  We present a method of calculating the energy gap of a charge-neutral
excitation using only ground-state calculations. We report Quantum Monte Carlo
calculations of $\Gamma\rightarrow\Gamma$ and $\Gamma\rightarrow X$
particle-hole excitation energies in diamond carbon. We analyze the finite-size
effect and find the same $1/L$ decay rate as that in a charged excitation,
where $L$ is the linear extension of the supercell. This slow decay is
attributed to the delocalized nature of the excitation in supercells too small
to accommodate excitonic binding effects. At larger system sizes, the apparent
$1/L$ decay crosses over to a $1/L^3$ behavior. Estimation of the scale of
exciton binding can be used to correct finite-size effects of neutral gaps.
