Angular momentum projection on a mesh of cranked Hartree-Fock wave functions

A method for projecting on angular momentum wave functions discretized on a three-dimensional Cartesian mesh is presented. The method is based on a matrix representation of the rotation operator. It is applied to cranked Hartree-Fock wave functions calculated for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ with a simple interaction. In this case, the accuracy of the projected matrix elements is estimated to be of the order of 0.1%. An extensive comparison of the projected and cranking energies is made. The validity of the cranking method as an approximation to a variation-after-projection calculation seems to be wider than usually expected. The study of the fission barrier of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ for the channel ${}_{}{}^4{}_{}{}^{}\mathrm{He}$-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ shows that the cranking predictions for these very deformed states are quite reliable.