In this work, we carried out the theoretical analysis of
isospin breaking in nuclei around 
=
based on the density functional theory. We show that the spontaneous breaking of isospin symmetry inherent to MF limits the applicability of self-consistent theories, such as HF and DFT, to nuclear states with 
=0. To remedy this problem, we propose
a new isospin-symmetry restoration scheme based on the rediagonalization
technique in good-isospin basis.
The isospin projection algorithm is described in detail, including the derivation of essential Hamiltonian kernels. We demonstrate that isospin projection is free from problems plaguing other symmetry restoration schemes (particle number, angular momentum) related to kernel singularities.
Applications of the isospin-projected DFT approach include the
SD bands in 
Ni and terminating states in = medium-mass
nuclei. In both cases, the symmetry restoration remedies previously noted deficiencies of the HF method and significantly improves agreement with experiment. The results for terminating states corroborate previous suggestions that large isoscalar effective masses are needed to
reproduce experimental spectroscopic data involving s.p. levels.
The examples presented in this work primarily concern high-spin configurations in medium mass nuclei in which pairing correlations are expected to be weak.
To be able to address theoretically a variety of low-spin phenomena and observables around the = line, such as ground states of odd-odd nuclei, binding energy staggering, superallowed beta decays, and charge-exchange reactions, isovector and isoscalar pairing correlations must be incorporated and the proton-neutron symmetry of HF must be broken before isospin projection [46,47]. Those will be subjects of our forthcoming studies.
This work was supported in part by the Polish Ministry of Science under Contracts No. N N202 328234 and N N202 239037, Academy of Finland and University of Jyväskylä within the FIDIPRO programme, and by the Office of Nuclear Physics, U.S. Department of Energy under Contract Nos. DE-FG02-96ER40963 (University of Tennessee) and and DE-FC02-07ER41457 (UNEDF SciDAC Collaboration).