Classical solutions in string field theory around the tachyon vacuum

In a previous paper 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. For the other D-brane solutions the matter states are constructed using a solution generating technique outlined in. 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.