The topological features of the intracule density of the uniform electron gas

The Laplacian of the self-consistent-field radial intracule density of the uniform electron gas has been analyzed. It reaches its absolute maximum at the electron–electron coalescence point with a value of 0.3ρ2, where ρ is the electron charge density. Then, it decreases as the interlectronic distance increases and has an attenuated oscillatory decay at larger distances. Further examination of this function yields an onion-like representation of the spatial structure of the uniform electron gas from the viewpoint of an arbitrary reference electron. Our calculations demonstrate that the radius of the first layer is 13.069rs and the remaining layers obey a simple relationship with respect to the layer number with a separation of 6.065rs between adjacent layers.