  We investigated properties of a singular billiard, that is, a quantum
billiard which contains a pointlike (zero-range) perturbation. A singular
billiard was simulated experimentally by a rectangular microwave flat resonator
coupled to microwave power via wire antennas which act as singular scatterers.
The departure from regularity was quantitatively estimated by the short-range
plasma model in which the parameter $\eta$ takes the values $1$ and $2$ for the
Poisson and semi-Poisson statistics, respectively. We show that in the regime
of semi-Poisson statistics the experimental power spectrum and the second
nearest-neighbor spacing distribution $P(2,s)$ are in good agreement with their
theoretical predictions. Furthermore, the measurement of the two-port
scattering matrix allowed us to evaluate experimentally the enhancement factor
$F(\gamma^{tot})$ in the regime of the semi-Poisson statistics as a function of
the total absorption factor $\gamma^{tot}$. The experimental results were
compared with the analytical formula for $F(\gamma^{tot})$ evaluated in this
article. The agreement between the experiment and theory is good.
