The change of picture contribution to relativistic corrections to second-order properties

The effect of the so-called change of picture for operators in approximate relativistic theories on the second-order properties arising from some exte rnal perturbation, is considered. By means of the direct perturbation theor y the general formula for the lowest-order relativistic correction to secon d-order properties is derived. The term which arises from the change of pic ture for the external perturbation operator is identified and evaluated for dipole and quadrupole polarizabilities. For the 1s(1/2) state of the hydro gen-like ions this term is found to bring about 16% and 7% of the total low est-order irelativistic correction to the dipole and quadrupole polarizabil ities, respectively. This finding is discussed in terms of its importance f or long range interactions between heavy systems. (C) 2001 Elsevier Science B.V. Ail rights reserved.