Classical Solutions in String Field Theory Around the Tachyon Vacuum

In a previous paper [hep-th/0012251] we proposed a simple class of actions for string field theory around the tachyon vacuum. In this paper we search for classical solutions describing D-branes of different dimensions using the ansatz that the solutions factorize into the direct product of a matter state and a universal ghost state. We find closed form expressions for the matter state describing D-branes of all dimensions. For the space filling D25-brane the state is the matter part of the zero angle wedge state, the ``sliver'', built in [hep-th/0006240]. For the other D-brane solutions the matter states are constructed using a solution generating technique outlined in [hep-th/0008252]. The ratios of tensions of various D-branes, requiring evaluation of determinants of infinite dimensional matrices, are calculated numerically and are in very good agreement with the known results.