Pseudospin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line

Abstract

Based on the Relativistic continuum Hartree-Bogoliubov (RCHB) theory, the pseudo-spin approximation in exotic nuclei is investigated in Zr and Sn isotopes from the proton drip line to the neutron drip line. The quality of the pseudo-spin approximation is shown to be connected with the competition between the centrifugal barrier (CB) and the pseudo-spin orbital potential ( PSOP ). The PSOP depends on the derivative of the difference between the scalar and vector potentials dV /dr. If dV /dr = 0, the pseudo-spin symmetry is exact. The pseudo-spin symmetry is found to be a good approximation for normal nuclei and to become much better for exotic nuclei with highly diffuse potential, which have dV /dr ∼ 0. The energy splitting of the pseudo-spin partners is smaller for orbitals near the Fermi surface ( even in the continuum ) than the deeply bound orbitals. The lower components of the Dirac wave functions for the pseudo-spin partners are very similar and almost equal in 1 magnitude.

Relativistic continuum Hartree Bogoliubov theory for ground-state properties of exotic nuclei

“…The one neutron separation energies S n predicted by RCHB and their experimental counterparts [18] for the nuclei 11−22 C, 13−24 N, 15−26 O and 17−25 F are given in Fig.1 as open and solid circles respectively. For carbon isotopes, the theoretical one neutron separation energies for [11][12][13][14][15][16][17][18]20,22 C are in agreement with the data. The calculated S n is less than 0 (-0.003 MeV) for the odd-A nucleus 19 C which is bound from experiment.…”

“…The RCHB theory [6][7][8], which is an extension of the relativistic mean field (RMF) [9][10][11] and the Bogoliubov transformation in the coordinate representation, can describe satisfactorily the ground state properties for nuclei both near and far from the β-stability line and from light to heavy or super heavy elements, as well as for the understanding of pseudo-spin symmetry in finite nuclei [12][13][14][15]. A remarkable success of the RCHB theory is the self-consistent reproduction of the halo in 11 Li [7] and the prediction of giant halo [8].…”

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.…”

Description of carbon isotopes within relativistic Hartree-Fock-Bogoliubov theory

“…In terms of Bogoliubov quasi-particle, the relativistic Hartree-Bogoliubov (RHB) theory [15][16][17] has unified the descriptions of relativistic Hartree (RH) mean field and pairing correlations, and consequently the continuum effects are involved automatically. Since the first self-consistent description of nuclear halo structure in 11 Li [13], the RHB theory has been successfully applied in predicting the giant halos in Ca [18,19] and Zr [14,19,20] isotopes, as well as the restoration of relativistic symmetry [21] and superheavy magic structures [22].…”