  Static dipole polarizabilities are calculated in the ground and metastable
states of Sr$^+$, Ba$^+$ and Ra$^+$ using the relativistic coupled-cluster
method. Trends of the electron correlation effects are investigated in these
atomic ions. We also estimate the Stark and black-body radiation shifts from
these results for these systems for the transitions proposed for the optical
frequency standards and compare them with available experimental data.
