The Resurrection of a Symmetry in Nucleon - Nucleus Scattering

We re-examine a symmetry in nucleon nucleus scattering that previously had been proclaimed to be dead. We show that this symmetry is the continuum analog of pseudospin symmetry, a relativistic symmetry which manifests itself in the spectra of nuclei. Using experimental data only we show that pseudospin symmetry in nucleon nucleus scattering is not dead but only modestly broken for 800 MeV proton scattering on nuclei. Typeset using REVTEX 1 For nucleons moving in a relativistic mean field with scalar VS and vector potentials VV , an SU(2) symmetry exists for the case for which VS = −VV [1]. This symmetry manifests itself in nuclear spectra as a slightly broken symmetry [2–5] since |SV VS−VV | is small for realistic mean fields [6–9] and QCD sum rules [10], and, in fact, gives rise to what has been called “pseudospin symmetry”. The original observations that led to the coining of the word “pseudospin symmetry” were quasi-degeneracies in spherical shell model orbitals with non relativistic quantum numbers (nr, l, j = l + 1/2) and (nr − 1, l + 2, j = l + 3/2) where nr, l, and j are the single-nucleon radial, orbital, and total angular momentum quantum numbers, respectively [11,12]. This doublet structure is expressed in terms of a “pseudo” orbital angular momentum l̃ = l + 1, the average of the orbital angular momentum of the two states in doublet, and “pseudo” spin, s̃ = 1/2. For example, (nrs1/2, (nr − 1)d3/2) will have l̃ = 1 , (nrp3/2, (nr −1)f5/2) will have l̃ = 2, etc. These doublets are almost degenerate with respect to pseudospin, since j = l̃ ± s̃ for the two states in the doublet. Pseudospin “symmetry” was shown to exist in deformed nuclei as well [13,14] and has been used to explain features of deformed nuclei, including superdeformation [15] and identical bands [16,17]. However, the origin of pseudospin symmetry remained a mystery and “no deeper understanding of the origin of these (approximate) degeneracies” existed [18]. The source of pseudospin symmetry as a broken relativistic symmetry of the Dirac Hamiltonian with VS ≈ −VV was pointed out [2–5]. For spherical nuclei, pseudo-orbital angular momentum l̃ is also conserved and physically is the “orbital angular momentum” of the lower component of the Dirac wavefunction. One consequence of this relativistic SU(2) pseudospin symmetry is that the spatial wavefunction for the lower component of the Dirac wavefunctions will be equal in shape and magnitude for the two states in the doublet. This has been shown to be approximately valid for realistic relativistic mean fields [3–5,9]. Recently this approximate equality has been