Bound states for A-body nuclear systems

Abstract

In this work we calculate the binding energies and root-mean-square radii for A−body nuclear bound state systems, where A ≥ 3. To study three−body systems, we employ the three−dimensional differential Faddeev equations with nucleon-nucleon semi-realistic potentials. The equations are solved numerically. For this purpose, the equations are transformed into an eigenvalue equation via the orthogonal collocation procedure using triquintic Hermite splines. The resulting eigenvalue equation is solved using the Restarted Arnoldi Algorithm. Ground state binding energies of the 3H nucleus are determined. For A > 3, the Potential Harmonic Expansion Method is employed. Using this method, the Schr¨odinger equation is transformed into coupled Faddeev-like equations. The Faddeevlike amplitudes are expanded on the potential harmonic basis. To transform the resulting coupled differential equations into an eigenvalue equation, we employ again the orthogonal collocation procedure followed by the Gauss-Jacobi quadrature. The corresponding eigenvalue equation is solved using the Renormalized Numerov Method to obtain ground state binding energies and root-mean-square radii of closed shell nuclei 4He, 8Be, 12C, 16O and 40Ca.