Abstract:
Calculations of the axial-vector component to the radiative correction for superallowed Fermi $0^+ \rightarrow 0^+$ nuclear beta decay are here modified with quenched rather than free-nucleon coupling constants for the axial-vector and electromagnetic interactions with nucleons. The result increases the deduced value of $V_{ud}$ but does not restore unitarity in the CKM matrix.

Abstract:
Measured magnetic moments of single-particle states in the Pb region differ significantly from their Schmidt values. We discuss the reasons for this in terms of meson-exchange currents, isobar currents, core polarisation and other effects.

Abstract:
A new critical survey is presented of all half-life, decay-energy and branching-ratio measurements related to 20 0+ to 0+ beta decays. Compared with our last review, there are numerous improvements: First, we have added 27 recently published measurements and eliminated 9 references; of particular importance, the new data include a number of high-precision Penning-trap measurements of decay energies. Second, we have used the recently improved isospin symmetry-breaking corrections. Third, our calculation of the statistical rate function now accounts for possible excitation in the daughter atom. Finally, we have re-examined the systematic uncertainty associated with the isospin symmetry-breaking corrections by evaluating the radial-overlap correction using Hartree-Fock radial wave functions and comparing the results with our earlier calculations, which used Saxon-Woods wave functions; the provision for systematic uncertainty has been changed as a consequence. The new corrected Ft values are impressively constant and their average, when combined with the muon liftime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, V_{ud} = 0.97425(22). The unitarity test on the top row of the matrix becomes |V_{ud}|^2 + |V_{us}|^2 + |V_{ub}|^2 = 0.99995(61). Both V_{ud} and the unitarity sum have significantly reduced uncertainties compared with our previous survey, although the new value of V_{ud} is statistically consistent with the old one. From these data we also set limits on the possible existence of scalar interactions, right-hand currents and extra Z bosons. Finally, we discuss the priorities for future theoretical and experimental work with the goal of making the CKM unitarity test even more definitive.

Abstract:
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.

Abstract:
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 assess the likelihood of even higher quality nuclear data becoming available to confirm or deny the discrepancy. Some of the required experiments depend upon the availability of intense radioactive beams. Others are possible today.

Abstract:
The most precise value of V_{ud}, which is obtained from superallowed nuclear beta decay, leads to a violation of CKM unitarity by 2.2 sigma. Experiments are underway on two continents to test and improve this result through decay studies of odd-odd N = Z nuclei with A >or= 62. We show, in a series of illustrative shell-model calculations, that numerous weak Gamow-Teller branches are expected to compete with the superallowed branch in each of these nuclei. Though the total Gamow-Teller strength is significant, many of the individual branches will be unobservably weak. Thus, new techniques must be developed if reliable ft-values are to be obtained with 0.1% precision for the superallowed branches.

Abstract:
Beta-decay and muon-capture experiments in nuclei are reviewed. The conserved vector current hypothesis is confirmed through the observed constancy of the vector coupling constant determined from the superallowed Fermi transitions and from the measurement of the weak-magnetism term in mirror Gamow-Teller transitions. The axial-vector and pseudoscalar coupling constants in the nucleon are determined from neutron decay and muon capture on the proton respectively. In finite nuclei, evidence for these coupling constants being reduced relative to their free-nucleon values is discussed. Meson-exchange currents are shown to be an important correction to the time-like part of the axial current as evident in first-forbidden beta decays. Tests of the Standard Model are discussed, as well as extensions beyond it involving right-hand currents and scalar interactions.

Abstract:
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.

Abstract:
A new critical survey is presented of all half-life, decay-energy and branching-ratio measurements related to 20 0+ to 0+ beta decays. Compared with our last review, there are numerous improvements: First, we have added 27 recently published measurements and eliminated 9 references; of particular importance, the new data include a number of high-precision Penning-trap measurements of decay energies. Second, we have used the recently improved isospin symmetry-breaking corrections. Third, our calculation of the statistical rate function now accounts for possible excitation in the daughter atom. Finally, we have re-examined the systematic uncertainty associated with the isospin symmetry-breaking corrections by evaluating the radial-overlap correction using Hartree-Fock radial wave functions and comparing the results with our earlier calculations, which used Saxon-Woods wave functions; the provision for systematic uncertainty has been changed as a consequence. The new corrected Ft values are impressively constant and their average, when combined with the muon liftime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, V_{ud} = 0.97425(22). The unitarity test on the top row of the matrix becomes |V_{ud}|^2 + |V_{us}|^2 + |V_{ub}|^2 = 0.99995(61). Both V_{ud} and the unitarity sum have significantly reduced uncertainties compared with our previous survey, although the new value of V_{ud} is statistically consistent with the old one. From these data we also set limits on the possible existence of scalar interactions, right-hand currents and extra Z bosons. Finally, we discuss the priorities for future theoretical and experimental work with the goal of making the CKM unitarity test even more definitive.

Abstract:
Expressions for the P,T-violating NN potentials are derived for $\pi$, $\rho$ and $\omega$ exchange. The nuclear matrix elements for $\rho$ and $\omega$ exchange are shown to be greatly suppressed, so that, under the assumption of comparable coupling constants, $\pi$ exchange would dominate by two orders of magnitude. The ratio of P,T-violating to P-violating matrix elements is found to remain approximately constant across the nuclear mass table, thus establishing the proportionality between time-reversal-violation and parity-violation matrix elements. The calculated values of this ratio suggest a need to obtain an accuracy of order $ 5 \times 10^{-4}$ for the ratio of the PT-violating to P-violating asymmetries in neutron transmission experiments in order to improve on the present limits on the isovector pion coupling constant.