  This paper supplements and partly extends an earlier publication, Phys. Rev.
Lett. 95, 265501 (2005). In $d$-dimensional continuous space we describe the
infinite volume ground state configurations (GSCs) of pair interactions $\vfi$
and $\vfi+\psi$, where $\vfi$ is the inverse Fourier transform of a nonnegative
function vanishing outside the sphere of radius $K_0$, and $\psi$ is any
nonnegative finite-range interaction of range $r_0\leq\gamma_d/K_0$, where
$\gamma_3=\sqrt{6}\pi$. In three dimensions the decay of $\vfi$ can be as slow
as $\sim r^{-2}$, and an interaction of asymptotic form
$\sim\cos(K_0r+\pi/2)/r^3$ is among the examples. At a dimension-dependent
density $\rho_d$ the ground state of $\vfi$ is a unique Bravais lattice, and
for higher densities it is continuously degenerate: any union of Bravais
lattices whose reciprocal lattice vectors are not shorter than $K_0$ is a GSC.
Adding $\psi$ decreases the ground state degeneracy which, nonetheless, remains
continuous in the open interval $(\rho_d,\rho_d')$, where $\rho_d'$ is the
close-packing density of hard balls of diameter $r_0$. The ground state is
unique at both ends of the interval. In three dimensions this unique GSC is the
bcc lattice at $\rho_3$ and the fcc lattice at $\rho_3'=\sqrt{2}/r_0^3$.
