Eigenvalue problem for a coupled channel Schrödinger equation with application to the description of deformed nuclear systems

We discuss the accurate computation of the eigensolutions of systems of coupled channel Schrödinger equations as they appear in studies of real physical phenomena like fission, alpha decay and proton emission. A specific technique is used to compute the solution near the singularity in the origin, while on the rest of the interval the solution is propagated using a piecewise perturbation method. Such a piecewise perturbation method allows us to take large steps even for high energy-values. We consider systems with a deformed potential leading to an eigenvalue problem where the energies are given and the required eigenvalue is related to the adjustment of the potential, viz, the eigenvalue is the depth of the nuclear potential. A shooting technique is presented to determine this eigenvalue accurately.