Accuracy of nuclear density matrix expansion in the calculation of alpha-alpha interaction potential

An expansion for nuclear density matrix (DME) in relative r and center of mass R co-ordinates has been developed. The expansion is truncated beyond r2 term and an extremely simple form for nuclear ground state energy density is obtained. The DME has been subsequently used to evaluate the product of densities and density matrices of two colliding ions that appears in the calculation of their interaction potential. In this work the accuracy of DME was tested in the folding model calculation of alpha-alpha interaction potential using finite range density dependent Brink-Boeker two-body effective interaction