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.
Highlights
Quarks in hadrons are relativistic while for the most part the properties of nuclei can be explained by non-relativistic physics
Pseudospin symmetry was later revealed to be a relativistic symmetry of the Dirac Hamiltonian [5,6]
QCD sum rules predict that the vector and scalar potentials of nucleons in nuclear matter approximately satisfy the conditions for pseudospin symmetry
Summary
Quarks in hadrons are relativistic while for the most part the properties of nuclei can be explained by non-relativistic physics. The states in question have quantum numbers (nj , n0 `0j0 ) where n0 = n − 1, `0 = ` + 2, j0 = j + 1 and n, `, j are the radial, orbital angular momentum, and total angular momentum quantum numbers, respectively [1,2]. These quasi-degeneracies persist in recent measurements in nuclei far from stability [3]. Pseudospin symmetry was later revealed to be a relativistic symmetry of the Dirac Hamiltonian [5,6].
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