arXiv subjects

Peter Ring

Publications and source records attributed to Peter Ring.

At least 37 records · Page 2Linked to original sources

arXiv2017

Leading order relativistic chiral nucleon-nucleon interaction

Motivated by the successes of relativistic theories in studies of atomic/molecular and nuclear systems and the need for a relativistic chiral force in relativistic nuclear structure studies, we explore a new relativistic scheme to construct the nucleon-nucleon interaction in the framework of covariant chiral effective field theory. The chiral interaction is formulated up to leading order with covariant power counting and a Lorentz invariant chiral Lagrangian. We find that the relativistic scheme induces all six spin operators needed to describe the nuclear force. A detailed investigation of the partial wave potentials shows a better description of the $^1S_0$ and $^3P_0$ phase shifts than the leading order Weinberg approach, and similar to that of the next-to-leading order Weinberg approach. For the other partial waves with angular momenta $J\geq 1$, the relativistic results are almost the same as their leading order non-relativistic counterparts.

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arXiv2017

Fully self-consistent relativistic Brueckner-Hartree-Fock theory for finite nuclei

Starting from the relativistic form of the Bonn potential as a bare nucleon-nucleon interaction, the full Relativistic Brueckner-Hartree-Fock (RBHF) equations are solved for finite nuclei in a fully self-consistent basis. This provides a relativistic ab initio calculation of the ground state properties of finite nuclei without any free parameters and without three-body forces. The convergence properties for the solutions of these coupled equations are discussed in detail at the example of the nucleus $^{16}$O. The binding energies, radii, and spin-orbit splittings of the doubly magic nuclei $^{4}$He, $^{16}$O, and $^{40}$Ca are calculated and compared with the earlier RBHF calculated results in a fixed Dirac Woods-Saxon basis and other non-relativistic ab initio calculated results based on pure two-body forces.

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arXiv2017

Spin-orbit splittings of neutron states in $N = 20$ isotones from covariant density functionals and their extensions

Spin-orbit splitting is an essential ingredient for our understanding of the shell structure in nuclei. One of the most important advantages of relativistic mean-field (RMF) models in nuclear physics is the fact that the large spin-orbit (SO) potential emerges automatically from the inclusion of Lorentz-scalar and -vector potentials in the Dirac equation. It is therefore of great importance to compare the results of such models with experimental data. We investigate the size of $2p$ and $1f$ splittings for the isotone chain $^{40}$Ca, $^{38}$Ar, $^{36}$S, and $^{34}$Si in the framework of various relativistic and nonrelativistic density functionals. They are compared with the results of nonrelativistic models and with recent experimental data.

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arXiv2017

Influence of pairing correlations on the radius of neutron-rich nuclei

The influence of pairing correlations on the neutron root mean square (rms) radius of nuclei is investigated in the framework of self-consistent Skyrme Hartree-Fock-Bogoliubov calculations. The continuum is treated appropriately by the Green's function techniques. As an example the nucleus $^{124}$Zr is treated for a varying strength of pairing correlations. We find that, as the pairing strength increases, the neutron rms radius first shrinks, reaches a minimum and beyond this point it expands again. The shrinkage is due to the the so-called `pairing anti-halo effect', i. e. due to the decreasing of the asymptotic density distribution with increasing pairing. However, in some cases, increasing pairing correlations can also lead to an expansion of the nucleus due to a growing occupation of so-called `halo' orbits, i.e. weakly bound states and resonances in the continuum with low-$\ell $ values. In this case, the neutron radii are extended just by the influence of pairing correlations, since these `halo' orbits cannot be occupied without pairing. The term `anti-halo effect' is not justified in such cases. For a full understanding of this complicated interplay self-consistent calculations are necessary.

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arXiv2016

Relativistic Brueckner-Hartree-Fock theory for finite nuclei

Starting with a bare nucleon-nucleon interaction, for the first time the full relativistic Brueckner-Hartree-Fock equations are solved for finite nuclei in a Dirac-Woods-Saxon basis. No free parameters are introduced to calculate the ground-state properties of finite nuclei. The nucleus $^{16}$O is investigated as an example. The resulting ground-state properties, such as binding energy and charge radius, are considerably improved as compared with the non-relativistic Brueckner-Hartree-Fock results and much closer to the experimental data. This opens the door for \emph{ab initio} covariant investigations of heavy nuclei.

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arXiv2013

Implementation of the finite amplitude method for the relativistic quasiparticle random-phase approximation

A new implementation of the finite amplitude method (FAM) for the solution of the relativistic quasiparticle random-phase approximation (RQRPA) is presented, based on the relativistic Hartree-Bogoliubov (RHB) model for deformed nuclei. The numerical accuracy and stability of the FAM -- RQRPA is tested in a calculation of the monopole response of $^{22}$O. As an illustrative example, the model is applied to a study of the evolution of monopole strength in the chain of Sm isotopes, including the splitting of the giant monopole resonance in axially deformed systems.

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arXiv2013

Relativistic two-phonon model for low-energy nuclear response

A two-phonon version of the relativistic quasiparticle time blocking approximation introduces as a new class of many-body models for nuclear structure calculations based on the covariant energy density functional. As a fully consistent extension of the relativistic quasiparticle random phase approximation, the relativistic two-phonon model implies fragmentation of nuclear states over two-quasiparticle and two-phonon configurations coupled to each other. In particular, we show how the lowest two-phonon $1^-$ state, identified as a member of the $[2^+\otimes 3^-]$ quintuplet, emerges from the coherent two-quasiparticle pygmy dipole mode in vibrational nuclei. The inclusion of the two-phonon configurations into the model space allows a quantitative description of the positions and the reduced transition probabilities of the lowest 1$^-$ states in tin isotopes $^{112,116,120,124}$Sn as well as the low-energy fraction of the dipole strength below the giant dipole resonance without any adjustment procedures. The model is applied to the low-lying dipole strength in neutron-rich $^{68,70,72}$Ni isotopes. Recent experimental data for $^{68}$Ni are reproduced fairly well.

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arXiv2013

Pairing strength on the nuclear size in relativistic continuum Hartree-Bogoliubov theory

The influence of pairing correlations on the nuclear size and in particular on the formation of nuclear halos is studied in the framework of relativistic continuum Hartree-Bogoliubov (RCHB) theory. It turns out that the contributions from the weakly-bound orbits with low orbital angular momenta $l$ play an important role. As an example, we investigate the neutron-rich Mg isotopes as a function of the pairing strength in situations, where the neuron Fermi surface are below, between and above two weakly-bound $2p$ levels. We find that the size of the pairing correlations has a two-fold influence on the density distribution of the neutrons and therefore on the total nuclear size. First it can change the root mean square (rms) radius of the individual weakly-bound orbits and second it can enhance the occupation probabilities of these orbits in the nuclear system. On one side increasing pairing correlations reduce the rms radii of the orbits with small orbital angular momenta close to the continuum limit (pairing anti-halo effect), on the other side they also can lead to an enhanced occupation of low-$l$ orbits above the Fermi surface producing in this way a strong increase of the total radius of the nuclear system. As a consequence, a nuclear halo can form even in cases, where non of the individual low-$l$ orbits is very close to the continuum. This leads to the fact that compared with well-bound nuclei, the impact of the pairing strength on the nuclear size is more pronounced in weakly-bound nuclei than in well-bound systems.

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arXiv2012

Localized form of Fock terms in nuclear covariant density functional theory

In most of the successful versions of covariant density functional theory in nuclei, the Fock terms are not included explicitly, which leads to local functionals and forms the basis of their widespread applicability at present. However, it has serious consequences for the description of Gamow-Teller resonances (GTR) and spin-dipole resonances (SDR) which can only be cured by adding further phenomenological parameters. Relativistic Hartree-Fock models do not suffer from these problems. They can successfully describe the GTR and SDR as well as the isovector part of the Dirac effective mass without any additional parameters. However, they are non-local and require considerable numerical efforts. By the zero-range reduction and the Fierz transformation, a new method is proposed to take into account the Fock terms in local functionals, which retains the simplicity of conventional models and provides proper descriptions of the spin-isospin channels and the Dirac masses.

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arXiv2011

Nuclear structure in strong magnetic fields: nuclei in the crust of a magnetar

Covariant density functional theory is used to study the effect of strong magnetic fields, up to the limit predicted for neutron stars (for magnetars $B \approx10^{18}$G), on nuclear structure. All new terms in the equation of motion resulting from time reversal symmetry breaking by the magnetic field and the induced currents, as well as axial deformation, are taken into account in a self-consistent fashion. For nuclei in the iron region of the nuclear chart it is found that fields in the order of magnitude of $10^{17}$G significantly affect bulk properties like masses and radii.

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arXiv2011

Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond

Relativistic energy density functionals (EDF) have become a standard tool for nuclear structure calculations, providing a complete and accurate, global description of nuclear ground states and collective excitations. Guided by the medium dependence of the microscopic nucleon self-energies in nuclear matter, semi-empirical functionals have been adjusted to the nuclear matter equation of state and to bulk properties of finite nuclei, and applied to studies of arbitrarily heavy nuclei, exotic nuclei far from stability, and even systems at the nucleon drip-lines. REDF-based structure models have also been developed that go beyond the static mean-field approximation, and include collective correlations related to the restoration of broken symmetries and to fluctuations of collective variables. These models are employed in analyses of structure phenomena related to shell evolution, including detailed predictions of excitation spectra and electromagnetic transition rates.

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arXiv2010

Nuclear halo structure and pseudo-spin symmetry

Nuclear halo structure and restoration of relativistic symmetry are studied within the framework of the relativistic Hartree-Fock-Bogoliubov (RHFB) theory. Giant halos as well as ordinary ones are found in Cerium isotopes close to the neutron drip line. Bridged by T=0 {channel}, the restoration of pseudo-spin symmetry (PSS) plays an essential role in stabilizing the neutron halo structures. The Fock terms, especially the $ρ$-tensor couplings, not only play significant role in the PSS restoration but also present substantial contributions to the T=0 {channel}, from which is well demonstrated the necessity of Fock terms.

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arXiv2009

Mode-coupling and the pygmy dipole resonance in a relativistic two-phonon model

A two-phonon version of the relativistic quasiparticle time blocking approximation (RQTBA-2) represents a new class of many-body models for nuclear structure calculations based on the covariant energy density functional. As a fully consistent extension of the relativistic quasiparticle random phase approximation (RQRPA), the two-phonon RQTBA implies a fragmentation of nuclear states over two-quasiparticle and two-phonon configurations. This leads, in particular, to a splitting-out of the lowest 1$^-$ state as a member of the two-phonon $[2^+\otimes3^-]$ quintuplet from the RQRPA pygmy dipole mode, thus establishing a physical mixing between these three modes. The inclusion of the two-phonon configurations in the model space allows to describe the positions and the reduced transition probabilities of the lowest 1$^-$ states in isotopes $^{116,120}$Sn as well as the low-energy fraction of the dipole strength without any adjustment procedures. The model is also applied to the low-lying dipole strength in neutron-rich $^{68,70,72}$Ni isotopes. Recent experimental data for $^{68}$Ni are reproduced fairly well.

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arXiv2009

Relativistic Hartree-Fock-Bogoliubov theory with Density Dependent Meson-Nucleon Couplings

Relativistic Hartree-Fock-Bogoliubov (RHFB) theory with density-dependent meson-nucleon couplings is presented. The integro-differential RHFB equations are solved by expanding the different components of the quasi-particle spinors in the complete set of eigen-solutions of the Dirac equations with Woods-Saxon potentials. Using the finite-range Gogny force D1S as an effective interaction in the pairing channel, systematic RHFB calculations are performed for Sn isotopes and N=82 isotones. It is demonstrated that an appropriate description of both mean field and pairing effects can be obtained within RHFB theory with finite range Gogny pairing forces. Better systematics are also found in the regions from the stable to the neutron-rich side with the inclusion of Fock terms, especially in the presence of $ρ$-tensor couplings.

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arXiv2009

A Separable Pairing Force for Relativistic Quasiparticle Random Phase Approximation

We have introduced a separable pairing force, which was adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. This separable pairing force is able to describe in relativistic Hartree-Bogoliubov (RHB) calculations the pairing properties in the ground state of finite nuclei on almost the same footing as the original Gogny interaction. In this work we investigate excited states using the Relativistic Quasiparticle Random Phase Approximation (RQRPA) with the same separable pairing force. For consistency the Goldstone modes and the convergence with various cutoff parameters in this version of RQRPA are studied. The first excited $2^+$ states for the chain of Sn-isotopes with Z=50 and the chain of isotones with N=82 isotones are calculated in RQRPA together with the $3^-$ states of Sn-isotopes. Comparing with experimental data and with the results of original Gogny force we find that this simple separable pairing interaction is very successful in depicting the pairing properties of vibrational excitations.

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arXiv2009

Axially deformed relativistic Hartree Bogoliubov with separable pairing force

A separable form of pairing interaction in the $^{1}S_{0}$ channel has been introduced and successfully applied in the description of both static and dynamic properties of superfluid nuclei. By adjusting the parameters to reproduce the pairing properties of the Gogny force in nuclear matter, this separable pairing force is successful in depicting the pairing properties of ground states and vibrational excitations of spherical nuclei on almost the same footing as the original Gogny force. In this article, we extend these investigations for Relativistic Hartree Bogoliubov theory in deformed nuclei with axial symmetry (RHBZ) using the same separable pairing interaction. In order to preserve translational invariance we construct one- and two-dimensional Talmi-Moshinsky brackets for the cylindrical harmonic oscillator basis. We show that the matrix elements of this force can then be expanded in a series of separable terms. The convergence of this expansion is investigated for various deformations. We observe a relatively fast convergence. This allows for a considerable reduction in computing time as compared to RHBZ-calculations with the full Gogny force in the pairing channel. As an example we solve the RHBZ equations with this separable pairing force for the ground states of the chain of Sm-isotopes. Good agreement with the experimental data as well as with other theoretical results is achieved.

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arXiv2008

The isovector dipole strength in nuclei with extreme neutron excess

The E1 strength is systematically analyzed in very neutron-rich Sn nuclei, beyond $^{132}$Sn until $^{166}$Sn, within the Relativistic Quasiparticle Random Phase Approximation. The great neutron excess favors the appearance of a deformed ground state for $^{142-162}$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 stable spherical nuclei like $^{132}$Sn for the experimental study of low-lying E1 strength.

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arXiv2008

Deformed relativistic Hartree-Bogoliubov model for exotic nuclei

A deformed relativistic Hartree-Bogoliubov (DRHB) model is developed aiming at a proper description of exotic nuclei, particularly deformed ones with large spatial extension. In order to give an adequate description of both the contribution of the continuum and the large spatial distribution in exotic nuclei, the DRHB equations are solved in a Woods-Saxon basis in which the radial wave functions have proper asymptotic behaviors at large distance from the nuclear center which is crucial for the formation of halo. The formalism and the numerical procedure of the DRHB model in a Woods-Saxon basis are briefly presented.

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