Temperature and Density Conditions for Alpha Clustering in Excited Self-Conjugate Nuclei

Starting from experimental studies on alpha-clustering in excited self-conjugate nuclei (from $^{16}$O to $^{28}$Si), temperature and density conditions for such a clustering are determined. Measured temperatures have been found in the range of 5.5 - 6.0 MeV whereas density values of 0.3 - 0.4 times the saturation density are deduced, i.e., 0.046 to 0.062 $fm^{-3}$. Such a density domain is also predicted by constrained self-consistent mean field calculations. These results constitute a benchmark for alpha clustering from self-conjugate nuclei in relation to descriptions of stellar evolution and supernovae.