Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations

Abstract

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.

31 pages, 11 figures, 2 tables

References in corpus (23)

• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• Nuclear magic numbers: new features far from stability
• Collapse of the N=28 shell closure in ${}^{42}$Si
• Shell Structure and $\rho$-Tensor Correlations in Density-Dependent Relativistic Hartree-Fock theory
• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Pseudospin symmetry in single particle resonant states
• Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator
• Nuclear halo structure and pseudo-spin symmetry
• Pseudo-spin symmetry in density-dependent relativistic Hartree-Fock theory
• Non-local mean field effect on nuclei near Z=64 sub-shell
• Perturbative interpretation of relativistic symmetries in nuclei
• Spin symmetry in Dirac negative energy spectrum in density-dependent relativistic Hartree-Fock theory
• Isospin dependence of pseudospin symmetry in nuclear resonant states
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles
• A mean field study of single-particle spectra evolution in Z=14 and N=28 chains
• Symmetries and Supersymmetries of the Dirac Hamiltonian with Axially-Deformed Scalar and Vector Potentials
• Pseudospin, supersymmetry and the shell structure of atomic nuclei
• Generalized Spin and Pseudo-Spin Symmetry: Relativistic Extension of Supersymmetric Quantum Mechanics
• Dynamical symmetry of Dirac hydrogen atom with spin symmetry and its connection with Ginocchio's oscillator
• Relativistic U(3) Symmetry and Pseudo-U(3) Symmetry of the Dirac Hamiltonian
• Pseudospin symmetry and structure of nuclei with $Z\ge$ 100
• Supersymmetric analysis for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions

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