  Two-loop corrections with scalar and vector form factors are calculated for
nuclear matter in the Walecka model. The on-shell form factors are derived from
vertex corrections within the framework of the model and are highly damped at
large spacelike momenta. The two-loop corrections are evaluated first by using
the one-loop parameters and mean fields and then by refitting the total
energy/baryon to empirical nuclear matter saturation properties. The modified
two-loop corrections are significantly smaller than those computed with bare
vertices. Contributions from the anomalous isoscalar form factor of the nucleon
are included for the first time. The effects of the implicit density dependence
of the form factors, which arise from the shift in the baryon mass, are also
considered. Finally, necessary extensions of these calculations are discussed.
