  We focus upon the raison d'etre of the alpha-chain states on the basis of the
fully microscopic framework, where the Pauli principle among all the nucleons
is fully taken into account. Our purpose is to find out the limiting number of
alpha clusters, on which the linear alpha-cluster state can stably exist. How
many alpha-clusters can stably make an alpha-chain state? We examine the
properties of equally separated alpha clusters on a straight line and compare
its stability with that on a circle. We also confirm its stability in terms of
break-up and binary disintegrations including alpha-decay and fission modes.
For the effective nucleon-nucleon interaction, we employ the F1 force, which
has finite-range three-body terms and guarantees overall saturation properties
of nuclei. This interaction also gives reasonable binding energy and size of
the alpha particle and the alpha-alpha scattering phase shift. The result
astonishes us because we can point out a possible existence of alpha-chain
states with vast numbers of alpha clusters.
