Spin Density Matrices for Nuclear Density Functionals with Parity Violation

Within the context of the radial density functional [1], we apply the spin density matrix (SDM) used in atomic and molecular physics [2] to nuclear physics. The vector part of the SDM defines a ``hedgehog'' situation, which exists only if nuclear states contain some amount of parity violation. Thus, looking for the vector profile of the SDM could be used as a test for parity violation in nuclei. The difference between the scalar profile and the vector profile of the SDM will be illustrated by a toy model. \\[4pt] [1] B. G. Giraud, Phys. Rev. C 78, 014307 (2008).\\[0pt] [2] A. Goerling, Phys. Rev. A 47, 2783 (1993).