  Many ground state studies of $^4$He using a shadow wave function with an
inverse fifth power McMillan particle-particle correlation function have
yielded radial distribution functions with misplaced peaks. It has been
conjectured that this is due to the specific choice of the McMillan correlation
function. However, beyond the use of fully optimized two-particle correlation
functions, there has been little study of simple alternatives that can correct
this defect. In this work we show that the remedy is surprisingly simple. When
a shadow wavefunction with an inverse seventh power particle-particle
correlation function is used to study $^4$He, it gives a correctly peaked
radial distribution function, lowers the energy at all liquid and solid
densities, and produces an excellent equation of state.
