Shihang Shen

Pseudospin symmetry in supersymmetric quantum mechanics: Schrodinger equations

The origin of pseudospin symmetry (PSS) and its breaking mechanism are explored by combining supersymmetry (SUSY) quantum mechanics, perturbation theory, and the similarity renormaliza- tion group (SRG) method. The Schrodinger 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 ˜ H. The eigenstates of Hamiltonians H and ˜

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

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

^{16}

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

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.

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

Following a previous paper [Haozhao Liang et al., Phys. Rev. C 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.

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

Abstract 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.

Pseudospin symmetry: Recent progress with supersymmetric quantum mechanics

CITATION: Shen, S., et al. 2017. Fully self-consistent relativistic Brueckner-Hartree-Fock theory for finite nuclei. Physical Review C, 96(1):1-19, doi:10.1103/PhysRevC.96.014316.

Signature for rotational to vibrational evolution along the yrast line

Abstract 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.

Relativistic Brueckner-Hartree-Fock in nuclear matter without the average momentum approximation.

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.

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

The excitation spectra of nuclei in the regions 150<A<190 and 220<A<250 are commonly considered as showing characteristics of the rotational motion. In the present work, however, there is evidence indicating that the nuclei can evolve from rotation to vibration. We have used two simple models to discuss the collective motions of a nucleus for different spin ranges. In addition, in order to get the insight into the rotational-like properties of nuclei, as an example, shape calculations using the total Routhian surfaces (TRS) model have been carried out for positive-parity states in {sup 156}Gd. Also we have shown the result of the nucleus {sup 102}Ru which is given as an example of the reverse transition, i.e., vibration to rotation. The TRS plots reveal that, with increasing spin, the former nucleus becomes slightly soft in {gamma} and {beta} deformations, while the latter one becomes rigid in the {gamma} deformation.