The superallowed β-decay rates that provide stringent constraints on physics beyond the standard model of particle physics are affected by nuclear structure effects through isospin-breaking corrections. The self-consistent isospin- and angular-momentum-projected nuclear density functional theory is used for the first time to compute those corrections for a number of Fermi transitions in nuclei from A=10 to A=74. The resulting leading element of the Cabibbo-Kobayashi-Maskawa matrix, |V(ud)|=0.97447(23), agrees well with the recent result of Towner and Hardy [Phys. Rev. C 77, 025501 (2008)].
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