Alpha-Particles within Nuclei

Abstract

We present a formalism describing the bound state of a large number of bosons and apply it to study nuclei consisting of A α particles. The method has its roots in a few-body approach and is based on the expansion of the many-body Faddeev components in Potential Harmonics, and the subsequent reduction of the Faddeev equation into a two-variable, integro-differential equation. For A → ∞ this equation is transformed into a new simpler integro-differential equation, which is easy to use in calculations for A up to as large as 1000. We use both integro-differential equations to investigate the behavior of nuclei subject to the assumption that they are composed of α particles. Various αα forces were employed. For the Ali-Bodmer potential we found that the A = 5 system (i.e. 20Ne) is the most stable, while for the A = 10 system (i.e. 40Ca) the binding energy has a maximum. The formalism predicts α-decay for larger nuclei, but the value of A where this begins to happen is strongly dependent on the αα potential.