Solid angle a solid angle in steradians is the following ratio: where A is the spherical surface area and r is the radius of the considered sphere. Solid angles are often used in physics, in particular astrophysics. The solid angle of an object that is very far away is roughly proportional to the ratio of area to squared distance. Here "area" means the area of the object when projected along the viewing direction. The solid angle of a sphere measured from any point in its interior is 4 sr, and the solid angle subtended at the center of a cube by one
Surface states expected. A simplified model of the crystal potential in one dimension can be sketched as shown in Figure 1 . In the crystal, the potential has the periodicity, "a", of the lattice while close to the surface it has to somehow attain the value of the vacuum level. The step potential (solid line) shown in Figure 1 is an oversimplification which is mostly convenient for simple model calculations. At a real surface the potential is influenced by image charges and the formation of surface dipoles and it rather looks as indicated by the dashed line. Given the potential in Figure