A new correlation measure, the product of the Shannon entropy power and the Fisher
information of the electron density, is introduced by analyzing the Fisher–Shannon
information plane of some two-electron systems He-like ions, Hooke's atoms. The
uncertainty and scaling properties of this information product are pointed out. In addition, the
Fisher and Shannon measures of a finite many-electron system are shown to be bounded by
the corresponding single-electron measures and the number of electrons of the system.© …