  Modern effective-theory techniques are applied to the nuclear many-body
problem. A novel approach is proposed for the renormalization of operators in a
manner consistent with the construction of the effective potential. To test
this approach, a one-dimensional, yet realistic, nucleon-nucleon potential is
introduced. An effective potential is then constructed by tuning its parameters
to reproduce the exact effective-range expansion and a variety of bare
operators are renormalized in a fashion compatible with this construction.
Predictions for the expectation values of these effective operators in the
ground state reproduce the results of the exact theory with remarkable accuracy
(at the 0.5% level). This represents a marked improvement over a widely
practiced approach that uses effective interactions but retains bare operators.
Further, it is shown that this improvement is more impressive as the operator
becomes more sensitive to the short-range structure of the potential. We
illustrate the main ideas of this work using the elastic form factor of the
deuteron as an example.
