How does the ambiguity of the electronic stress tensor influence its ability to reveal the atomic shell structure

The electronic stress tensor is not uniquely defined. Therefore, shell indicators stemming from the quantum stress tensor may inherit this ambiguity. Based on a general formula of the stress tensor this ambiguity can be described by an external parameter λ. Two functions derived from the quantum stress tensor have been evaluated according to their ability to serve as shell indicators. The influence of λ is analyzed and the consequences for the representation of the atomic shell structure are discussed in detail. It is found that the trace of the stress tensor does not fully reveal the atomic shell structure. In contrast, the scaled trace (whereby the scaling function is proportional to the Thomas-Fermi kinetic energy density) produces fairly good representation of the atomic shell structure over a wide range of λ values.