Relativistic Quasiparticle Random Phase Approximation Research Articles

Relativistic QRPA description of nuclear excitations

Self-consistent relativistic mean-field models have been applied to the description of a variety of nuclear structure phenomena, not only in stable nuclei but also in systems far from the valley of β stability. The relativistic quasiparticle random-phase approximation (RQRPA) has been used to study dynamical aspects of exotic nuclear structure. Interesting results have been obtained for the evolution of low-lying dipole strength in neutron-rich nuclei and the isotopic dependence of the pygmy dipole resonance, the relation between the neutron skin of nuclei and the excitation energies of Gamow–Teller resonances and isobaric analog states, the occurrence of pygmy dipole states in proton-rich nuclei and beta-decay rates of r-process nuclei.

Exotic nuclear structure: Relativistic mean-field and beyond

The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions, and the geometry is restricted to axially symmetric shapes. The relativistic (quasiparticle) random-phase approximation is applied in the description of the evolution of low-lying dipole strength in neutron-rich and proton-rich nuclei.

Dynamics of Exotic Nuclear Systems: Covariant QRPA and Extensions

Quasiparticle Random Phase Approximation (QRPA) based on covariant density functional theory provides a universal and self-consistent description of collective and noncollective excitations in nuclei. So far is was only possible to investigate spherical nuclei and all the investigations have been restricted to 1 p -1 h (or two-quasiparticle) configurations. We report on recent progress in this field: (i) we perform fully self-consistent axially deformed QRPA calculations in the framework of relativistic models with nonlinear meson couplings and (ii) we go beyond the mean field approximation and use the collective phonons obtained in relativistic QRPA to construct dressed particle and hole configurations. This leads to an enhancement of the level density in the neighborhood of the Fermi surface and to an increasing fragmentation of the giant resonances. This allows a microscopic description of the corresponding damping mechanism.

Magnetic dipole moment of the first excited [formula omitted] state of [formula omitted] isotopes and [formula omitted] isotones in relativistic QRPA

Following relativistic quasiparticle random phase approximation we have calculated the magnetic dipole moment ( g factor) of the first excited 2 + sate in even- A spherical Z = 50 isotopes with A = 100 – 134 , and N = 82 isotones with A = 134 – 152 . The overall agreement with available experimental data is very satisfactory. We also discuss our findings in light of some other available theoretical results. However, these investigations also indicate that there is still a necessity to improve upon the values of the Lagrangian parameters in order to be able to describe well the properties of the excited states of nuclei over a wide range of mass numbers.

Calculation of β-decay rates in a relativistic model with momentum-dependent self-energies

The relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is applied in the calculation of \ensuremath{\beta}-decay half-lives of neutron-rich nuclei in the $Z\ensuremath{\approx}28$ and $Z\ensuremath{\approx}50$ regions. The study is based on the relativistic Hartree-Bogoliubov calculation of nuclear ground states, using effective Lagrangians with density-dependent meson-nucleon couplings, and also extended by the inclusion of couplings between the isoscalar meson fields and the derivatives of the nucleon fields. This leads to a linear momentum dependence of the scalar and vector nucleon self-energies. The residual QRPA interaction in the particle-hole channel includes the $\ensuremath{\pi}+\ensuremath{\rho}$ exchange plus a Landau-Migdal term. The finite-range Gogny interaction is employed in the $T=1$ pairing channel, and the model also includes a proton-neutron particle-particle interaction. The results are compared with available data, and it is shown that an extension of the standard relativistic mean-field framework to include momentum-dependent nucleon self-energies naturally leads to an enhancement of the effective (Landau) nucleon mass, and thus to an improved PN-QRPA description of ${\ensuremath{\beta}}^{\ensuremath{-}}$-decay rates.

Relativistic quasiparticle random phase approximation in deformed nuclei

The first results of the solution of the Relativistic Quasiparticle Random Phase Approximation (QRPA) in axial symmetry are presented. Three different relativistic density functionals have been implemented in a fully self-consistent fashion. Example applications for E1 and M1 excitations in 20Ne, 26Ne and 160Gd are studied.

Lowest lying2+and3−vibrational states in Pb, Sn, and Ni isotopes in relativistic quasiparticle random-phase approximation

The excitation energies and electric multipole decay rates of the lowest lying 2{sup +} and 3{sup -} vibrational states in Pb, Sn, and Ni nuclei are calculated following relativistic quasiparticle random-phase approximation formalism based on the relativistic Hartree-Bogoliubov mean field. Two sets of Lagrangian parameters, NL1 and NL3, are used to investigate the effect of the nuclear force. Overall there is good agreement with the available experimental data for a wide range of mass numbers considered here, and the NL3 set seems to be a better choice. However, strictly speaking, these studies point toward the need of a new set of force parameters that could produce more realistic single-particle levels, at least in vicinity of the Fermi surface, of a wide range of nuclear masses.

Relativistic quasiparticle random-phase approximation description of isoscalar compression modes in open-shell nuclei in theA≈60mass region

Very recent inelastic $\alpha$-scattering data on the isoscalar monopole and dipole strength distributions in $^{56}$Fe, $^{58}$Ni, and $^{60}$Ni are analyzed in the relativistic quasiparticle random-phase approximation (RQRPA) with the DD-ME2 effective nuclear interaction (nuclear matter compression modulus K$_{nm}= 251$ MeV). In all three nuclei the calculation nicely reproduces the observed asymmetric shapes of the monopole strength, and the bimodal structure of the dipole strength distributions. The calculated centroid and mean energies are in very good qualitative agreement with the experimental values both for the monopole, and for the low- and high-energy components of the dipole transition strengths. It is noted, however, that while DD-ME2 reproduces in detail the excitation energies of the giant monopole resonances (GMR) in nuclei with $A \ge 90$, the theoretical centroids are systematically above the experimental values in lighter nuclei with $A \leq 60$. The latter can be reproduced with an effective interaction with a lower value of K$_{nm} \approx $ 230 MeV but, because of the asymmetric shapes and pronounced fragmentation of the monopole strength distributions, isoscalar GMR data in light nuclei cannot provide accurate estimates of the nuclear matter compression modulus.

COVARIANT DENSITY FUNCTIONAL THEORY FOR COLLECTIVE EXCITATIONS IN NUCLEI FAR FROM STABILITY

Modern methods for the description of the nuclear many-body system use the concepts of density functional theory (DFT) and of effective field theory (EFT). Relativistic Hartree Bogoliubov (RHB) theory is a covariant version of this method, which takes into account Lorentz symmetry and pairing correlations in a fully self-consistent way. This theory has been used in the past for a very successful phenomenological description of ground state properties of nuclei all over the periodic table. Recently is also has been extended for the investigation of excited states. We discuss the calculation of rotational bands within cranked RHB-theory and recent investigations of vibrational excitations within the framework of relativistic Quasiparticle Random Phase Approximation (QRPA).

Study of the lowest [formula omitted] excitations and B(E2) transition strengths in relativistic QRPA for Sn-, and Pb-isotopes

In a relativistic quasiparticle random phase approximation (RQRPA) we have calculated the excitation energies of the first 2+ excited states and reduced B(E2;0+→2+) transition rates for very neutron-defficient to neutron-rich long chain of Sn-isotopes with even mass numbers A=100–136. In RQRPA approach this is the first such attempt and a very satisfactory agreement with the available experimental data is obtained. Furthermore, we predict a substantial rise of the B(E2) values at neutron magic numbers 50 and 82, where the E2 energy also goes up, rather substantially, compared to that for the immediate neighbours. This feature is quite similar to the already experimentally known behaviour of E2 and B(E2) around 208Pb, which are also well reproduced in the present calculation.

Collective excitations in the unitary correlation operator method and relativistic QRPA studies of exotic nuclei

The collective excitation phenomena in atomic nuclei are studied in two different formulations of the Random Phase Approximation (RPA): (i) RPA based on correlated realistic nucleon-nucleon interactions constructed within the Unitary Correlation Operator Method (UCOM), and (ii) relativistic RPA (RRPA) derived from effective Lagrangians with density-dependent meson-exchange interactions. The former includes the dominant interaction-induced short-range central and tensor correlations by means of an unitary transformation. It is shown that UCOM-RPA correlations induced by collective nuclear vibrations recover a part of the residual long-range correlations that are not explicitly included in the UCOM Hartree-Fock ground state. Both RPA models are employed in studies of the isoscalar monopole resonance (ISGMR) in closed-shell nuclei across the nuclide chart, with an emphasis on the sensitivity of its properties on the constraints for the range of the UCOM correlation functions. Within the Relativistic Quasiparticle RPA (RQRPA) based on Relativistic Hartree-Bogoliubov model, the occurrence of pronounced low-lying dipole excitations is predicted in nuclei towards the proton drip-line. From the analysis of the transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance.

Proton Electric Pygmy Dipole Resonance

The evolution of the low-lying E1 strength in proton-rich nuclei is analyzed in the framework of the self-consistent relativistic Hartree-Bogoliubov model and the relativistic quasiparticle random-phase approximation (RQRPA). Model calculations are performed for a series of N=20 isotones and Z=18 isotopes. For nuclei close to the proton drip line, the occurrence of pronounced dipole peaks is predicted in the low-energy region below 10 MeV excitation energy. From the analysis of the proton and neutron transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance.

Self-consistent relativistic QRPA studies of soft modes and spin-isospin resonances in unstable nuclei

The excitation phenomena in unstable nuclei are investigated in the framework of the relativistic quasiparticle random-phase approximation (RQRPA) in the relativistic Hartree-Bogoliubov model (RHB) which is extended to include effective interactions with explicit density-dependent meson-nucleon couplings. The properties of the pygmy dipole resonance (PDR) are examined in 132Sn and within isotopic chains, showing that already at moderate proton-neutron asymmetry the PDR peak energy is located above the neutron emission threshold. A method is suggested for determining the size of the neutron skin within an isotopic chain, based on the measurement of the excitation energies of the Gamow-Teller resonance relative to the isobaric analog state. In addition, for the first time the relativistic RHB + RQRPA model, with tensor ω meson-nucleon couplings, is employed in calculations of β-decay half-lives of nuclei of the relevance for the r-process.

New relativistic mean-field interaction with density-dependent meson-nucleon couplings

We adjust a new improved relativistic mean-field effective interaction with explicit density dependence of the meson-nucleon couplings. The effective interaction DD-ME2 is tested in relativistic Hartree-Bogoliubov and quasiparticle random-phase approximation (QRPA) calculations of nuclear ground states and properties of excited states, in calculation of masses, and it is applied to the analysis of very recent data on superheavy nuclei.

RELATIVISTIC DESCRIPTION OF EXOTIC COLLECTIVE EXCITATION PHENOMENA IN ATOMIC NUCLEI

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-neutron separation energies. Already at moderate proton–neutron asymmetry the PDR peak is calculated above the neutron emission threshold, indicating important implications for the observation of the PDR in (γ, γ′) scattering, and on the theoretical predictions of the radiative neutron capture rates in neutron-rich nuclei. In addition, a novel method is suggested for determining the neutron skin of nuclei, based on measurement of excitation energies of the Gamow–Teller resonance relative to the isobaric analog state.

β-decay rates ofr-process nuclei in the relativistic quasiparticle random phase approximation

The fully consistent relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is employed in the calculation of beta-decay half-lives of neutron-rich nuclei in the N$\approx$50 and N$\approx$82 regions. A new density-dependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic Hartree-Bogoliubov calculation of nuclear ground states and in the particle-hole channel of the PN-RQRPA. The finite range Gogny D1S interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The theoretical half-lives reproduce the experimental data for the Fe, Zn, Cd, and Te isotopic chains, but overestimate the lifetimes of Ni isotopes and predict a stable 132Sn.

Isotopic dependence of the pygmy dipole resonance

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 energies of isovector giant dipole resonances in Ni, Sn and Pb nuclei. In all three isotopic chains the one-neutron separation energies decrease with mass number much faster than the excitation energies of the PDR. As a result, already at moderate proton–neutron asymmetry the PDR peak energy is calculated above the neutron emission threshold. This result has important implications for the observation of the PDR in (γ,γ′) experiments.

Quasiparticle random phase approximation based on the relativistic Hartree-Bogoliubov model. II. Nuclear spin and isospin excitations

The proton-neutron relativistic quasiparticle random-phase approximation (PN-RQRPA) is formulated in the canonical single-nucleon basis of the relativistic Hartree-Bogoliubov model, for an effective Lagrangian characterized by density-dependent meson-nucleon couplings. The model includes both the $T=1$ and $T=0$ pairing channels. Pair configurations formed from the fully or partially occupied states of positive energy in the Fermi sea, and the empty negative-energy states from the Dirac sea, are included in PN-RQRPA configuration space. The model is applied to the analysis of charge-exchange modes: isobaric analog resonances and Gamow-Teller resonances.

Relativistic QRPA description of low-lying dipole strength in neutron-rich nuclei

The relativistic quasi-particle random phase approximation (RQRPA) is applied in the analysis of the evolution of isovector dipole response in nuclei with large neutron excess. In neutron-rich nuclei the dipole response is characterized by the fragmentation of the strength distribution and its spreading into the low-energy region. In light nuclei the onset of dipole strength in the low-energy region is due to non-resonant single-particle excitations of the loosely bound neutrons. In heavier neutron-rich nuclei low-lying dipole states appear which display a more distributed structure of the RQRPA amplitudes. For these nuclei a single collective dipole state is identified in the low-energy region, and an analysis of the corresponding transition densities and velocity distributions reveals the dynamics of the pygmy resonance.

Relativistic QRPA description of low-lying dipole strength in neutron-rich nuclei

The relativistic quasi-particle random phase approximation (RQRPA) is applied in the analysis of the evolution of isovector dipole response in nuclei with large neutron excess. In neutron-rich nuclei the dipole response is characterized by the fragmentation of the strength distribution and its spreading into the low-energy region. In light nuclei the onset of dipole strength in the low-energy region is due to non-resonant single-particle excitations of the loosely bound neutrons. In heavier neutron-rich nuclei low-lying dipole states appear which display a more distributed structure of the RQRPA amplitudes. For these nuclei a single collective dipole state is identified in the low-energy region, and an analysis of the corresponding transition densities and velocity distributions reveals the dynamics of the pygmy resonance.