  By means of resonant inelastic x-ray scattering at the Cu L$_3$ edge, we
measured the spin wave dispersion along $\langle$100$\rangle$ and
$\langle$110$\rangle$ in the undoped cuprate Ca$_2$CuO$_2$Cl$_2$. The data
yields a reliable estimate of the superexchange parameter $J$ = 135 $\pm$ 4 meV
using a classical spin-1/2 2D Heisenberg model with nearest-neighbor
interactions and including quantum fluctuations. Including further exchange
interactions increases the estimate to $J$ = 141 meV. The 40 meV dispersion
between the magnetic Brillouin zone boundary points (1/2,\,0) and (1/4,\,1/4)
indicates that next-nearest neighbor interactions in this compound are
intermediate between the values found in La$_{2}$CuO$_4$ and
Sr$_2$CuO$_2$Cl$_2$. Owing to the low-$Z$ elements composing
Ca$_2$CuO$_2$Cl$_2$, the present results may enable a reliable comparison with
the predictions of quantum many-body calculations, which would improve our
understanding of the role of magnetic excitations and of electronic
correlations in cuprates.
