Relativistic general-order coupled-cluster method for high-precision calculations: Application to Al+ atomic clock

We report the implementation of a general-order relativistic coupled-cluster method for performing high-precision calculations of atomic and molecular properties. As a first application, the static dipole polarizabilities of the ground and first excited states of Al+ have been determined to precisely estimate the uncertainty associated with the BBR shift of its clock frequency measurement. The obtained relative BBR shift is -3.66+-0.44 for the 3s^2 ^1S_0^0 --> 3s3p ^3P_0^0 transition in Al+ in contrast to the value obtained in the latest clock frequency measurement, -9+-3 [Phys. Rev. Lett. 104, 070802 (2010)]. The method developed in the present work can be employed to study a variety of subtle effects such as fundamental symmetry violations in atoms.