  We report on our recent study of flavor singlet matrix elements calculated
with the wall source method without gauge fixing. Results are presented for the
mass difference between $\eta^{\prime}$ and pseudoscalar octet mesons, the
$\pi$-N $\sigma$ term and the proton axial vector matrix elements. An
exploratory calculation of the N-N scattering lengths is also discussed
including a phenomenological study with one-boson exchange potentials.
