Stability of $alpha$-chain states against disintegrations

We focus on 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 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 binary and ternary 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 a 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 the possible existence of alpha-chain states with vast numbers of alpha clusters.