Ab initio Calculations of the Isotopic Dependence of Nuclear Clustering

Abstract

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.

Microscopic clustering in light nuclei

“…Another development in Ref. (Elhatisari et al, 2017) was the determination of α-cluster correlations in the carbon isotopes 12 C, 14 C, and 16 C by measuring density correlations among the three spin-up protons. This approach relies on the fact that, on average, there is only one spin-up proton within each α-cluster.…”

NN interaction and the spectrum of light and medium-mass nuclei using Lattice Effective Field Theory

“…In the past fifteen years, it has been witnessed that the nuclear lattice effective field theory has achieved great success in researches of the structure and scattering of atomic nuclei [1,2,3,4,5,6]. However, the treatment of nuclear forces at higher orders in the chiral EFT expansion is more difficult on the lattice due to the breaking of rotational invariance produced by nonzero lattice spacing [7,8].…”

Scattering phase shifts and mixing angles for an arbitrary number of coupled channels on the lattice

“…This method was also employed to study the dependence of the triple-alpha process on the fundamental constants of nature [39,40], see Ref. [41] for a related discussion, to investigate the isotopic dependence of nuclear clustering [42] and to determine the features of the nuclear force essential for nuclear binding [43]. It is important to emphasize that the development of chiral EFT interactions is more difficult on the lattice than in the continuum as it requires establishing efficient techniques for extracting the scattering amplitude from the finite-volume discrete spectra and for dealing with the breaking of rotational [44,45] and Galilean invariance [46] due to nonzero lattice spacing.…”