Renormalized interacting theories: redefining free parameters

The usual renormalization scheme for the variational approximation with a trial Gaussian ansatz for the $\lap$ model in 3+1 dimensions is re-analysed. The so called asymmetric phase of the model (where $ \neq 0$) is considered with the search for conditions that the parameters of the theory (mass and coupling constant) would respect to obtain the vacuum state. The minimization of the energy with relation to the renormalized mass is done and the resulting expression is faced as a new GAP equation. The minimization of the energy with respect to the renormalized coupling constant is also done resulting in expression for the check of reliability of the approximation. A sort of ``scale invariant'' solutions for the renormalized mass and coupling constant values are found. A non trivial solution for the model with strong coupling constant is found. Ranges of these values, mass and coupling constant, in which the approximation is expected to be more reliable as well as instabilities are found. A different interpretation for the so called symmetry restoration is found