Information entropy as a measure of the quality of a nuclear density distribution

The information entropy of a nuclear density distribution is calculated for a number of nuclei. Various phenomenological models for the density distribution using different geometry are employed. Nuclear densities calculated within various microscopic mean field approaches are also employed. It turns out that the entropy increases on going from crude phenomenological models to more sophisticated (microscopic) ones. It is concluded that the larger the information entropy, the better the quality of the nuclear density distribution. An alternative approach is also examined: the net information content i.e. the sum of information entropies in position and momentum space $S_{r}+S_{k}$. It is indicated that $S_{r}+S_{k}$ is a maximum, when the best fit to experimental data of the density and momentum distributions is attained.