[en] A variational approach is applied to the calculation of the zero-temperature equation of state of an infinite collection of neutral, point alpha particles interacting via two-body potentials fitted to α-αscattering data. Four potentials are considered, two with soft cores (Ali-Bodmer, Darriulat-Igo-Pugh-Holmgren) and two with infinitely hard cores. A trial ground-state wave function psi=πsub(i< j)f(rsub(ij)) of Bose-Jastrow form is assumed, and the energy expectation value is calculated within the hypernetted-chain scheme neglecting elementary diagrams. The S-wave component of the given potential model is taken to act in all (even) partial waves. Within this framework an optimal two-body correlation function is determined by paired-phonon analysis. The resulting energy estimate may reasonably be regarded as un upper bound on the exact groundstate energy for the L-dependent potential model in question. The results depend sensitively on the short-range character of the α-α force. Relative to the situation for the hard potential models, the soft interactions enhance the inclination toward clustering of nucleons into alpha particles and tend to inhibit the formation of a solid ground state of ideal alpha matter. (author)