Comparison between different computational schemes for variational calculations in nuclear structure

We compare several iteration methods for angular-momentum- and parity-projected Hartree-Fock calculations. We used the Anderson update, the modified Broyden method, newly introduced in nuclear-structure calculations, and variants of the Broyden-Fletcher-Goldhaber-Shanno methods (BFGS). We performed ground-state calculations for ¹⁸C and ⁶Li using the two-body Hamiltonian obtained from the CDBonn-2000 potential via the Lee-Suzuki renormalization method. We found that BFGS methods are superior to both the Anderson update and to the modified Broyden method. In the case of ⁶Li we found that the Anderson update and modified Broyden method do not converge to the angular-momentum- and parity-projected Hartree-Fock minimum. The reason is traced back to the lack of a mechanism that guarantees a decrease of the energy from one iteration to the next and to the fact that these methods guarantee a stationary solution rather than a minimum of the energy.