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Georgia Journal of Science

Article Title

ELEMENTARY DERIVATION OF THE NUCLEAR FORCE RANGE-POTENTIAL DEPTH RELATIONSHIP

Abstract

The simplest nucleus to study the basic nuclear force is the deuteron. A first approximation is to assume the proton-neutron interaction potential to be a square-well with range R0 and depth V0. Using this representation, a relationship can be calculated between R0 and V0 using quantum mechanics. We demonstrate that this formula can be directly derived from an application of the uncertainty principle. In addition to being algebraic, this method of derivation gives an easily understood physical interpretation of the dynamics of the nuclear force. Our results can also be used to determine conditions for which a two-body system, with an attractive force, does not allow the existence of bound states.

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