  The operator in a parton shower algorithm that represents the imaginary part
of virtual Feynman graphs has a non-trivial color structure and is large
because it is proportional to a factor of $4\pi$. In order to improve the
treatment of color in a parton shower, it may help to exponentiate this phase
operator. We show that it is possible to do so by exponentiating matrices that
are no larger than $14\times14$. Using the example of the probability to have a
gap in the rapidity interval between two high transverse momentum jets, we test
this exponentiation algorithm by comparing to the result of treating the phase
operator perturbatively. We find that the exponentiation works, but that the
net effect of the exponentiated phase operator is quite small for this problem,
so that one can as well use the perturbative approach.
