  We address again the old problem of calculating the radion effective
potential in Randall-Sundrum scenarios, with the Goldberger-Wise stabilization
mechanism. Various prescriptions have been used in the literature, most of them
based on heuristic derivations and then applied in some approximations. We
define rigorously a light radion 4D effective action by using the interpolating
field method. For a given choice of the interpolating field, defined as a
functional of 5D fields, the radion effective action is uniquely defined by the
procedure of integrating out the other fields, with the constrained 5D
equations of motion always satisfied with help of the Lagrange multipliers.
Thus, for a given choice of the interpolating fields we obtain a precise
prescription for calculating the effective potential. Different choices of the
interpolating fields give different prescriptions but in most cases very
similar effective potentials. We confirm the correctness of one prescription
used so far on a more heuristic basis and also find several new, much more
economical, ways of calculating the radion effective potential. Our general
considerations are illustrated by several numerical examples. It is shown that
in some cases the old methods, especially in models with strong back-reaction,
give results which are off even by orders of magnitude. Thus, our results are
important e.g. for estimation of critical temperature in phase transitions.
