Characterizing nuclear pasta with alpha shapes

Abstract

Nuclear pasta structures, which emerge in large nucleon systems at subsaturation densities and near-zero temperatures, have traditionally been analyzed using Minkowski Functionals, particularly through the correlation between Curvature and Euler Characteristic. Previous methods relied on cubic voxelization to create three-dimensional bodies from nuclear theory data points, leading to inaccurate estimations of geometric properties. This work introduces the alpha shapes method as a superior alternative for constructing three-dimensional solid bodies from point cloud data and calculating Minkowski Functionals. Through test cases comparing voxelization and alpha shapes, as well as analysis of pasta structures obtained through classical molecular dynamics, we demonstrate that the alpha shapes method provides more accurate geometric representations and simplifies the calculation of Minkowski Functionals. We use Diode, a Python library implementing alpha shape calculations, to verify previously observed correlations between pasta shapes and their position in the Curvature-Euler Characteristic plane. Our analysis, extending across various temperatures and densities, reveals a density-dependent trend in pasta shapes that is relatively temperature-independent. The method is also tested satisfactorily with neutron star matter. These findings provide a quantitative framework for characterizing the evolution of nuclear pasta structures and offer a new computational tool for researchers studying these phenomena through different theoretical approaches.