The X sub 9 Catastrophe as the Organizing Center of Crystal Rainbows

The crystal rainbow effect is modeled by the catastrophe theory. It is shown that the exp 4 X sub 9 catastrophe can be treated as the organizing center of the crystal rainbows in the cases of square, rectangular, centered rectangular and hexagonal very thin crystals (e.g. Au, W) with one atomic string per primitive cell. This results in a universal, simple and accurate approximation to the continuum potential in the crystal.