the partial intermediate scattering function $F_{s,\alpha}(\vec{k},t)$ can be calculated directly using [@Hansen] $$F_{s,\alpha}(\vec{k},t)=\frac{1}{N_{\alpha}}\left\langle
\sum_{i=1}^{N_{\alpha}}e^{i\vec{k}\cdot(\vec{r}_{i}(t)-\vec{r}_{i}(0))}
\right\rangle
\label{eq:SelfFkt}$$ where the subscript $\alpha$ refers to the particle type, A or B. $\vec{r}_{i}(t)$ is the position of particle $i$ at time $t$, and $\langle ...\rangle$ refers to an average over different configurations. The wave vector $\vec{k}=2\pi\vec{q}/L$ where $\vec{q}$ is a vector of integers. For an isotropic system $F_{s,\alpha}(\vec{k},t)$ depends only on the magnitude $k=|\vec{k}|$. We will choose $k=k_{max}$ where $k_{max}$ is the position of the first maximum of the partial static structure factor $S_{\alpha}(k)$. In Figure \[fig:selfFkt\] we show the self intermediate scattering function $F_{s,B}(k,t)$ versus time at temperatures below the caging temperature ($T\approx 0.4$). The caging temperature is the highest temperature at which a plateau is present in the intermediate scattering function versus time. The plateau represents the temporary localization of a particle by a cage of other particles surrounding it.

[Fig1.eps]{}

Mode coupling theory is applicable in the temperature range below the caging temperature and somewhat above the mode coupling $T_C$. We define the relaxation time $\tau_s$ by $F_{s}(k,\tau_s)=1/e$. We determine the relaxation times for the seven highest temperatures shown in Figure \[fig:selfFkt\] and then fit the temperature dependence of $\tau_s(T)$ to 