Stability of $\alpha$-chain states against disintegrations

We focus on the raison d’être 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.