  It has been conjectured that at the stationary point of the tachyon potential
for the D-brane-anti-D-brane pair or for the non-BPS D-brane of superstring
theories, the negative energy density cancels the brane tensions. We study this
conjecture using a Wess-Zumino-Witten-like open superstring field theory free
of contact term divergences and recently shown to give 60% of the vacuum energy
by condensation of the tachyon field alone. While the action is non-polynomial,
the multiscalar tachyon potential to any fixed level involves only a finite
number of interactions. We compute this potential to level three, obtaining 85%
of the expected vacuum energy, a result consistent with convergence that can
also be viewed as a successful test of the string field theory. The resulting
effective tachyon potential is bounded below and has two degenerate global
minima. We calculate the energy density of the kink solution interpolating
between these minima finding good agreement with the tension of the D-brane of
one lower dimension.
