Localization of two interacting particles in a one-dimensional random potential

We investigate the localization of two interacting particles in a one-dimensional random potential. Our definition of the two-particle localization length, xi, is the same as that of von Oppen et al. [Phys. Rev. Lett. 76, 491 (1996)]. xi's for chains of finite lengths are calculated numerically using the recursive Green's function method for several values of the strength of the disorder, W, and the strength of interaction, U. When U = 0, xi approaches a value larger than half the single-particle localization length as the system size tends to infinity and behaves as xi similar to W-upsilon 0 for small W with upsilon(0) = 2.1 +/- 0.1. When U not equal 0, we use the finite size scaling ansatz and find the relation xi similar to W-upsilon with upsilon = 2.9 +/- 0.2. Moreover, data show the scaling behavior xi similar to W-upsilon 0(b\U\/W-Delta) with Delta = 4.0 +/- 0.5.