Pseudospin symmetry in relativistic framework with harmonic oscillator potential and Woods-Saxon potential

Based on the Dirac equation, we discuss the exact pseudospin symmetry and some examples are presented. For harmonic oscillator potential there exist bound states under the condition of the exact pseudospin symmetry, V-s + V-v = 0, and even usual intruder orbits will have degenerated pseudospin partners. Apart from the harmonic oscillator potential, a Woods-Saxon potential is introduced to eliminate the redundant degeneracies due to the speciality of harmonic oscillator potential except the pseudospin degeneracy.