Scaling laws for atomic compressibility

Abstract

We consider the concept of atomic pressure for atoms subjected to quantum confinement. New scaling rules are introduced which allow the compressibility to be expressed as the product of two factors. The first is a term independent of compression, which varies widely from atom to atom, but can be computed in the free atom limit. The second is a term expressed in dimensionless variables, whose dependence on compression is in general nonlinear and may exhibit discontinuities. However, it is shown not to vary much from one atom to another and to follow general rules which are easily understood. We have performed fully relativistic ab initio calculations to illustrate these general rules of atomic compressibility, and we characterize the variation of atomic compressibility for both soft and hard atoms.