Lattice QCD calculation of s-wave hadron scattering lengths in the channels π-π, π-N, K-N,K-N and N-N is carried out in the quenched approximation at β = 6/g 2 = 5.7. A variant of the method of wall source is developed for this purpose, which reduces the computer time by a factor L 3 on an L 3 × T lattice compared to the conventional point source method and avoids the Fierz mixing problem. A version of the method in which gauge configurations are not fixed to any gauge can be extended to calculate disconnected quark loop contributions in hadron two-and three-point functions. An analytical estimate of statistical errors for this method is worked out, and the magnitude of errors without and with gauge fixing is compared for the case of π-π four-point functions calculated with the Kogut-Susskind quark action. For π-π scattering both I = 0 and 2 scattering lengths are evaluated using the Kogut-Susskind and Wilson quark actions on a 12 3 ×20 lattice. For the same size of lattice, π-N, K-N andK-N scattering lenghts are calculated with the Wilson quark action. For the π-π and π-N cases simulation results are consistent with the predictions of current algebra and PCAC within one to two standard deviations up to quite heavy quark masses corresponding to m π /m ρ ≈ 0.74, while for the K-N andK-N cases the agreement is within a factor of two. For N-N scattering a phenomenological study with one-boson exchange potentials indicate that the deuteron becomes unbound if the quark mass is increased beyond 30-40% of the physical value. Simulations with the Wilson action on a 20 4 lattice with heavy quarks with m π /m ρ ≈ 0.74 − 0.95 show that the nucleon-nucleon force is attractive for both spin triplet and singlet channels, and that the scattering lengths are substantially larger compared to those for the π-π and π-N cases even for such heavy quarks. Problem of statistical errors which has to be overcome toward a more realistic calculation of hadron scattering lengths is discussed.

Full pion four-point functions at zero momentum are calculated with Kogut-Susskind quarks on a 12 3 x20 lattice at ^ = 5.7 and ^=0.01 in quenched lattice QCD, employing the wall source method without gauge fixing. For both 7=0 and 2 channels, results for the s-wave scattering lengths are in agreement with the prediction of current algebra and PCAC (partial conservation of axial-vector current).