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 ρ1and 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
Schleef, David; Parry, Michelle; Tu, Shu-Ju; Woodahl, Brian; and Fischbach, Ephraim, "Application of Geometric Probability Techniques to the Evaluation of Interaction Energies Arising from a General Radial Potential" (1999). Chemistry and Physics Faculty Publications. 5.
J. Math. Phys. 40, 1103 (1999)