  We construct a classical solution in the GSO(-) sector in the framework of a
Wess-Zumino-Witten-like open superstring field theory on a non-BPS D-brane. We
use an su(2) supercurrent, which is obtained by compactifying a direction to a
circle with the critical radius, in order to get analytical tachyonic lump
solutions to the equation of motion. By investigating the action expanded
around a solution we find that it represents a deformation from a non-BPS
D-brane to a D-brane-anti-D-brane system at the critical value of a parameter
which is contained in classical solutions. Although such a process was
discussed in terms of boundary conformal field theory before, our study is
based on open superstring field theory including interaction terms.
