Spin Symmetry in the Antinucleon Spectrum

Abstract

We discuss spin and pseudo-spin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single anti-nucleon spectra. We find a very well developed spin symmetry in single anti-neutron and single anti-proton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in anti-particle spectra and the pseudo-spin symmetry in particle spectra have the same origin. However it turns out that the spin symmetry in anti-nucleon spectra is much better developed than the pseudo-spin symmetry in normal nuclear single particle spectra. 21.10.Hw, 21.10.Pc, 21.60.Jz Symmetries in single particle spectra of atomic nuclei have been discussed extensively in the literature, as the violation of spin-symmetry by the spin-orbit term and approximate pseudo-spin symmetry in nuclear single particle spectra: atomic nuclei are characterized by a very large spin-orbit splitting, i.e. pairs of single particle states with opposite spin (j = l ± 1 2 ) have very different energies. This fact allowed the understanding of magic numbers in nuclei and forms the basis of nuclear shell structure. More than thirty years ago [1, 2] pseudo-spin quantum numbers have been introduced byl = l ± 1 and j = j for j = l ± 1 2 and it has been observed that the splitting between pseudo-spin doublets in nuclear single particle spectra is by an order of magnitude smaller than the normal spin-orbit splitting.After the observation that relativistic mean field models yield spectra with nearly degenerate pseudo spin-orbit partners [3], Ginocchio showed clearly that the origin of pseudo-spin symmetry in nuclei is given by a relativistic symmetry in the Dirac Hamiltonian ([4, 5] and references given therein). He found that pseudo-spin symmetry becomes exact in the limiting case, where the strong scalar and vector potentials have the same size but opposite sign. However, this condition is never fulfilled exactly in real nuclei, because in this limit the average nuclear potential vanishes and nuclei are no longer bound. It has been found that the quality of pseudo-spin symmetry is related to the competition between the centrifugal barrier and the pseudo-spin orbital potential [6].In relativistic investigations a Dirac Hamiltonian is used. In its spectrum one finds single particle levels with positive energies as well as those with negative energies. The latter are interpreted as anti-particles under charge conjugation. This has lead to much efforts to explore configurations with anti-particles and their interaction with nuclei. The possibility of producing a new kind of nuclear system by putting one or more anti-baryons inside ordinary nuclei has recently gained renewed interest [7]. For future studies of anti-particles in nuclei it is therefore of great importance to investigate the symmetries of such configurations.In a relativistic description nuclei are characterized by two strong potentials, an attactive scalar fiel...

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.…”

“…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.…”

The limits of the nuclear landscape explored by the relativistic continuum Hartree–Bogoliubov theory

“…It includes naturally the nucleonic spin degree of freedom and automatically results in the nuclear spin-orbit potential with the empirical strength in a covariant way. It can reproduce well the isotopic shifts in the Pb region [35], and give naturally the origin of the pseudospin symmetry [36] and the spin symmetry in the anti-nucleon spectrum [37,38]. Furthermore, it can include the nuclear magnetism [39], that is, a consistent description of currents and time-odd fields, which plays an important role in nuclear magnetic moments [40][41][42][43][44] and nuclear rotations [33,[45][46][47][48][49][50][51].…”

Shell-model-like Approach (SLAP) for the Nuclear Properties in Relativistic Mean Field Theory

“…During the past two decades, it has received wide attention due to its success in describing many nuclear phenomena for the stable nuclei [2,3] as well as nuclei even far from stability [4,5]. It has been shown that the relativistic Brueckner theory can reproduce better the nuclear saturation properties (the Coester line) in nuclear matter [6], present a new explanation for the identical bands in superdeformed nuclei [7] and the neutron halo [8], predict a new phenomenon -giant neutron halos in heavy nuclei close to the neutron drip line [9], give naturally the spin-orbit potential, the origin of the pseudospin symmetry [10,11] as a relativistic symmetry [12,13,14] and spin symmetry in the anti-nucleon spectrum [15], and present good description for the magnetic rotation [16] and the collective multipole excitations [17], etc.…”