where k 2D F is the 2D-surface Fermi wavevector and v 2D F is the corresponding 2D-surface Fermi velocity. In 2006, 139 they moved to the general description of the (111) noble metal surfaces (in this particular case Ag(111)) for which they got the checker-like structure close to the very surface caused by both 2D-and 3D-system responses, and there also appeared an interesting off-angle peak of charge-density-change going deep into the Ag bulk at an angle of circa ≈ 45 • due to only the 3D bulk electrons. Furthermore, in 2010 140 they described the complete procedure of obtaining their results, which is mostly numerical. It does consist of the following points: (1) obtaining the reliable z-dependent pseudo-potential of the metal bulk with surface, (2) computing the wavefunctions from the Schrödinger's equation with the potential from ( ), ( ) determining the Lindhard response function from the definition (i.e. they calculate the integral numerically with the η parameter cutoff set to be η = 1 meV, and lastly (4) by repeating this integral in a self-consistent manner. The induced charge density can be described by the following equation