Pseudospin Symmetry as a Bridge between Hadrons and Nuclei

Abstract

Atomic nuclei exhibit approximate pseudospin symmetry. We review the arguments that this symmetry is a relativistic symmetry. The condition for this symmetry is that the sum of the vector and scalar potentials in the Dirac Hamiltonian is a constant. We give the generators of pseudospin symmetry. We review some of the predictions that follow from the insight that pseudospin symmetry has relativistic origins . We show that approximate pseudospin symmetry in nuclei predicts approximate spin symmetry in anti-nucleon scattering from nuclei. Since QCD sum rules predict that the sum of the scalar and vector potentials is small, we discuss the quark origins of pseudospin symmetry in nuclei and spin symmetry in hadrons.

Fermion interparticle potentials in 5D and a dimensional restriction prescription to 4D

“…Once S − is formed by two spin σ/2 and under parity satisfies S − ′ = − S − , we shall call it pseudo-spin. We highlight that the pseudo-spin we introduce here is not the same as the pseudo-spin that appears in other contexts; for example, in Condensed Matter Systems [23] and Nuclear Physics [24] [25].…”

Spin and Pseudo-Spin Symmetries in Radial Dirac Equation and Exceptional Hermite Polynomials

“…which are coefficients of first order derivative and derivative-free terms in (7). Let us apply a mapping to (7) given below…”

“…The experimental analysis of spin and pseudospin symmetries can be found in [6]. Moreover, the relevance of QCD sum rules with pseudospin symmetries were shown in [7]. Spin symmetry shows up in the spectrum of mesons with one heavy quark, also hadrons, antinucleons have spin symmetry [7].…”

“…Moreover, the relevance of QCD sum rules with pseudospin symmetries were shown in [7]. Spin symmetry shows up in the spectrum of mesons with one heavy quark, also hadrons, antinucleons have spin symmetry [7]. Pseudospin symmetry in heavy nuclei originates from the nucleons in a nucleus move in an attractive scalar and repulsive vector potential [8], [9] which is used to explain the observed degeneracies of some shell-model orbitals in nuclei.…”