<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-nucleus optical potential in the double-folding model

Abstract

The double-folding formalism for the $\ensuremath{\alpha}$-nucleus optical potential is revised to study the exchange effects and density dependence of the effective nucleon-nucleon $(\mathrm{NN})$ interaction in detail. A realistic density dependent M3Y interaction, based on the G-matrix elements of the Paris NN potential, has been used in the folding calculation. The local approximation for the nonlocal one-body density matrix in the calculation of the exchange potential was tested by using the harmonic oscillator representation of the nonlocal density matrices of the $\ensuremath{\alpha}$-particle and target nucleus. The inclusion of a realistic density dependence into the effective NN interaction was shown to be vital for a correct description of the refractive $\ensuremath{\alpha}$-nucleus scattering data. A high sensitivity of the density distributions of the $\ensuremath{\alpha}$-particle and target nucleus to the shape of the $\ensuremath{\alpha}$-nucleus potential was found, which can be used in the folding analysis to test various density models for the $\ensuremath{\alpha}$-particle and target as well as to choose the most realistic approximation for the overlap density in the dinuclear system. Our results also stress the importance of $\ensuremath{\alpha}$-nucleus scattering experiment in the nuclear structure study.