Shifted COCG Method in Nuclear Physics

Solving the 3-dimensional Schr\^odinger equations in nuclear many-body problems is always costly in time and resources. Recently, the Shifted Conjugate-Orthogonal-Conjugate-Gradient(COCG) Method has been widely used to calculate the Green's function of a many-electron Hamiltonian. Using this method, we find an approach to solving the density of nuclear matter and energy-levels. Performed in parallel, it can be very fast and with high accuracy. This is quite useful in the calculation of deformed nuclei, and the shell corrections in nuclear binding energy. In this work, we applied COCG method to a 3d Wood-Saxon Hamiltonian with pairing and calculate the density distribution of nuclear matter.