The energy density formalism (EDF) is used to investigate two problems. The EDF is a phenomenological method that incorporates as much knowledge of infinite nuclear matter as possible. In this formalism the energy of the nucleus is expressed as a functional of its density. The nucleus energy is obtained by minimizing the function, with respect to the density. In this report, the EDF is used to investigate the mercury isotope shift anomaly following the aforementioned suggestion. Specifically, nucleon densities with different degrees of central depression are generated. Energies corresponding to these densities are obtained. The density with the minimum energy is the preferred one. Based on the findings of the present work, it can be concluded that a central depression in the lighter mercury isotopes does not-appear- to be a possible explanation for the isotope shift anomaly. And the anomaly remains unresolved.