Spin and pseudospin symmetries in the antinucleon spectrum of nuclei

Abstract

Spin and pseudospin symmetries in the spectra of nucleons and antinucleons are studied in a relativistic mean-field theory with scalar and vector Woods-Saxon potentials, in which the strength of the latter is allowed to change. We observe that, for nucleons and antinucleons, the spin symmetry is of perturbative nature and it is almost an exact symmetry in the physical region for antinucleons. The opposite situation is found in the pseudospin symmetry case, which is better realized for nucleons than for antinucleons, but is of dynamical nature and cannot be viewed in a perturbative way for either nucleons or antinucleons. This is shown by computation of the spin-orbit and pseudospin-orbit couplings for selected spin and pseudospin partners in both spectra.

Spin and pseudospin symmetries in the Dirac equation with central Coulomb potentials

“…The structure (44) also holds for antiparticles in Woods-Saxon scalar and vector mean-field potentials, as shown in Refs. [3,6]. This may be because these potentials are finite at r = 0, as are the nuclear mean-field scalar and vector potentials, and thus the behavior of the respective radial functions at the origin is different from the present case of Coulomb potentials.…”

“…In this case, one cannot have exact spin symmetry (i.e., V = S) since now − = −(V − S) acts as binding potential. This behavior has been related by several authors to the perturbative nature of spin and pseudospin symmetry, namely that in the case of fermions (antifermions) the pseudospin (spin) symmetry is nonperturbative for nuclear mean-field potentials [6,[8][9][10]. Note, however, that for harmonic oscillator systems one can have exact pseudospin and spin symmetries for fermions and antifermions respectively [11].…”

“…In Ref. [6] one was able to show that in the limit of vanishing (spin) or (pseudospin) for nucleon and antinucleons respectively those spin-orbit or pseudospin-orbit terms fully account for the splitting of spin or pseudospin doublets. These terms can be obtained from the second-order radial equations for g κ (r) and f κ (r), respectively (see, for instance, Ref.…”

“…In previous works in which the perturbative nature of pseudospin (or spin in the case of antifermions) was related to the onset of the respective symmetry, one would either examine the effect the pseudospin-orbit or spin-orbit term on the energy splittings of the respective doublets [6,8,9] or analyze the convergence of a perturbation expansion in the respective potential strength [10]. In Ref.…”

“…However, for bound systems whose potentials go to zero at infinity, pseudospin symmetry cannot be realized, because = S + V (which must go to zero in the limit of exact pseudospin symmetry) is also the binding potential. Recently there has been a considerable interest in studying antifermions in the context of spin and pseudospin symmetries, for antinucleon systems [3][4][5][6] and antihyperons systems [7]. In this case, one cannot have exact spin symmetry (i.e., V = S) since now − = −(V − S) acts as binding potential.…”