Hidden pseudospin and spin symmetries and their origins in atomic nuclei

TL;DR

This review discusses recent advances in understanding pseudospin and spin symmetries in atomic nuclei, highlighting their origins, extensions to various nuclear systems, and unresolved issues in the field.

Contribution

It provides a comprehensive overview of the latest progress on pseudospin and spin symmetries across diverse nuclear systems and potentials, including new theoretical insights and open questions.

Findings

PSS and SS are crucial for understanding nuclear structure and magic numbers.

Extensions of PSS to exotic, deformed, and non-local potentials have been developed.

Open issues include the perturbative nature and supersymmetric representations of these symmetries.

Abstract

Symmetry plays a fundamental role in physics. The quasi-degeneracy between single-particle orbitals $(n, l, j = l + 1/2)$ and $(n-1, l + 2, j = l + 3/2)$ indicates a hidden symmetry in atomic nuclei, the so-called pseudospin symmetry (PSS). Since the introduction of the concept of PSS in atomic nuclei, there have been comprehensive efforts to understand its origin. Both splittings of spin doublets and pseudospin doublets play critical roles in the evolution of magic numbers in exotic nuclei discovered by modern spectroscopic studies with radioactive ion beam facilities. Since the PSS was recognized as a relativistic symmetry in 1990s, many special features, including the spin symmetry (SS) for anti-nucleon, and many new concepts have been introduced. In the present Review, we focus on the recent progress on the PSS and SS in various systems and potentials, including extensions of the PSS study from stable to exotic nuclei, from non-confining to confining potentials, from local to non-local potentials, from central to tensor potentials, from bound to resonant states, from nucleon to anti-nucleon spectra, from nucleon to hyperon spectra, and from spherical to deformed nuclei. Open issues in this field are also discussed in detail, including the perturbative nature, the supersymmetric representation with similarity renormalization group, and the puzzle of intruder states.