arXiv:1002.3309v1 [nucl-th] 17 Feb 2010 1 Spin symmetry in Dirac negative energy spectrum in density-dependent relativistic Hartree-Fock theory Haozhao Liang, 1, 2 Wen Hui Long, 1, 3 Jie Meng, 4, 1, 5 and Nguyen Van Giai 2 $^{1}$State Key Lab Nucl. Phys. & Tech., School of Physics, Peking University, Beijing 100871, China $^{2}$Institut de Physique Nucl´ eaire, IN2P3-CNRS and Universit´ e Paris-Sud, F-91406 Orsay Cedex, France $^{3}$Physik-Department der Technischen Universit¨ at M¨ unchen, D-85748 Garching, Germany $^{4}$School of Physics and Nuclear Energy, Beihang University, Beijing 100191, China $^{5}$Department of Physics, University of Stellenbosch, Stellenbosch, South Africa (Dated: September 14, 2018) The spin symmetry in the Dirac negative energy spectrum and its origin are investigated for the first time within the density-dependent relativistic Hartree-Fock (DDRHF) theory. Taking the nucleus $^{16}$O as an example, the spin symmetry in the negative energy spectrum is found to be a good approximation and the dominant components of the Dirac wave functions for the spin doublets are nearly identical. In comparison with the relativistic Hartree approximation where the origin of spin symmetry lies in the equality of the scalar and vector potentials, in DDRHF the cancellation between the Hartree and Fock terms is responsible for the better spin symmetry properties and determines the subtle spin-orbit splitting. These conclusions hold even in the case when significant deviations from the G-parity values of the meson-antinucleon couplings occur. PACS numbers: 21.10.Hw, 21.10.Pc, 21.60.Jz, 24.10.Jv Abstract