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Register a new userMicroscopic calculations of isospin mixing in N~Z nuclei and isospin-symmetry-breaking corrections to the superallowed beta-decay
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Recently, we have applied for the first time the angular momentum and isospin projected nuclear density functional theory to calculate the isospin-symmetry breaking (ISB) corrections to the superallowed beta-decay. With the calculated set of the ISB corrections we found |V_{ud}|=0.97447(23) for the leading element of the Cabibbo-Kobayashi-Maskawa matrix. This is in nice agreement with both the recent result of Towner and Hardy [Phys. Rev. {bf C77}, 025501 (2008)] and the central value deduced from the neutron decay. In this work we extend our calculations of the ISB corrections covering all superallowed transitions A,I^pi=0^+,T=1,T_z rightarrow A,I^pi=0^+,T=1,T_z+1 with T_z =-1,0 and A ranging from 10 to 74.
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We report new shell-model calculations of the isospin-symmetry-breaking correction to superallowed nuclear beta decay. The most important improvement is the inclusion of core orbitals, which are demonstrated to have a significant impact on the mismatch in the radial wave functions of the parent and daughter states. We determine which core orbitals are important to include from an examination of measured spectroscopic factors in single-nucleon pick-up reactions. We also examine the new radiative-correction calculation by Marciano and Sirlin and, by a simple reorganization, show that it is possible to preserve the conventional separation into a nucleus-independent inner radiative term and a nucleus-dependent outer term. We tabulate new values for the three theoretical corrections for twenty superallowed transitions, including the thirteen well-studied cases. With these new correction terms the corrected Ft values for the thirteen cases are statistically consistent with one another and the anomalousness of the 46V result disappears. These new calculations lead to a lower average Ft value and a higher value of Vud. The sum of squares of the top-row elements of the CKM matrix now agrees exactly with unitarity.
Background: The superallowed beta-decay rates provide stringent constraints on physics beyond the Standard Model of particle physics. To extract crucial information about the electroweak force, small isospin-breaking corrections to the Fermi matrix element of superallowed transitions must be applied. Purpose: We perform systematic calculations of isospin-breaking corrections to superallowed beta-decays and estimate theoretical uncertainties related to the basis truncation, time-odd polarization effects related to the intrinsic symmetry of the underlying Slater determinants, and to the functional parametrization. Methods: We use the self-consistent isospin- and angular-momentum-projected nuclear density functional theory employing two density functionals derived from the density independent Skyrme interaction. Pairing correlations are ignored. Our framework can simultaneously describe various effects that impact matrix elements of the Fermi decay: symmetry breaking, configuration mixing, and long-range Coulomb polarization. Results: The isospin-breaking corrections to the I=0+,T=1 --> I=0+,T=1 pure Fermi transitions 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 nuclei from A=11 to A=49. We carefully analyze various model assumptions impacting theoretical uncertainties of our calculations and provide theoretical error bars on our predictions. Conclusions: The overall agreement with empirical isospin-breaking corrections is very satisfactory. Using computed isospin-breaking corrections we show that the unitarity of the CKM matrix is satisfied with a precision better than 0.1%.
We investigate the radial-overlap part of the isospin-symmetry breaking correction to superallowed $0^+to 0^+$-decay using the shell-model approach similar to that of Refs. [1, 2]. The 8 sd-shell emitters with masses between $A=22$ and $A=38$ have been re-examined. The Fermi matrix element is evaluated with realistic spherical single-particle wave functions, obtained from spherical Woods-Saxon (WS) or Hartree-Fock (HF) potentials, fine-tuned to reproduce the experimental data on charge radii and separation energies for nuclei of interest. The elaborated adjustment procedure removes any sensitivity of the correction to a specific parametrisation of the WS potential or to vario
Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the $N=Z$ line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton-neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the $T=frac12$ doublets and $T=1$ triplets, and TDEs for the $T=1$ triplets. Relative strengths of the obtained isospin-symmetry-breaking terms {em are not} consistent with the differences in the $NN$ scattering lengths, $a_{nn}$, $a_{pp}$, and $a_{np}$. Based on low-energy experimental data, it seems thus impossible to delineate the strong-force ISB effects from beyond-mean-field Coulomb-energy corrections.
Superallowed $0^+ to 0^+$ nuclear beta decay provides a direct measure of the weak vector coupling constant, $GV$. We survey current world data on the nine accurately determined transitions of this type, which range from the decay of $^{10}$C to that of $^{54}$Co, and demonstrate that the results confirm conservation of the weak vector current (CVC) but differ at the 98% confidence level from the unitarity condition for the Cabibbo-Kobayashi-Maskawa (CKM) matrix. We examine the reliability of the small calculated corrections that have been applied to the data, and conclude that there are no evident defects although the Coulomb correction, $delta_C$, depends sensitively on nuclear structure and thus needs to be constrained independently. The potential importance of a result in disagreement with unitarity, clearly indicates the need for further work to confirm or deny the discrepancy. We examine the options and recommend priorities for new experiments and improved calculations. Some of the required experiments depend upon the availability of intense radioactive beams. Others are possible with existing facilities.
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