Relativistic single-particle potentials for nuclei

The Dirac equation with general local, Lorentz covariant, interactions is investigated as the appropriate wave equation for the description of single-nucleon motion inside nuclei. Four of the original 16 potential components are shown to satisfy the requirements of angular momentum and parity conservation. Only three of these four components are capable of satisfying simultaneously the requirements of hermiticity and time reversal invariance. Nevertheless, state-dependent potentials involving all four components are found which are completely equivalent to nonlocal state-independent potentials satisfying all of the above requirements. Using the three well behaved state-independent potentials, only two local qualitatively distinct models are capable of producing an eigenvalue spectra similar to the experimental single-nucleon removal energies which show strong spin-orbit splittings. All such models are shown to predict large relativistic corrections to the single-particle Dirac magnetic moments unless a strong contribution to the unusual fourth component of the potentials is also included. The success of the nonrelativistic Schmidt estimates in predicting the magnetic moments of light, odd Z-even N nuclei leads one to conclude that any internally consistent shell model of nuclear single-particle states must be strongly nonlocal. Any equivalent local representations of this model must be state-dependent in order to satisfy the usual conservation requirements of the shell model.