Ab initio Calculations of the Isotopic Dependence of Nuclear Clustering

Nuclear clustering describes the appearance of structures resembling smaller nuclei such as alpha particles (^{4}He nuclei) within the interior of a larger nucleus. In this Letter, we present lattice Monte Carlo calculations based on chiral effective field theory for the ground states of helium, beryllium, carbon, and oxygen isotopes. By computing model-independent measures that probe three- and four-nucleon correlations at short distances, we determine the shape of the alpha clusters and the entanglement of nucleons comprising each alpha cluster with the outside medium. We also introduce a new computational approach called the pinhole algorithm, which solves a long-standing deficiency of auxiliary-field Monte Carlo simulations in computing density correlations relative to the center of mass. We use the pinhole algorithm to determine the proton and neutron density distributions and the geometry of cluster correlations in ^{12}C, ^{14}C, and ^{16}C. The structural similarities among the carbon isotopes suggest that ^{14}C and ^{16}C have excitations analogous to the well-known Hoyle state resonance in ^{12}C.