Brian Woodahl

Application of geometric probability techniques to the evaluation of interaction energies arising from a general radial potential

A formalism is developed for using geometric probability techniques to evaluate interaction energies arising from a general radial potential V(r12), where r12=|r2−r1|. The integrals that arise in calculating these energies can be separated into a radial piece that depends on r12 and a nonradial piece that describes the geometry of the system, including the density distribution. We show that all geometric information can be encoded into a “radial density function” G(r12;ρ1,ρ2), which depends on r12 and the densities ρ1 and ρ2 of two interacting regions. G(r12;ρ1,ρ2) is calculated explicitly for several geometries and is then used to evaluate interaction energies for several cases of interest. Our results find application in elementary particle, nuclear, and atomic physics.