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

David Schleef, Michelle Parry, Shu-Ju Tu, Brian Woodahl, Ephraim Fischbach
1999 Journal of Mathematical Physics  
A formalism is developed for using geometric probability techniques to evaluate interaction energies arising from a general radial potential V(r 12 ), where r 12 ϭ͉r 2 Ϫr 1 ͉. The integrals that arise in calculating these energies can be separated into a radial piece that depends on r 12 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(r 12 ; 1 , 2 ),
more » ... 12 ; 1 , 2 ), which depends on r 12 and the densities 1 and 2 of two interacting regions. G(r 12 ; 1 , 2 ) 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.
doi:10.1063/1.532709 fatcat:7znljlyuxvfj5ejbu3ao3chzvm