Use of Gaussian Expansion Method for Analysis of the Strong Force in Few Body Systems

The analysis of few-body systems is central to many areas of modern physics, including nuclear and particle physics. In this talk, we study particles in a harmonic trap interacting via a singular two-body contact interaction, which we regularize with a Gaussian potential. By tuning the Gaussian potential to the unitary limit (near-zero two-body binding energy), we show that the ground-state energy approaches the universal fixed point. We also compute the gaps between the first few excited states. Since this problem has no analytical solution, we employ the Gaussian Expansion Method (GEM), which approximates the wave function with a series of Gaussian functions and yields highly accurate energy levels, as established by Hiyama et al. (2003). This approach effectively demonstrates the energy reduction that occurs when two nucleons form a bound state. In addition, we examine the effect of the Coulomb force for a system of two protons and discuss the potential extension of this method to systems of three or more nucleons.