- Title
- Analysis of certain lattice sums*
- Creator
- Borwein, D.; Borwein, J. M.; Shail, R.
- Relation
- Journal of Mathematical Analysis and Applications Vol. 143, Issue 1, p. 126-137
- Publisher Link
- http://dx.doi.org/10.1016/0022-247X(89)90032-2
- Publisher
- Academic Press
- Resource Type
- journal article
- Date
- 1989
- Description
- The genesis of this paper lies in the physical model we now describe. We believe the theorems presented to be of independent mathematical interest. In 1934 Wigner [7] introduced the concept of an electron gas bathed in a compensating background of positive charge as a model for a metal. He stated that in the static case the electrons would form a b.c.c. lattice in the background of positive charge. In 1938 he presented a quantitative treatment of this problem, following a calculation by Fuchs [5], who showed that for a given number density, the b.c.c. lattice was the most stable of the three common cubic structures, namely s.c., b.c.c., and fc.c. lattices - see Coldwell-Horsfall and Maradudin [3]. The evaluation of U (lattice)-the energy of an electron in a given lattice-involved finding by some means or other the difference of two divergent quantities. Of these, one term U₁ measures the interaction of an electron with all the other electrons on their lattice sites. The second term U₂ measures the interaction of an electron with the compensating positive background charge.
- Subject
- lattice sums; cubic structures; electron lattices
- Identifier
- http://hdl.handle.net/1959.13/941069
- Identifier
- uon:13171
- Identifier
- ISSN:0022-247X
- Language
- eng
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