Summary

In the present study, we presented a new theoretical tool that allowed for isospin projection of Slater determinants and we discussed first applications of the formalism to calculate the isospin-mixing parameters $\alpha _C$ and total binding energies in $N=Z$ nuclei. In particular, we discussed the basis-size dependence of $\alpha _C$ and we showed that the basis truncation may introduce about $\pm 4$% uncertainty in $\alpha _C$.

We also discussed the role and magnitude of the spurious isospin-symmetry-violating response of the self-consistent mean field against the physical symmetry-breaking effects of the Coulomb field. We showed that even in $N=Z$ nuclei, the self-consistent mean-field may induce unphysical isospin mixing that reduces $\alpha _C$ by as much as 30% in $^{100}$Sn. This unphysical mechanism is due to the very variational nature of the self-consistent mean-field scheme, which introduces its own isospin-symmetry breaking field and partly counterbalances the repulsive symmetry-breaking Coulomb field so as to minimize the total binding energy. Nevertheless, our calculations show that the HF binding energies follow extremely closely those obtained by rediagonalizing the Hamiltonian within the set of isospin-projected states.

This work was supported in part by the Polish Ministry of Science under Contract No. N N202 328234 and by the Academy of Finland and University of Jyväskylä within the FIDIPRO programme.