Pseudospin symmetry as a relativistic dynamical symmetry in the nucleus

Relativistic Pseudospin Symmetry in Nuclei

Relativistic Pseudospin Symmetry as a Supersymmetric Pattern in Nuclei

The doublet structure (for n ≥ 1) is expressed in terms of a “pseudo” orbital angular momentum l̃ = l + 1 and “pseudo” spin, s̃ = 1/2, coupled to j = l̃ − 1/2 and j = l̃ + 1/2. For example, [ns1/2, (n − 1) d3/2] will have l̃ = 1, etc. The states in Eq. (1) involve only normal-parity shellmodel orbitals. The states (n = 0, l, j = l + 1/2), with aligned spin and no nodes, are not part of a doublet. Th...

Pseudospin symmetry and the relativistic harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r. Setting either or both combinations S=S+V and D=V−S to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies a...

On the Relativistic Foundations of Pseudospin Symmetry in Nuclei

We show that the generators of pseudospin symmetry are the non relativistic limit of the generators of an SU(2) symmetry which leaves invariant the Dirac Hamiltonian with scalar and vector potentials equal in magnitude but opposite in sign, VV = −VS. Furthermore, within this framework, we demonstrate that this symmetry may be approximately conserved for realistic scalar and vector potentials. P...

Relativistic Pseudospin Symmetry and the Structure of Nuclear States