Precise estimation of shell model energy by second-order extrapolation method

A second-order extrapolation method is presented for shell model calculations, where shell model energies of truncated spaces are well described as a function of energy variance by quadratic curves, and exact shell model energies can be obtained by the extrapolation. This new extrapolation can give more precise energy than those of first-order extrapolation method. It is also clarified that first-order extrapolation gives a lower limit of shell model energy. In addition to the energy, we derive the second-order extrapolation formula for expectation values of other observables.