  We present calculations of the localisation length, $\lambda_{2}$, for two
interacting particles (TIP) in a one-dimensional random potential, presenting
its dependence on disorder, interaction strength $U$ and system size.
$\lambda_{2}(U)$ is computed by a decimation method from the decay of the Green
function along the diagonal of finite samples. Infinite sample size estimates
$\xi_{2}(U)$ are obtained by finite-size scaling. For U=0 we reproduce
approximately the well-known dependence of the one-particle localisation length
on disorder while for finite $U$, we find that $ \xi_{2}(U) \sim
\xi_2(0)^{\beta(U)} $ with $\beta(U)$ varying between $\beta(0)=1$ and
$\beta(1) \approx 1.5$. We test the validity of various other proposed fit
functions and also study the problem of TIP in two different random potentials
corresponding to interacting electron-hole pairs. As a check of our method and
data, we also reproduce well-known results for the two-dimensional Anderson
model without interaction.
