A formalism is developed for using geometric probability techniques to evaluate interaction energies arising from a general radial potential where The integrals that arise in calculating these energies can be separated into a radial piece that depends on 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” which depends on and the densities and of two interacting regions. 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.
REFERENCES
1.
E.
Fischbach
, D. E.
Krause
, C.
Talmadge
, and D.
Tadić
, Phys. Rev. D
52
, 5417
(1995
).2.
3.
4.
5.
6.
G. F. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, San Diego, 1995), p. 749.
7.
A. Bohr and B. R. Mottelson, Nuclear Structure (Benjamin, New York, 1969), Vol. I, p. 141.
8.
9.
10.
11.
A. W. Overhauser (unpublished).
12.
M. G. Kendall and P. A. P. Moran, Geometrical Probability (Hafner, New York, 1963).
13.
L. A. Santaló, Integral Geometry and Geometric Probability (Addison-Wesley, Reading, MA, 1976), p. 212.
14.
J. N. Israelachvili, Intermolecular and Surface Forces, 2nd ed. (Academic, London, 1992).
15.
B.
Gady
, D.
Schleef
, R.
Reifenberger
, D.
Rimai
, and L. P.
DeMejo
, Phys. Rev. B
53
, 8065
(1996
).16.
M. Parry, Ph.D. thesis, Purdue University, 1998 (unpublished).
This content is only available via PDF.
© 1999 American Institute of Physics.
1999
American Institute of Physics
You do not currently have access to this content.