  New QCD sum rules for nucleons in nuclear matter are derived from a mixed
correlation function of spin-1/2 and spin-3/2 interpolating fields. These sum
rules allow a determination of the scalar self-energy of the nucleon
independent of the poorly known four-quark condensates. An analysis of these
new sum rules in concert with previous nucleon sum rules from spin-1/2
interpolators indicates consistency with the expectations of relativistic
mean-field phenomenology. We find $M^* = 0.68 \pm 0.08$ GeV and $\Sigma_v =
0.31 \pm 0.06$ GeV at nuclear matter saturation density.
