Reaction Cross Sections and $\alpha$-Cluster Geometry in ${}^{12}$C and Be Isotopes

Abstract

Reaction cross sections ${\sigma }_{\mathrm{R}}$ are widely used to infer matter radii, yet their sensitivity to nuclear structure beyond radial one-body distributions is less well understood. We combine complete $A$-body nucleon configurations sampled from \textit{ab initio} nuclear lattice effective field theory (NLEFT) with event-by-event Monte Carlo Glauber calculations, thereby retaining the many-body correlations encoded in NLEFT. Using a fixed binary-collision prescription determined by the measured energy- and isospin-dependent total nucleon-nucleon cross sections, the calculations capture the overall magnitudes and energy dependence simultaneously for the available data on ${}^{12}$C and ${}^9$Be projectiles on carbon and hydrogen. Controlled randomization of angular correlations at fixed matter root-mean-square radius and spherically averaged one-body radial density produces only a weak change in ${\sigma }_{\mathrm{R}}$ for ${}^{12}$C but approximately a $10\%$ increase for ${}^9\mathrm{Be}+{}^1\mathrm{H}$. The calculations also capture the measured rise--plateau--sharp-rise--reduction trend across ${}^{7,9\text{–}12}$Be, a distinctive pattern reflecting the evolution of cluster and halo structures along the isotopic chain. These results show that ${\sigma }_{\mathrm{R}}$ retains sensitivity to intrinsic many-body geometry beyond a single inferred matter radius, opening a route to studies of exotic $\alpha$-cluster geometries and spatial nucleon correlations through reaction cross sections.