arXiv subjects

Shihang Shen

Publications and source records attributed to Shihang Shen.

33 records · Page 2Linked to original sources

arXiv2021

Extended Lipkin-Meshkov-Glick Hamiltonian

The Lipkin-Meshkov-Glick (LMG) model was devised to test the validity of different approximate formalisms to treat many-particle systems. The model was constructed to be exactly solvable and yet non-trivial, in order to capture some of the main features of real physical systems. In the present contribution, we explicitly review the fact that different many-body approximations commonly used in different fields in physics clearly fail to describe the exact LMG solution. With similar assumptions as those adopted for the LMG model, we propose a new Hamiltonian based on a general two-body interaction. The new model (Extended LMG) is not only more general than the original LMG model and, therefore, with a potentially larger spectrum of applicability, but also the physics behind its exact solution can be much better captured by common many-body approximations. At the basis of this improvement lies a new term in the Hamiltonian that depends on the number of constituents and polarizes the system; the associated symmetry breaking is discussed, together with some implications for the study of more realistic systems.

nucl-th↗

arXiv2020

Particle-vibration coupling for giant resonances beyond the diagonal approximation

A self-consistent particle-vibration coupling (PVC) model without diagonal approximation is presented. The diagonal approximation, that neglects completely the interaction between the doorway states, has been removed by taking into account the interaction between the two particle-holes inside the doorway states. As applications, isoscalar giant monopole, dipole, and quadrupole resonances in 16O are investigated based on the use of Skyrme functionals. The diagonal approximation is found to clearly impact the strength distribution of the giant quadrupole resonance, and the description of the experimental data is improved without this approximation. The impact of the diagonal approximation is analyzed in detail, especially its effect on the eigenenergies and the induced coupling between neutron and proton particle-hole configurations. The latter is a direct and physically sound effect of the improvement on our formalism. The importance of using self-consistently the full effective interaction in the PVC vertex, and the effect of its renormalization via the subtraction method, are also discussed. For completeness, we also analyze the dependence of our results on the Skyrme parametrization.

nucl-th↗

arXiv2019

Volution of nuclear spin-orbit splittings with Skyrme functional SAMi-T

A new Skyrme functional has been developed with tensor term guided by ab initio relativistic Brueckner-Hartree-Fock (RBHF) studies on neutron-proton drops. Instead of extracting information on the tensor force from experimental single-particle energy splittings, the RBHF calculations do not contain beyond mean-field effects such as particle-vibration coupling and therefore the information on the tensor force can be obtained without ambiguities. The new functional gives a good description of nuclear ground-state properties as well as various giant resonances. The description for the evolution of single-particle energy splittings is also improved by the new functional.

nucl-th↗

arXiv2019

Skyrme Functional with Tensor Terms from ab initio Calculations: Results for the Spin-Orbit Splittings

A new Skyrme functional including tensor terms is presented. The tensor terms have been determined by fitting the results of relativistic Brueckner-Hartree-Fock (RBHF) studies on neutron-proton drops. Unlike all previous studies, where the tensor terms were usually determined by fitting to experimental data of single-particle levels, the pseudodata calculated by RBHF does not contain beyond mean-field effect such as the particle-vibration coupling and, therefore, can provide information on the tensor term without ambiguities. The obtained new functional, named SAMi-T, can describe well ground-state properties such as binding energies, radii, spin-orbit splittings and, at the same time, the excited state properties such as those of the Giant Monopole Resonance (GMR), Giant Dipole Resonance (GDR), Gamow-Teller Resonance (GTR), and Spin-Dipole Resonance (SDR).

nucl-th↗

arXiv2019

Towards an ab initio covariant density functional for nuclear structure

Nuclear structure models built from phenomenological mean fields, the effective nucleon-nucleon interactions (or Lagrangians), and the realistic bare nucleon-nucleon interactions are reviewed. The success of covariant density functional theory (CDFT) to describe nuclear properties and its influence on Brueckner theory within the relativistic framework are focused upon. The challenges and ambiguities of predictions for unstable nuclei without data or for high-density nuclear matter, arising from relativistic density functionals, are discussed. The basic ideas in building an ab initio relativistic density functional for nuclear structure from ab initio calculations with realistic nucleon-nucleon interactions for both nuclear matter and finite nuclei are presented. The current status of fully self-consistent relativistic Brueckner-Hartree-Fock (RBHF) calculations for finite nuclei or neutron drops (ideal systems composed of a finite number of neutrons and confined within an external field) is reviewed. The guidance and perspectives towards an ab initio covariant density functional theory for nuclear structure derived from the RBHF results are provided.

nucl-th↗

arXiv2019

Skyrme functional with tensor terms from \textit{ab initio} calculations of neutron-proton drops

A new Skyrme functional devised to account well for standard nuclear properties as well as for spin and spin-isospin properties is presented. The main novelty of this work relies on the introduction of tensor terms guided by \textit{ab initio} relativistic Brueckner-Hartree-Fock calculations of neutron-proton drops. The inclusion of tensor term does not decrease the accuracy in describing bulk properties of nuclei, experimental data of some selected spherical nuclei such as binding energies, charge radii, and spin-orbit splittings can be well fitted. The new functional is applied to the investigation of various collective excitations such as the Giant Monopole Resonance (GMR), the Isovector Giant Dipole Resonance (IVGDR), the Gamow-Teller Resonance (GTR), and the Spin-Dipole Resonance (SDR). The overall description with the new functional is satisfactory and the tensor terms are shown to be important particularly for the improvement of the Spin-Dipole Resonance results. Predictions for the neutron skin thickness based on the non-energy weighted sum rule of the Spin-Dipole Resonance are also given.

nucl-th↗

arXiv2018

Relativistic Brueckner-Hartree-Fock theory for neutron drops

Neutron drops confined in an external field are studied in the framework of relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. The ground state energies and radii of neutron drops with even numbers from $N = 4$ to $N=50$ are calculated and compared with results obtained from other nonrelativistic \textit{ab initio} calculations and from relativistic density functional theory. Special attention has been paid to the magic numbers and to the sub-shell closures. The single-particle energies are investigated and the monopole effect of the tensor force on the evolutions of the spin-orbit and the pseudospin-orbit splittings is discussed. The results provide interesting insight of neutron rich systems and can form an important guide for future density functionals.

nucl-th↗

arXiv2018

Spin symmetry in the Dirac sea derived from the bare nucleon-nucleon interaction

The spin symmetry in the Dirac sea has been investigated with relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. Taking the nucleus $^{16}$O as an example and comparing the theoretical results with the data, the definition of the single-particle potential in the Dirac sea is studied in detail. It is found that if the single-particle states in the Dirac sea are treated as occupied states, the ground state properties are in better agreement with experimental data. Moreover, in this case, the spin symmetry in the Dirac sea is better conserved and it is more consistent with the findings using phenomenological relativistic density functionals.

nucl-th↗

arXiv2018

Effects of Tensor Force in the Relativistic Scheme: A Case Study of Neutron Drops

Tensor force is an important component in the nucleon-nucleon interaction, nevertheless, the role of the tensor force in the spin properties in finite nuclei is much less clear. In this report, we mainly focus on our recent progress on this topic about the relativistic Brueckner-Hartree-Fock theory and the corresponding tensor effects on the spin-orbit splittings in neutron drops. This will serve as an important guide for future microscopic derivations of the relativistic and non-relativistic nuclear energy density functionals.

nucl-th↗

arXiv2018

Effects of tensor forces in nuclear spin-orbit splittings from ab initio calculations

A systematic and specific pattern due to the effects of the tensor forces is found in the evolution of spin-orbit splittings in neutron drops. This result is obtained from relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. It forms an important guide for future microscopic derivations of relativistic and nonrelativistic nuclear energy density functionals.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗

arXiv2013

Pseudospin symmetry: Recent progress with supersymmetric quantum mechanics

It is an interesting and open problem to trace the origin of the pseudospin symmetry in nuclear single-particle spectra and its symmetry breaking mechanism in actual nuclei. In this report, we mainly focus on our recent progress on this topic by combining the similarity renormalization group technique, supersymmetric quantum mechanics, and perturbation theory. We found that it is a promising direction to understand the pseudospin symmetry in a quantitative way.

nucl-th↗

arXiv2013

Pseudospin symmetry in supersymmetric quantum mechanics: II. Spin-orbit effects

Following a previous paper [Haozhao Liang \textit{et al.}, Phys. Rev. C \textbf{87}, 014334 (2013)], we discuss the spin-orbit effects on the pseudospin symmetry (PSS) within the framework of supersymmetric quantum mechanics. By using the perturbation theory, we demonstrate that the perturbative nature of PSS maintains when a substantial spin-orbit potential is included. With the explicit PSS-breaking potential, the spin-orbit effects on the pseudospin-orbit splittings are investigated in a quantitative way.

nucl-th↗

arXiv2013

Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations

The origin of pseudospin symmetry (PSS) and its breaking mechanism are explored by combining supersymmetry (SUSY) quantum mechanics, perturbation theory, and the similarity renormalization group (SRG) method. The Schrödinger equation is taken as an example, corresponding to the lowest-order approximation in transforming a Dirac equation into a diagonal form by using the SRG. It is shown that while the spin-symmetry-conserving term appears in the single-particle Hamiltonian $H$, the PSS-conserving term appears naturally in its SUSY partner Hamiltonian $\tilde{H}$. The eigenstates of Hamiltonians $H$ and $\tilde{H}$ are exactly one-to-one identical except for the so-called intruder states. In such a way, the origin of PSS deeply hidden in $H$ can be traced in its SUSY partner Hamiltonian $\tilde{H}$. The perturbative nature of PSS in the present potential without spin-orbit term is demonstrated by the perturbation calculations, and the PSS-breaking term can be regarded as a very small perturbation on the exact PSS limits. A general tendency that the pseudospin-orbit splittings become smaller with increasing single-particle energies can also be interpreted in an explicit way.

nucl-th↗