  We study Fermi transitions and isospin mixing in an isotopic chain 70-78 Kr
considering various approximations that use the same Skyrme-Hartree-Fock single
particle basis. We study Coulomb effects as well as the effect of BCS and
quasiparticle random phase approximation (QRPA) correlations. A measure of
isospin mixing in the approximate ground state is defined by means of the
expectation value of the isospin operator squared in N=Z nuclei (which is
generalized to N different from Z nuclei). Starting from strict Hartree-Fock
approach without Coulomb, it is shown that the isospin breaking is negligible,
on the order of a few per thousand for (N-Z)=6, increasing to a few percent
with Coulomb. Pairing correlations induce rather large isospin mixing and Fermi
transitions of the forbidden type (beta- for N<Z, and beta+ for N>Z). The
enhancement produced by BCS correlations is compensated to a large extent by
QRPA correlations induced by isospin conserving residual interactions that tend
to restore isospin symmetry.
