Isospin-breaking corrections to superallowed Fermi beta-decay in isospin- and angular-momentum-projected nuclear Density Functional Theory

摘要

Background: The superallowed beta-decay rates provide stringent constraintson physics beyond the Standard Model of particle physics. To extract crucialinformation about the electroweak force, small isospin-breaking corrections tothe Fermi matrix element of superallowed transitions must be applied. Purpose:We perform systematic calculations of isospin-breaking corrections tosuperallowed beta-decays and estimate theoretical uncertainties related to thebasis truncation, time-odd polarization effects related to the intrinsicsymmetry of the underlying Slater determinants, and to the functionalparametrization. Methods: We use the self-consistent isospin- andangular-momentum-projected nuclear density functional theory employing twodensity functionals derived from the density independent Skyrme interaction.Pairing correlations are ignored. Our framework can simultaneously describevarious effects that impact matrix elements of the Fermi decay: symmetrybreaking, configuration mixing, and long-range Coulomb polarization. Results:The isospin-breaking corrections to the I=0+,T=1 --> I=0+,T=1 pure Fermitransitions are computed for nuclei from A=10 to A=98 and, for the first time,to the Fermi branch of the I,T=1/2 --> I,T=1/2 transitions in mirror nucleifrom A=11 to A=49. We carefully analyze various model assumptions impactingtheoretical uncertainties of our calculations and provide theoretical errorbars on our predictions. Conclusions: The overall agreement with empiricalisospin-breaking corrections is very satisfactory. Using computedisospin-breaking corrections we show that the unitarity of the CKM matrix issatisfied with a precision better than 0.1%.