relevant observables are identified for dipole excitations, which strongly correlate with the neutron-skin thickness $(r_{np})$, symmetry energy at saturation density $(J)$ and slope of the symmetry energy $(L)$. Using the RNEDF framework and experimental data on pygmy dipole strength ($^{68}$Ni, $^{132}$Sn, $…
Laboratory experiments sensitive to the density dependence of the symmetry energy may place stringent constraints on the equation of state of neutron-rich matter and, thus, on the structure, dynamics, and composition of neutron stars. Understanding the equation of state of neutron-rich matter is a central goal of nuclear physics that cuts across a variety of disciplines. In this contribution I focus on how laboratory experiments on neutron skins and on both Pygmy and Giant resonances can help us elucidate the structure of neutron stars.
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.
Systematic studies of dipole and other multipole excitations in stable and exotic nuclei are discussed theoretically. Exploring the relation of the strengths of low-energy dipole and quadrupole pygmy resonances to the thickness of the neutron (proton) skin a close connection between static and dynamic properties of the nucleus is observed. The fine structure of low-energy dipole strength in 138Ba nucleus is revealed from E1 and spin-flip M1 strengths distributions.
We study theoretically the low-energy electric-dipole response of N=20 isotones. We present results from a quasiparticle random-phase approximation (QRPA) and a continuum random-phase approximation (CRPA), and we compare them with results for the mirror Z=20 nuclei. According to our analysis, enhanced E1 strength is expected energetically well below the giant dipole resonance in the proton-rich isotones. Large amounts of E1 strength in the asymmetric N=20 isotones are predicted, unlike their equally asymmetric Z=20 mirror nuclei, pointing unambiguously to the role of structural effects such as…
The relativistic random-phase approximation (RRPA) plus phonon-coupling (PC) model is applied in the analysis of E1 strength distributions in $^{208}$Pb and $^{132}$Sn, for which data on pygmy dipole resonances (PDR) have recently been reported. The covariant response theory is fully consistent: the effective nuclear interaction NL3 is used both to determine the spectrum of single-nucleon Dirac states, and as the residual interaction which determines the collective phonon states in the relativistic RPA. It is shown that the picture of the PDR as a resonant oscillation of the neutron skin again…
Understanding the equation of state (EOS) of neutron-rich matter is a central goal of nuclear physics that cuts across a variety of disciplines. Indeed, the limits of nuclear existence, the collision of energetic heavy ions, the structure of neutron stars, and the dynamics of core-collapse supernova all depend critically on the nuclear-matter EOS. In this contribution I focus on the EOS of cold baryonic matter with special emphasis on its impact on the structure, dynamics, and composition of neutron stars. In particular, I discuss how laboratory experiments on neutron skins as well as on Pygmy…
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…
Dipole excitations below the neutron threshold in neutron rich Sn isotopes are studied theoretically in the Quasiparticle-Phonon Model with HFB single particle input. Of special interest are the low-lying two-phonon 1- states and the Pygmy Dipole Resonance (PDR). The evolution of low-energy dipole excitations with neutron excess is investigated over the Sn isotopic chain including the experimentally unknown regions close to 132Sn. A dependence of the PDR strengths and centroid energies on the neutron skin thickness is found. Despite significant multi-phonon contributions to mean energies and t…
Recently, new low-energy modes of excitation called pygmy resonances have been observed. Their distinct feature is the close connection to nuclear skin oscillations. A successful description of the pygmy resonances could be achieved in a microscopic theoretical approach which incorporates the density functional theory and QRPA formalism extended with multi-phonon degrees of freedom. The latter is found of crucial importance for the understanding of the fine structure of nuclear electric and magnetic excitations at low energies. Corresponding microscopic multi-phonon response functions are impl…
The centroid, width and percentage of energy weighted sum rule of dipole resonances can be strongly affected by dynamical fluctuations and static deformations of the nuclear surface, deformations and fluctuations which, in turn, depend on pairing, and thus on Cooper pairs. Because of angular momentum conservation, such insight is restricted, to lowest order, to deformations of quadrupole and monopole type. The latter being closely connected with the neutron (excess) skin and thus with soft dipole modes. From the values $(N-Z)/A \approx 0.18$, 0.21, and 0.45 for the nuclei $^{122}$Sn, $^{208}$P…
We carry out a systematic study of electric dipole mode (E1) for neutron-rich isotopes from nickel (Z=28) to tin (Z=50) using a time-dependent mean-field theory. Our time-dependent scheme is the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory which can self-consistently describe nuclear dynamics with pairing correlation. We focus our discussion on the pygmy dipole resonance (PDR) and E1 polarizability. The correlation between neutron-skin thickness and PDR strongly depends on the neutron number, but the correlation between the skin thickness and E1 polarizability is much more sta…
Low-energy dipole excitations have been investigated theoretically in N=50, several N=82 isotones and the Z=50 Sn isotopes. For this purpose a method incorporating both HFB and multi-phonon QPM theory is applied. A concentration of one-phonon dipole strength located below the neutron emission threshold has been calculated in these nuclei. The analysis of the corresponding neutron and proton dipole transition densities allows to assign a genuine pattern to the low-energy excitations and making them distinct from the conventional GDR modes. Analyzing also the QRPA wave functions of the states we…
Background: The electric dipole strength detected around the particle threshold and commonly associated to the pygmy dipole resonance offers a unique information on neutron skin and symmetry energy, and is of astrophysical interest. The nature of such a resonance is still under debate. Purpose: We intend to describe the giant and pygmy resonances in 208 Pb by enhancing their fragmentation with respect to the random-phase approximation. Method: We adopt the equation of motion phonon method to perform a fully self-consistent calculation in a space spanned by one-phonon and two-phonon basis state…
Low-energy dipole excitations are analyzed for the stable isotopes $^{40}$Ca and $^{48}$Ca in the framework of the Skyrme-second random-phase approximation. The corresponding random-phase approximation calculations provide a negligible strength distribution for both nuclei in the energy region from 5 to 10 MeV. The inclusion and the coupling of 2 particle-2 hole configurations in the second random-phase approximation lead to an appreciable dipole response at low energies for the neutron-rich nucleus $^{48}$Ca. The presence of a neutron skin in the nucleus $^{48}$Ca would suggest the interpreta…
Giant resonances encapsulate the dynamic response of the nuclear ground state to external perturbations. As such, they offer a unique view of the nucleus that is often not accessible otherwise. Although interesting in their own right, giant resonances are also enormously valuable in providing stringent constraints on the equation of state of asymmetric matter. We this view in mind, we focus on two modes of excitation that are essential in reaching this goal: the isoscalar giant monopole resonance (GMR) and the isovector giant dipole resonance (GDR). GMR energies in heavy nuclei are sensitive t…
In 16O and 40Ca an isoscalar, low-energy dipole transition (IS-LED) exhausting approximately 4% of the isoscalar dipole (ISD) energy-weighted sum rule is experimentally known, but conspicuously absent from recent theoretical investigations of ISD strength. The IS-LED mode coincides with the so-called isospin-forbidden E1 transition. We report that for N=Z nuclei up to 100Sn the fully self-consistent Random-Phase-Approximation with finite-range forces, phenomenological and realistic, yields a collective IS-LED mode, typically overestimating its excitation energy, but correctly describing its IS…
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…
The low-lying dipole and quadrupole states in neutron rich nuclei, are studied within the fully self-consistent relativistic quasiparticle random-phase approximation (RQRPA), formulated in the canonical basis of the Relativistic Hartree-Bogoliubov model (RHB), which is extended to include the density dependent interactions. In heavier nuclei, the low-lying E1 excited state is identified as a pygmy dipole resonance (PDR), i.e. as a collective mode of excess neutrons oscillating against a proton-neutron core. Isotopic dependence of the PDR is characterized by a crossing between the PDR and one-n…
Inelastic proton scattering under extreme forward angles including $0^\circ$ and at energies of a few hundred MeV has been established as a new spectroscopic tool for the study of complete dipole strength distributions in nuclei. Such data allow an extraction of the electric dipole polarizability which provides important constraints parameters of the symmetry energy, which determine the neutron skin thickness and the equation of state (EOS) of neutron-rich matter. Also new insight into the much-debated nature of the pygmy dipole resonance (PDR) is obtained. Additionally, the isovector spin-M1 …
The determination of nuclear symmetry energy, and in particular, its density dependence, is a long-standing problem for nuclear physics community. Previous studies have found that the product of electric dipole polarizability $α_D$ and symmetry energy at saturation density $J$ has a strong linear correlation with $L$, the slope parameter of symmetry energy. However, current uncertainty of $J$ hinders the precise constraint on $L$. We investigate the correlations between electric dipole polarizability $α_D$ (or times symmetry energy at saturation density $J$) in Sn isotopes and the slope parame…
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…
The radiative neutron capture reaction rates of the r-process nucleosynthesis are immensely affected by the microscopic structure of the low-energy spectra of compound nuclei. The relativistic (quasiparticle) time blocking approximation (R(Q)TBA) has successfully provided a good description of the low-energy strength, in particular, the strength associated with pygmy dipole resonance, describing transitions from and to the nuclear ground state. The finite-temperature generalization of this method is designed for thermally excited compound nuclei and has the potential to enrich the fine structu…
