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 and total binding energies in
nuclei. In particular, we discussed the basis-size dependence
of
and we showed that the basis truncation may introduce
about
% uncertainty in
.
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 nuclei, the self-consistent mean-field
may induce unphysical isospin mixing that reduces
by
as much as 30% in
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.