Mass Dependence of Binding Energy in Three-Nucleon System

Abstract

We consider the \(^{3}\hbox {H}\) nucleus within the AAA model that includes mass identical particles interacting through a phenomenological nuclear potential. We extend the three-nucleon Hamiltonian \(\beta {\widehat{{H}}}_{0}+{V}_{nucl.}\) using the parameter \(\beta =m_{0}/{m^*}\) that determines the variations \(m^*\) of the averaged nucleon mass \(m_{0} = (m_{n} + m_{p})/2\). It was found that the \(^{3}\hbox {H}\) binding energy is a linear function of the mass \({m^*}/m_0\) when it changes within the ranges \(0.9{<}{m^*}{/m}_{0}{<}1.25\). Thus, the relation between energy and mass is expressed by an analogy to the well-known formula \(E=mc^{2}\). This effect takes a place in small vicinity around the experimentally motivated value of the nucleon mass due to Taylor expanding the general relation \(E\sim 1/m\). The equivalent mass of a nucleon, defined by using this energy-mass dependence, can phenomenologically describe the effect of the proton/nucleon mass difference on 3N binding energy.