DETERMINING THE THEORETICAL CONDITIONS UNDER WHICH TWO, THREE, AND FOUR NEUTRONS BIND IN A HARMONIC OSCILLATOR TRAP

Abstract

We consider the general two, three, and four neutron systems in a harmonic oscillator (HO) trap. By constructing a model for the 2, 3, and 4-neutron interactions, we make predictions about the theoretical conditions that produce a 2, 3, and 4 body bound state. We do so using an Effective Field Theory (EFT) in a No Core Shell Model (NCSM) basis space. The HO dependence is added to discretize the problem into a finite number of energy eigenstates in which the NCSM basis states are written. We find that as the width parameter (b) of the well tends to infinity, a bound 2-body state reproduces a bound 3 and 4-body state, that 2- body bound states do not reproduce 3 and 4 body bound states in the regime of 0.6760 < b/a < 1.7467, and we also show below scattering lengths of a = 4.438 X 10-15 m, 1.700 X 10- 15 m, and 1.866 X 10-15 m the 2, 3, and 4 body states are bound, respectively, for a width parameter of 3 Fermi’s.