  We use the perturbed relativistic coupled-cluster theory to compute the
static electric dipole polarizabilities of the singly ionized alkali atoms,
namely, Na$^+$, $^+$, Rb$^+$, Cs$^+$ and Fr$^+$. The computations use the
Dirac-Coulomb-Breit Hamiltonian with the no-virual-pair approximation and we
also estimate the correction to the static electric dipole polarizability
arising from the Breit interaction.
