Pseudo-spin Symmetry and Relativistic Single-nucleon Wave Functions

We show that the occurrence of approximate pseudo-spin symmetry in nuclei is connected with certain similarities in the relativistic single-nucleon wave functions of the corresponding pseudo-spin doublets. We perform a case study in which several examples and the systematics of this connection are explored. PACS numbers: 24.10.Jv, 21.60.Cs, 21.10.-k, 24.80+y. I. INTRODUCTION In a recent paper [1] it was shown that quasi-degenerate pseudo-spin doublets in nuclei, discovered almost thirty years ago [2,3], arise from the near equality in magnitude of attractive scalar, V S , and repulsive vector, V V , relativistic mean fields, V S ¸ \GammaV V , in which the nucleons move. Pseudo-spin doublets have non-relativistic quantum numbers (n r , `,j = ` + 1=2) and (n r \Gamma 1; ` + 2, j = ` + 3=2) where n r ,`, and J are the single-nucleon radial, orbital, and total angular momentum quantum numbers, respectively. These authors defined a "pseudo" orbital angular momentum ~ ` = ` + 1; for exam..