Island Distance in One-Dimensional Epitaxial Growth

The typical island distance $\ell$ in submonlayer epitaxial growth depends on the growth conditions via an exponent $\gamma$. This exponent is known to depend on the substrate dimensionality, the dimension of the islands, and the size $i^*$ of the critical nucleus for island formation. In this paper we study the dependence of $\gamma$ on $i^*$ in one--dimensional epitaxial growth. We derive that $\gamma = i^*/(2i^* + 3)$ for $i^*\geq 2$ and confirm this result by computer simulations.