# Ab initio calculations of the isotopic dependence of nuclear clustering

## TL;DR

This paper uses lattice Monte Carlo calculations based on chiral effective field theory to explore nuclear clustering, revealing the shape and correlations of alpha clusters in various isotopes and introducing a new computational method called the pinhole algorithm.

## Contribution

It presents a novel computational approach, the pinhole algorithm, and applies it to analyze clustering and nucleon correlations in multiple isotopes, advancing understanding of nuclear structure.

## Key findings

- Alpha clusters' shape and entanglement are characterized.
- Density distributions and cluster geometries are determined for isotopes.
- Structural similarities suggest analogous excitations in carbon isotopes.

## Abstract

Nuclear clustering describes the appearance of structures resembling smaller nuclei such as alpha particles (4He nuclei) within the interior of a larger nucleus. While clustering is important for several well-known examples, much remains to be discovered about the general nature of clustering in nuclei. 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 12C, 14C, and 16C. The structural similarities among the carbon isotopes suggest that 14C and 16C have excitations analogous to the well-known Hoyle state resonance in 12C.