Superallowed Fermi Transitions Research Articles

Observation of β-delayed two-proton emission in the decay of 22Si

The decay of the lightest nucleus with Tz=−3 , 22 Si, was studied by a silicon array. A charged-particle group at 5600 (70) keV in the decay-energy spectrum was identified experimentally as β -delayed two-proton emission from the isobaric analog state (IAS) of 22 Al. Experimental results of the IAS fed by a superallowed Fermi transition were compared with our large-scale shell-model calculations. The ground-state mass of 22 Si was obtained indirectly in the experiment for the first time. Two-proton separation energy for 22 Si is deduced to be −108 (125) keV, which indicates that it is a very marginal candidate for two-proton ground-state emission.

βdecay of32Cl: Precisionγ-ray spectroscopy and a measurement of isospin-symmetry breaking

Background: Models to calculate small isospin-symmetry-breaking effects in superallowed Fermi decays have been placed under scrutiny in recent years. A stringent test of these models is to measure transitions for which the correction is predicted to be large. The decay of ${}^{32}$Cl decay provides such a test case.Purpose: The purpose of this paper is to improve the $\ensuremath{\gamma}$ yields following the $\ensuremath{\beta}$ decay of ${}^{32}$Cl and to determine the $ft$ values of the the $\ensuremath{\beta}$ branches, particularly the one to the isobaric-analog state in ${}^{32}$S.Method: Reaction-produced and recoil-spectrometer-separated ${}^{32}$Cl is collected in a tape and transported to a counting location where $\ensuremath{\beta}\ensuremath{-}\ensuremath{\gamma}$ coincidences are measured with a precisely calibrated high-purity germanium detector.Results: The precision on the $\ensuremath{\gamma}$ yields for most of the known $\ensuremath{\beta}$ branches has been improved by about an order of magnitude, and many new transitions have been observed. We have determined ${}^{32}$Cl-decay transition strengths extending up to ${E}_{x}\ensuremath{\sim}11$ MeV. The $ft$ value for the decay to the isobaric-analog state in ${}^{32}$S has been measured. A comparison to a shell-model calculation shows good agreement.Conclusions: We have experimentally determined the isospin-symmetry-breaking correction to the superallowed transition of this decay to be ${({\ensuremath{\delta}}_{C}\ensuremath{-}{\ensuremath{\delta}}_{\mathrm{NS}})}_{\mathrm{exp}}=5.4(9)%$, significantly larger than for any other known superallowed Fermi transition. This correction agrees with a shell-model calculation, which yields ${\ensuremath{\delta}}_{C}\ensuremath{-}{\ensuremath{\delta}}_{\mathrm{NS}}=4.8(5)%$. Our results also provide a way to improve the measured $ft$ values for the $\ensuremath{\beta}$ decay of ${}^{32}$Ar.

Superallowed Fermi transitions in RPA with a relativistic point-coupling energy functional

The self-consistent random phase approximation (RPA) approach with the residual interaction derived from a relativistic point-coupling energy functional is applied to evaluate the isospin symmetry-breaking corrections {\delta}c for the 0+\to0+ superallowed Fermi transitions. With these {\delta}c values, together with the available experimental ft values and the improved radiative corrections, the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is examined. Even with the consideration of uncertainty, the sum of squared top-row elements has been shown to deviate from the unitarity condition by 0.1% for all the employed relativistic energy functionals.

R-parity violating supersymmetric contributions to the neutron beta decay

We investigate the contribution to the angular correlation coefficients of the neutron beta decay within the R-parity violating (RPV) minimal supersymmetric standard model (MSSM). The RPV effects contribute to the scalar interaction at the tree level. The coefficient of the effective scalar interaction of the nucleon is determined in terms of the nucleon mass difference. On the basis of the recent update of the analyses of the superallowed Fermi transitions and the recent measurement of transverse polarization of the emitted electrons at PSI, we deduce new upper limits on the RPV couplings and compare them with those obtained through the pion decay and atomic electric dipole moment (EDM). We also give a comprehensive analysis of angular correlations sensitive to the RPV interactions.

High precision corrections to the neutron beta decay rate and electron asymmetry and current determination of Vud

The goal of the present analysis is to find, in the free neutron beta decay, the expressions for the decay rate and the electron asymmetry that contain all the theoretical effects at the 10−4 level. This accuracy is better than the current experimental precision that modern experiments allow. For this aim it is necessary to study the strong interaction effects, the radiative corrections and the recoil of the proton. A conceptual problem that we discuss in detail is the Fermi function additivity. The model dependence in the radiative corrections yields important effects which must be incorporated. We show that this is the only source of uncertainty that is out of control still at the mentioned order. As an application, we compare the values of the CKM matrix element |Vud | from this decay with the values both from the superallowed Fermi transition beta decays and the unitarity of the CKM matrix. We discuss the relevance of the observed discrepancies.

Super-allowed Fermi beta-decay

A final analysis of J π = 0 + → 0 + super-allowed Fermi transitions yields | V ud | 2 = 0.9500 ± 0.0007 ; | V ud | 2 + | V us | 2 + | V ub | 2 = 0.9999 ± 0.0011 with the operational vector coupling constant G V * / ( ℏ c ) 3 = ( 1.15052 ± 0.00021 ) × 10 - 5 GeV - 2 .

Super-allowed Fermi beta-decay: a further visit

A re-analysis of J π=0 + → 0 + super-allowed Fermi transitions, following Wilkinson (Nucl. Instr. and Meth. A 488 (2002) 654), using further input and a more-detailed procedure yields | V ud | 2=0.9500±0.0009; | V ud | 2+| V us | 2+| V ub | 2=0.9982±0.0015 or | V ud | 2+| V us | 2+| V ub | 2=0.9993±0.0013 with the operational vector coupling constant G ∗ V/(ℏc) 3=(1.15050±0.00027)×10 −5 GeV −2 .

Super-allowed Fermi beta-decay revisited

Analysis of J π=0 +→0 + super-allowed Fermi transitions is limited with respect to the precision of its outcome in terms of the Fermi coupling constant neither by the accuracy of the experimental input data nor by the confidence with which the radiative corrections can be applied but rather by knowledge of the nuclear mismatch: the subversion of isospin symmetry along the multiplets. Theoretical estimates of this mismatch differ considerably from author to author; their direct nuclide-by-nuclide application results in an apparent clear violation of the hypothesis of conservation of the vector current and evident inconsistency with unitary of the Cabibbo–Kobayashi–Maskawa matrix. This paper pursues and elaborates the earlier suggestion that, in these unsatisfactory circumstances, the best procedure is to look to the experimental data themselves to determine and eliminate the mismatch by appropriate extrapolation to Z≈0 where the mismatch falls away. This is done: (i) without any prior correction for mismatch; (ii) after correction for the full theoretical mismatch as estimated by various authors; (iii) after correction for nuclide-to-nuclide fluctuations in the theoretical mismatch. These three procedures are individually statistically satisfactory and mutually consistent in their extrapolation to Z≈0 despite the wide variety of the theoretical mismatches upon which they are based; they together yield: V ud 2=0.9514±0.0014 . The resultant unitarity test for the first row of the CKM matrix is V ud 2+ V us 2+ V ub 2=1.0007±0.0017 with the operational vector coupling constant G V */(ℏc) 3=(1.15138±0.00048)×10 −5 GeV −2 .

Synthesis and halflives of heavy nuclei relevant for the rp-process

Neutron deficient nuclei up to 100Sn were produced by fragmentation of a 1A·GeV 112Sn beam in a Be target. After isotopic separation by a fragment separator, the radionuclides were implanted in a stack of position sensitive Si-detectors acting as a microcalorimeter. The halflives and other decay properties were measured. Here we report halflives of rp-process waiting point nuclei between 80Zr and 92,93Pd. In addition the halflifes of the very short lived odd-odd NZ nuclei 90Rh, 94Ag and 98In were determined and attributed to superallowed Fermi transitions. Two new isotopes close to the p-dripline, 76Y and 78Zr, were identified for the first time.

Large-basis no-core shell-model calculations and their application to 10 C → 10 B fermi beta decay

We use a 4ħΩ shell-model calculation with a two-body effective interaction derived microscopically from the Reid93 potential to calculate the isospin-mixing correction for the10C→10B superallowed Fermi transition. The effective interaction takes into account the Coulomb potential as well as the charge dependence ofT=1 partial waves. Our results suggest the isospin-mixing correctionδ c ≈ 0.1%, which is compatible with previous calculations obtained by other methods. The obtainedδ C correction is about a factor of four too small to obtain unitarity of the Cabibbo-Kobayashi-Maskawa matrix with the present experimental data.

Large-basis shell-model calculation of the10C→10BFermi matrix element

We use a 4\ensuremath{\Elzxh}\ensuremath{\Omega} shell-model calculation with a two-body effective interaction derived microscopically from the Reid93 potential to calculate the isospin-mixing correction for the ${}^{10}{\mathrm{C}\ensuremath{\rightarrow}}^{10}\mathrm{B}$ superallowed Fermi transition. The effective interaction takes into account the Coulomb potential as well as the charge dependence of $T=1$ partial waves. Our results suggest the isospin-mixing correction ${\ensuremath{\delta}}_{C}\ensuremath{\approx}0.1%,$ which is compatible with previous calculations. The correction obtained in those calculations, performed in a 0\ensuremath{\Elzxh}\ensuremath{\Omega} space, was dominated by deviation from unity of the radial overlap between the converted proton and the corresponding neutron. In the present calculation this effect is accommodated by the large model space. The obtained ${\ensuremath{\delta}}_{C}$ correction is about a factor of 4 too small to obtain unitarity of the Cabibbo-Kobayashi-Maskawa matrix with the present experimental data.

Isospin-mixing corrections for fp-shell Fermi transitions.

Isospin-mixing corrections for superallowed Fermi transitions in fp-shell nuclei are computed within the framework of the shell model. The study includes three nuclei that are part of the set of nine accurately measured transitions as well as five cases that are expected to be measured in the future at radioactive-beam facilities. We also include some new calculations for $^{10}\mathrm{C}$. With the isospin-mixing corrections applied to the nine accurately measured ft values, the conserved-vector-current hypothesis and the unitarity condition of the Cabbibo-Kobayashi-Maskawa matrix are tested.

Isospin mixing and the sum rule of super-allowed fermi β decay

The amplitudes of isospin mixing to the ground states of 14O and several odd-odd N  Z nuclei are studied in the Hartree-Fock approximation taking into account charge symmetry and charge independence breaking forces. We find that isospin mixing increases the sum rule of super-allowed Fermi transitions by 0.1 % in 14O and by more than 1 % in 54Co because of core effects, while valence particles tend to decrease the sum rule. It is shown that the sum rule increases due to the CSB and CIB interactions amounts to about 40% of that due to the Coulomb interaction alone.

Limits on the presence of scalar and induced-scalar currents in superallowed beta decay.

Limits on the scalar and induced-scalar coupling constants are established from experimental ft values of superallowed Fermi transitions. The role of the uncertainties in the ft values is discussed, leading to minimal coupling strengths that can be extracted from ft values. The implications for the Kobayashi-Maskawa mixing angles are also discussed.

Final-state electronic interactions in allowed beta decay.

We give a perturbative calculation of the effects of final state electronic interactions on the transition rates in allowed beta decay. The results include a simple relativistic expression for the electron screening correction to the total decay rate for low-Z nuclei which corrects a recent calculation by Drukarev and Strikman, and expressions for the corrections to the decay spectra for transitions to particular final atomic states. We discuss briefly applications to superallowed Fermi transitions and the beta decay of tritium.

Electron screening corrections to 0 +→0 + beta decays

We correct the perturbative calculation of the electron screening corrections to 0 +→0 + beta decays given by Drukarev and Strikman. The corrected calculation agrees with the standard Rose treatment of the screening corrections and eliminates the Z-dependent discrepancies in the corrected ft values for the superallowed Fermi transitions claimed by those authors.

Remarks concerning the O(Zα2) corrections to Fermi decays, conserved-vector-current predictions, and universality

Finite-nuclear-size contributions to the O(Z${\ensuremath{\alpha}}^{2}$) corrections to Fermi decays are studied for realistic nuclear-charge distributions. In conjunction with the results of Koslowsky et al. and recent papers by the author and Zucchini and by Jaus and Rasche, these refinements lead to an average value scrFt=3070.6\ifmmode\pm\else\textpm\fi{}1.6 s for the accurately measured superallowed Fermi transitions. Correspondingly, ${V}_{\mathrm{ud}}$=0.9744\ifmmode\pm\else\textpm\fi{}0.0010 and ${V}_{\mathrm{ud}}$${}^{2}$+${V}_{\mathrm{us}}$${}^{2}$+${V}_{\mathrm{ub}}$${}^{2}$=0.9979\ifmmode\pm\else\textpm\fi{}0.0021 in good agreement with the three-generation standard model at the level of its quantum corrections. The agreement with conserved-vector-current predictions is very good, with each of the eight transitions differing from the average by <1\ensuremath{\sigma}. The consequences of using two other calculations of the nuclear mismatch correction ${\ensuremath{\delta}}_{c}$, Wilkinson's microscopic analysis and the recent results of Ormand and Brown, are briefly discussed. A useful upper bound on scrFt, independent of the ${\ensuremath{\delta}}_{c}$ calculation, is given.

Current algebra formulation of radiative corrections in gauge theories and the universality of the weak interactions

A current algebra formulation of the radiative corrections in gauge theories, with special applications to the analysis of the universality of the weak interactions, is developed in the framework of quantum chromodynamics. For definiteness, we work in the SU(2)\ifmmode\times\else\texttimes\fi{}U(1) model with four quark flavors, but the methods are quite general and can be applied to other theories. The explicit cancellation of ultraviolet divergences for arbitrary semileptonic processes is achieved relying solely on the Ward identities and general considerations, both in the $W$ and Higgs sectors. The finite parts of order ${G}_{F}\ensuremath{\alpha}$ are then evaluated in the case of the superallowed Fermi transitions, including small effects proportional to ${g}_{s}^{\ensuremath{-}2}({\ensuremath{\kappa}}^{2})$, which are induced by the strong interactions in the asymptotic domain. We consider here both the simplest version of the Weinberg-Salam model in which the Higgs scalars transform as a single isospinor, as well as the case of general symmetry breaking. Except for the small effects proportional to ${g}_{s}^{\ensuremath{-}2}({\ensuremath{\kappa}}^{2})$, the results are identical to the answers previously found on the basis of heuristic arguments. The phenomenological verification of Cabibbo universality on the basis of these corrections and the superallowed Fermi transitions has been discussed before and found to be in very good agreement with present experimental evidence. The analogous calculation for the transition rate of pion $\ensuremath{\beta}$ decay is given. Theoretical alternatives to quantum chromodynamics as a framework for the evaluation of the radiative corrections are briefly discussed. The appendixes contain a generalization of an important result in the theory of radiative corrections due to L. S. Brown, G. Preparata, and W. I. Weisberger, an analysis of the hadronic contributions to the $W$ and $\ensuremath{\varphi}$ propagators, mathematical methods for evaluating the ${g}_{s}^{\ensuremath{-}2}({\ensuremath{\kappa}}^{2})$ corrections, and discussions of quark mass renormalization and the absence of operator seagulls in the hadronic correlation functions. Some of the methods discussed in this paper can also be applied to the study of radiative corrections of order ${G}_{F}\ensuremath{\alpha}$ to other processes affected by the strong interactions.

Super-allowed Fermi beta-decay

Recent measurements demonstrate for the first time a clear trend of ft with Z for the super-allowed Fermi transitions. The value g βV R = (1.41222 ± 0.00046) × 10 −49 erg cm 3 is recommended for the vector coupling constant effective for nucleon β-decay (including the “inner” radiative correction); consequences are discussed.

Effect of the diffused charge distribution in the analysis of β-decays

Abstract The uniform charge distribution inside a nucleus is re-examined by using a diffused charge distribution, which reduces to the uniform charge distribution when the thickness is taken to be zero. Electron radial wave functions and ft values of superallowed Fermi transitions are discussed in terms of these two different charge distributions.