  A method to extract simultaneously level densities and $\gamma$-ray
transmission coefficients has for the first time been tested on light nuclei
utilizing the $^{28}$Si($^3$He,$\alpha\gamma)^{27}$Si and
$^{28}$Si($^3$He,$^3$He'$\gamma)^{28}$Si reactions. The extracted level
densities for $^{27}$Si and $^{28}$Si are consistent with the level densities
obtained by counting known levels in the respective nuclei. The extracted
$\gamma$-ray strength in $^{28}$Si agrees well with the known $\gamma$-decay
properties of this nucleus. Typical nuclear temperatures are found to be $T\sim
2.4$ MeV at around 7 MeV excitation energy. The entropy gap between nuclei with
mass number $A$ and $A\pm 1$ is measured to be $\delta S\sim 1.0 k_B$, which
indicates an energy spacing between single-particle orbitals comparable with
typical nuclear temperatures.
