Isovector Dipole Strength Research Articles

Effects of ground-state correlations on the damping of giant dipole resonances in LS closed-shell nuclei

Abstract The effects of ground-state correlations on the damping of isovector giant dipole resonances in the LS closed-shell nuclei 16O and 40Ca are studied using extended random phase approximation (RPA) approaches derived from the time-dependent density matrix theory. It is pointed out that unconventional two-body amplitudes of one-particle–three-hole and three-particle–one-hole types that are neglected in most extended RPA theories play an important role in the fragmentation of isovector dipole strength.

Nuclear excitations within microscopic EDF approaches: Pairing and temperature effects on the dipole response

In the present work, the isovector dipole responses, both in the resonance region and in the low-energy sector, are investigated using the microscopic nuclear Energy Density Functionals (EDFs). The self-consistent QRPA model based on Skyrme Hartree Fock BCS approach is applied to study the evolution of the isovector dipole strength by increasing neutron number and temperature. First, the isovector dipole strength and excitation energies are investigated for the Ni isotopic chain at zero temperature. The evolution of the low-energy dipole strength is studied as a function of the neutron number. In the second part, the temperature dependence of the isovector dipole excitations is studied using the self-consistent finite temperature QRPA, below and above the critical temperatures. It is shown that new excited states become possible due to the thermally occupied states above the Fermi level, and opening of the new excitations channels. In addition, temperature leads to fragmentation of the low-energy strength around the neutron separation energies, and between 9 and 12 MeV. We find that the cumulative sum of the strength below E$\leq12$ MeV decreases in open-shell nuclei due to the vanishing of the pairing correlations as temperature increases up to T=1 MeV. The analysis of the transition densities in the low-energy region shows that the proton and neutron transition densities display a mixed pattern: both isoscalar and isovector motion of protons and neutrons are obtained inside nuclei, while the neutron transition density is dominant at the surface region.

Self-consistent Hartree–Fock RPA calculations in 208Pb

The nuclear structure of 208Pb is studied in the framework of the self-consistent random phase approximation (SCRPA). The Hartree–Fock mean field and single particle states are used to implement a completely SCRPA with Skyrme-type interactions. The Hamiltonian is diagonalised within a model space using five Skyrme parameter sets, namely LNS, SkI3, SkO, SkP and SLy4. In view of the huge number of the existing Skyrme-force parameterizations, the question remains which of them provide the best description of data. The approach attempts to accurately describe the structure of the spherical even–even nucleus 208Pb. To illustrate our approach, we compared the binding energy, charge density distribution, excitation energy levels scheme with the available experimental data. Moreover, we calculated isoscalar and isovector monopole, dipole, and quadrupole transition densities and strength functions.

Electric Dipole States and Time Reversal Violation in Nuclei.

The nuclear Schiff moment is essential in the mechanism that induces a parity and time reversal violation in the atom. In this presentation we explore theoretically the properties and systematics of the isoscalar dipole in nuclei with the emphasis on the low-energy strength and the inverse energy weighted sum which determines the Schiff moment. We also study the influence of the isovector dipole strength distribution on the Schiff moment. The influence of a large neutron excess in nuclei is examined. The centroid energies of the isoscalar giant resonance (ISGDR) and the overtone of the isovector giant dipole resonance (OIVGDR) are given for a range of nuclei.

Isovector dipole-resonance structure within the effective surface approximation

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.

Isoscalar and isovector dipole strength distributions in nuclei and the Schiff moment

It was pointed out that the isoscalar dipole strength distribution in nuclei contributes to the Schiff moment. The nuclear Schiff moment is essential in the mechanism that induces parity and time-reversal violations in the atom. In this paper, we explore, theoretically, the properties and systematics of the isoscalar dipole in nuclei with an emphasis on the low-energy strength and the inverse energy-weighted sum which determines the Schiff moment. We also study the influence of the isovector dipole strength distribution on the Schiff moment. The influence of large neutron excess in exotic nuclei is examined. The centroid energies of the isoscalar giant dipole resonance and the overtone of the isovector giant dipole resonance are given for a wide range of nuclei.

Linear responses in time-dependent Hartree-Fock-Bogoliubov method with Gogny interaction

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 quadrupole and isovector dipole strength functions are calculated from the expectation values of the isoscalar quadrupole and isovector dipole moments.

Finite temperature effects on monopole and dipole excitations

The relativistic random phase approximation based on effective Lagrangian with density dependent meson-nucleon couplings has been extended to finite temperature and employed in studies of multipole excitations within the temperature range T = 1 − 2 MeV. The model calculations showed that isoscalar giant monopole and isovector giant dipole resonances are only slightly modified with temperature, but additional transition strength appears at low energies because of thermal unblocking of single-particle orbitals close to the Fermi level. The analysis of low-lying states shows that isoscalar monopole response in 132Sn results from single particle transitions, while the isovector dipole strength for 60Ni, located around 10 MeV, is composed of several single particle transitions, accumulating a small degree of collectivity.

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.

Isovector dipole strength in nuclei with extreme neutron excess

The $E1$ strength is systematically analyzed in very neutron-rich Sn nuclei, beyond $^{132}\mathrm{Sn}$ until $^{166}\mathrm{Sn}$, within the relativistic quasiparticle random phase approximation. The great neutron excess favors the appearance of a deformed ground state for $^{142\ensuremath{-}162}\mathrm{Sn}$. The evolution of the low-lying strength in deformed nuclei is determined by the interplay of two factors, isospin asymmetry and deformation: while greater neutron excess increases the total low-lying strength, deformation hinders and spreads it. Very neutron rich deformed nuclei may not be as good candidates as spherical nuclei like $^{132}\mathrm{Sn}$ for the experimental study of low-lying $E1$ strength.

Low-lying dipole resonance in neutron-rich Ne isotopes

Microscopic structure of the low-lying isovector dipole excitation mode in neutron-rich $^{26,28,30}\mathrm{Ne}$ is investigated by performing deformed quasiparticle-random-phase-approximation (QRPA) calculations. The particle-hole residual interaction is derived from a Skyrme force through a Landau-Migdal approximation. We obtain the low-lying resonance in $^{26}\mathrm{Ne}$ at around 8.6 MeV. It is found that the isovector dipole strength at ${E}_{x}<10$ MeV exhausts about 6.0% of the classical Thomas-Reiche-Kuhn dipole sum rule. This excitation mode is composed of several QRPA eigenmodes, one is generated by a $\ensuremath{\nu}(2{s}_{1/2}^{\ensuremath{-}1}2{p}_{3/2})$ transition dominantly and the other mostly by a $\ensuremath{\nu}(2{s}_{1/2}^{\ensuremath{-}1}2{p}_{1/2})$ transition. The neutron excitations take place outside of the nuclear surface reflecting the spatially extended structure of the $2{s}_{1/2}$ wave function. In $^{30}\mathrm{Ne}$, the deformation splitting of the giant resonance is large, and the low-lying resonance overlaps with the giant resonance.

Microscopic description of the low lying and high lying electric dipole strength in stable Ca isotopes

Abstract The properties of the low lying and high lying electric dipole strength in the stable 40Ca, 44Ca and 48Ca isotopes have been calculated within the Extended Theory of Finite Fermi Systems (ETFFS). This approach is based on the random phase approximation (RPA) and includes the single particle continuum as well as the coupling to low lying collective states which are considered in a consistent microscopic way. For 44Ca we also include pairing correlations. We obtain good agreement with the existing experimental data for the gross properties of the low lying and high lying strength. It is demonstrated that the recently measured A-dependence of the electric dipole strength below 10 MeV is well understood in our model: due to the phonon coupling some of the strength in 48Ca is simply shifted beyond 10 MeV. The predicted fragmentation of the strength can be investigated in ( e , e ′ ) and ( γ , γ ′ ) experiments. The isovector dipole strength below 10 MeV is small in all Ca isotopes. Surprisingly, the proton and neutron transition densities of these low lying electric dipole states are in phase, which indicate isoscalar structure. We conclude that for the detailed understanding of the structure of excited nuclei e.g. the low lying and high lying electric dipole strength an approach like the present one is absolutely necessary.

Pygmy dipole resonance as a constraint on the neutron skin of heavy nuclei

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 use the recently measured Pygmy dipole resonance in 130Sn and 132Sn to discriminate among theoretical models? For the first question we found that while a strong correlation between the neutron skin and the Pygmy dipole resonance exists, a mild anti-correlation develops beyond 120Sn. The answer to the second question suggests that models with overly large neutron skins--and thus stiff symmetry energies--are in conflict with experiment.

Dipole giant resonances in deformed heavy nuclei

The spectral distribution of isovector dipole strength is computed using the time-dependent Skyrme-Hartree-Fock method with subsequent spectral analysis. The calculations are done without any imposed symmetry restriction, allowing any nuclear shape to be dealt with. The scheme is used to study the deformation dependence of giant resonances and its interplay with Landau fragmentation (owing to 1ph states). Results are shown for the chain of Nd isotopes, superdeformed $^{152}\mathrm{Dy}$, triaxial $^{188}\mathrm{Os}$, and $^{238}\mathrm{U}$.

Self-consistent description of multipole strength in exotic nuclei: Method

We use the canonical Hartree-Fock-Bogoliubov basis to implement a completely self-consistent quasiparticle-random-phase approximation with arbitrary Skyrme energy density functionals and density-dependent pairing functionals. The point of the approach is to accurately describe multipole strength functions in spherical even-even nuclei, including weakly-bound drip-line systems. We describe the method and carefully test its accuracy, particularly in handling spurious modes. To illustrate our approach, we calculate isoscalar and isovector monopole, dipole, and quadrupole strength functions in several Sn isotopes, both in the stable region and at the drip lines.

Unmasking the nuclear matter equation of state

Accurately calibrated (or ``best fit'') relativistic mean-field models are used to compute the distribution of isoscalar monopole strength in 90Zr and 208Pb, and the isovector dipole strength in 208Pb using a continuum random-phase-approximation approach. It is shown that the distribution of isoscalar monopole strength in 208Pb--but not in 90Zr--is sensitive to the density dependence of the symmetry energy. This sensitivity hinders the extraction of the compression modulus of symmetric nuclear matter from the isoscalar giant monopole resonance (ISGMR) in 208Pb. Thus, one relies on 90Zr, a nucleus with both a small neutron-proton asymmetry and a well developed ISGMR peak, to constrain the compression modulus of symmetric nuclear matter to the range K=(248 +/- 6) MeV. In turn, the sensitivity of the ISGMR in 208Pb to the density dependence of the symmetry energy is used to constrain its neutron skin to the range Rn-Rp<=0.22 fm. The impact of this result on the enhanced cooling of neutron stars is briefly addressed.

Quasiparticle random phase approximation based on the relativistic Hartree-Bogoliubov model

The relativistic quasiparticle random phase approximation (RQRPA) is formulated in the canonical single-nucleon basis of the relativistic Hartree-Bogoliubov (RHB) model. For the interaction in the particle-hole channel effective Lagrangians with nonlinear meson self-interactions are used, and pairing correlations are described by the pairing part of the finite range Gogny interaction. The RQRPA configuration space includes the Dirac sea of negative energy states. Both in the particle-hole and particle-particle channels, the same interactions are used in the RHB calculation of the ground state and in the matrix equations of the RQRPA. The RHB+RQRPA approach is tested in the example of multipole excitations of neutron rich oxygen isotopes. The RQRPA is applied in the analysis of the evolution of the low-lying isovector dipole strength in Sn isotopes and N=82 isotones.

The Giant Dipole Resonance in Ar-Isotopes in the Relativistic RPA

The isovector giant dipole resonance in Ar-isotopes is studied in the framework of the relativistic random phase approximation starting from effective Lagrangians originally pro­ posed for describing nuclear ground states. The calculations are done with the parameter set TMI which satisfactorily describes the ground states of stable and unstable nuclei up to the drip lines. It is found that the isovector dipole strength in nuclei near drip lines is split into two components: one peaks at the normal giant dipole energy, the other is located at low energy. The lower dipole state is due to the weakly bound neutron (or proton) excitation, which may cause large cross-sections in collisions with heavy nuclei by Coulomb excitation.

Low energy strength in low-multipole response function of nuclei near the neutron drip line.

The very low-energy transition strength unique in neutron drip line neclei is studied, taking an example of $_{8}^{28}\mathrm{O}_{20}$ and performing the Hartree-Fock plus RPA calculation with Skyrme interaction. The most dramatic example is monopole modes, however, an appreciable amount of isovector dipole strength may appear also in the very low excitation energy. Unperturbed response functions are carefully studied, which contain all basic information on the exotic behavior of the RPA strength function. The low-energy transition strength is induced by the excitations of neutrons, which have smaller binding energies and smaller angular momenta. The neutrons with a few MeV binding energies are sufficient for obtaining this strength, and the phenomena are differentiated from the so-called soft multipole excitations in halo nuclei.

Spreading effects on the isovector dipole strength distribution in 208Pb

There is seemingly a difficulty with all Hartree-Fock RPA calculations to describe correctly the distribution of dipole strength in heavy nuclei above the giant dipole region. We investigate in a consistent framework the effects of damping into more complex configurations. We show that in 208Pb, this damping leads to a smooth distribution at higher energies while it gives a satisfactory description of the spreading width of the giant dipole resonance.