Configuration mixing calculation for complete low-lying spectra with a mean-field Hamiltonian

We propose a new theoretical approach to ground and low-energy excited states of nuclei extending the nuclear mean-field theory. It consists of three steps: stochastic preparation of many Slater determinants, the parity and angular-momentum projection, and diagonalization of the generalized eigenvalue problems. The Slater determinants are constructed in the three-dimensional Cartesian coordinate representation capable of describing arbitrary shape of nuclei. We examine feasibility and usefulness of the method by applying the method with the Bonche-Koonin-Negele interaction to light $4N$ nuclei, $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, and $^{20}\mathrm{Ne}$. We discuss difficulties of keeping linear independence for basis states projected on good parity and angular momentum and present a possible prescription.