Abstract
Previous work on infinite one-dimensional systems of interacting particles is continued. In the case of two-body potentials φ( x) = φ(- x), whose Fourier transform ĝf( k) eicsts, it is shown that a necessary condition that the equidistant configuration has for a certain range of densities minimum potential energy per particle among all configurations of the same density, is that ĝf( k)⩾0 for all k. An analogous theorem is proved for systems of particles in two and three dimensions. Furthermore some properties are discussed of one-dimensional systems for which ĝf( k)⩾0 for all k and moreover ĝf( k) = 0 for | k|⩾ k 0.
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