  The localization length $L_2$ of two interacting particles in a
one-dimensional disordered system is studied for very large system sizes by two
efficient and accurate variants of the Green function method. The numerical
results (at the band center) can be well described by the functional form
$L_2=L_1[0.5+c(U) L_1]$ where $L_1$ is the one-particle localization length and
the coefficient $c(U)\approx 0.074 |U|/(1+|U|)$ depends on the strength $U$ of
the on-site Hubbard interaction. The Breit-Wigner width or equivalently the
(inverse) life time of non-interacting pair states is analytically calculated
for small disorder and taking into account the energy dependence of the
one-particle localization length. This provides a consistent theoretical
explanation of the numerically found $U$-dependence of $c(U)$.
