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We propose a new numerical method to compute quasi-equilibrium sequences ofgeneral relativistic irrotational binary neutron star systems. It is a goodapproximation to assume that (1) the binary star system is irrotational, i.e.the vorticity of the flow field inside component stars vanishes everywhere(irrotational flow), and (2) the binary star system is in quasi-equilibrium,for an inspiraling binary neutron star system just before the coalescence as aresult of gravitational wave emission. We can introduce the velocity potentialfor such an irrotational flow field, which satisfies an elliptic partialdifferential equation (PDE) with a Neumann type boundary condition at thestellar surface. For a treatment of general relativistic gravity, we use theWilson--Mathews formulation, which assumes conformal flatness for spatialcomponents of metric. In this formulation, the basic equations are expressed bya system of elliptic PDEs. We have developed a method to solve these PDEs withappropriate boundary conditions. The method is based on the establishedprescription for computing equilibrium states of rapidly rotating axisymmetricneutron stars or Newtonian binary systems. We have checked the reliability ofour new code by comparing our results with those of other computationsavailable. We have also performed several convergence tests. By using thiscode, we have obtained quasi-equilibrium sequences of irrotational binary starsystems with strong gravity as models for final states of real evolution ofbinary neutron star systems just before coalescence. Analysis of ourquasi-equilibrium sequences of binary star systems shows that the systems maynot suffer from dynamical instability of the orbital motion and that themaximum density does not increase as the binary separation decreases.Comment: 20 pages, 18 figures, more results of convergence tests are added,  revised version accepted for publication in PR

New numerical method for constructing quasiequilibrium sequences of irrotational binary neutron stars in general relativity