1207.6211 (Haozhao Liang et al.)

Pseudospin symmetry in supersymmetric quantum mechanics: I.
Schrödinger equations    [PDF]

Haozhao Liang, Shihang Shen, Pengwei Zhao, Jie Meng

The origin of the pseudospin symmetry (PSS) and its breaking mechanism are explored by combining the supersymmetry (SUSY) quantum mechanics, perturbation theory, and similarity renormalization group (SRG) method. The Schr\"odinger 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 the so-called intruder states. In such way, the origin of PSS deeply hidden in $H$ can be traced in its SUSY partner Hamiltonian $\tilde{H}$. The perturbative nature of PSS 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 the increasing single-particle energies can also be interpreted in an explicit way.

View original: http://arxiv.org/abs/1207.6211