where δ δ l ( E ) is the scattering phase shift that appears in the partial wave analysis in scattering theory. It is also easier to visualize the waves scattering from one atom to another, and l max = 3 can be used in many applications. The muffin-tin approximation is adequate for most metals in a close-packed arrangement. It cannot be used for calculating forces between atoms, or for important systems like semiconductors.