  A relativistic version of the coupled-cluster single-double (CCSD) method is
developed for atoms with a single valence electron. In earlier work, a
linearized version of the CCSD method (with extensions to include a dominant
class of triple excitations) led to accurate predictions for energies,
transition amplitudes, hyperfine constants, and other properties of monovalent
atoms. Further progress in high-precision atomic structure calculations for
heavy atoms calls for improvement of the linearized coupled-cluster
methodology. In the present work, equations for the single and double
excitation coefficients of the Dirac-Fock wave function, including all
non-linear coupled-cluster terms that contribute at the single-double level are
worked out. Contributions of the non-linear terms to energies, electric-dipole
matrix elements, and hyperfine constants of low-lying states in alkali-metal
atoms from Li to Cs are evaluated and the results are compared with other
calculations and with precise experiments.
