Light hadrons with improved staggered quarks: Approaching the continuum limit

We have extended our program of QCD simulations with an improved Kogut-Susskind quark action to a smaller lattice spacing, approximately 0.09 fm. Also, the simulations with aapproximate to0.12 fm have been extended to smaller quark masses. In this paper we describe the new simulations and computations of the static quark potential and light hadron spectrum. These results give information about the remaining dependences on the lattice spacing. We examine the dependence of computed quantities on the spatial size of the lattice, on the numerical precision in the computations, and on the step size used in the numerical integrations. We examine the effects of autocorrelations in simulation time on the potential and spectrum. We see possible effects of decays, or coupling to two-meson states in the 0(++) and 1(+) meson propagators. A state consistent with pi+K is seen as a parity partner in the Goldstone kaon propagator, and we make a preliminary mass computation for a radially excited 0(-) meson.