Lattice QCD Calculation of Flavor Singlet Matrix Elements and N-N Scattering Lengths

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 ${\eta }^{\mathrm{\prime }}$ 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.