We present a report on a calculation of scattering length for I=2 $S$-wave two-pion system from two-pion wave function. Calculations are made with an RG-improved action for gluons and improved Wilson action for quarks at $a^{-1}=1.207(12) {rm GeV}$ on $16^3 times 80$, $20^3 times 80$ and $24^3 times 80$ lattices. We investigate the validity of necessary condition for application of Luschers formula through the wave function. We find that the condition is satisfied for lattice volumes $Lge 3.92 {rm fm}$ for the quark mass range $m_pi^2 = 0.273-0.736 {rm GeV}^2$. We also find that the scattering length can be extracted with a smaller statistical error from the wave function than with a time correlation function used in previous studies.
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