Superallowed Fermi Research Articles

Charge-dependence in superallowed beta decay: A comment

Experimental ƒt-values are used to examine various theoretical treatments of analogue symmetry breaking in superallowed Fermi β-decay. None of the fits to experiment in more than barely acceptable and, contrary to a previous analysis, we find no clear preference for one type of treatment over another.

Isospin-symmetry-hindered branch of 42Sc β-decay

The branching fraction for the isospin-symmetry-hindered positron decay of 42Sc to 42Ca (1.837 MeV) was measured to be (6.3 ± 2.6) × 10 −5 by observation of delayed γ-rays. This branch alone corresponds to a reduction of the superallowed ground-state Fermi strength by (0.043 ± 0.018)%. The 42Sc sources were produced by the 42Ca(p, n) 42Sc reaction at 7.7 MeV.The measured branching agrees with Coulomb-mixing calculations by Rappleyea and Kunz and by Towner, but is smaller than other calculations.This result is of interest in connection with the intercomparison of the super-allowed 0 + → 0 + pure Fermi decays, which determine the effective vector coupling constant of nuclear β-decay.

Super-allowed Fermiβdecay: the lifetimes ofAlm26,V46, andCo54

The half-lives of the Fermi super-allowed ..beta..-ray transitions from /sup 26/Al/sup m/, /sup 46/V, and /sup 54/Co have been measured by multiscaling ..beta.. rays detected in a plastic scintillator. The activities were made via the reactions /sup 24/Mg(t,n)/sup 26/Al/sup m/ at E/sub t/ = 3.1 MeV, /sup 46/Ti(p,n)/sup 46/V at E/sub p/ = 10 MeV, and /sup 54/Fe(p,n)/sup 54/Co at E/sub p/ = 10 MeV, respectively. Results for the half-lives were as follows: /sup 26/Al/sup m/ - 6339.5 +- 4.5 msec; /sup 46/V - 422.52 +- 0.45 msec; and /sup 54/Co - 193.28 +- 0.18 msec. A previously published experiment on the /sup 46/V half-life has been reanalyzed and found to be in agreement with the present work. Recommended values for the half-lives of the eight accurately measured super-allowed Fermi ..beta.. emitters are presented. We discuss the effect of arbitrary symmetry breaking in gauge theories on the extraction of the mean quark charge and conclude that the associated uncertainty is unlikely to be large.

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.

A measurement of the half-life of the superallowed Fermi decay [formula omitted] and a study of some systematic errors involved

The half-life for 46V positon decay has been determined with high precision. Particular care has been taken to eliminate systematic effects introduced by inappropriate data analysis methods, by the presence of contaminant activities and by the occurrence of pulse pile-up in the electronic system. The final result obtained is 422.28 ± 0.23 ms, which is significantly lower than the presently accepted value.

The ft value of the superallowed Fermi decay [formula omitted

The 46 Ti(p, n) 46 V reaction threshold has been measured as 8007.7 ± 1.8 keV, equivalent to an energy release of 6030.6 ± 1.8 keV in the beta decay 46 V(β +) 46 Ti . The 46 V half-life has been measured as 422.28 + 0.23 ms. The corresponding ft value is reasonably consistent with those of other superallowed Fermi decays.

The mismatch problem in super-allowed Fermi β-decay

The accuracy with which the vector coupling constant can be extracted from superallowed Fermi β-decay is now limited by our ability to handle theoretically the mismatch between the initial and final states that is due to SU(2)- breaking. It is shown that differences of about six times the experimental error arise depending on how the symmetry breaking is estimated.

The half-life for the superallowed fermi beta decay 50Mn(β +) 50Cr

The half-life for the decay 50Mn(β +) 50Cr has been measured to be 282.8 ± 0.3 ms. This result is ≈ 1% lower than the accepted value. It would bring the ft value for 50Mn decay into agreement with recent measurements for other superallowed Fermi decays.

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.

The ft value for the superallowed fermi decay [formula omitted

The threshold for the reaction 54Fe(p,n) 54Co has been measured as 9192.4±1.8 keV. The corresponding end-point energy for the superallowed Fermi decay 54Co(β +) 54Fe is 7218.5 ± 1.8 keV. The half-life for 54Co decay was found to be 193.0 ± 0.3 ms. The calculated “effective” ft value is in good agreement with those of 14O, 26Al m and 34Cl.

The Nolen-Schiffer anomaly and the conserved vector current

It is shown that Noble's treatment of the Nolen-Schiffer anomaly in terms of the polarization of the core by valence nucleons permits the demonstration that admixing of the isovector breathing mode by Coulomb forces has a negligible effect of the ft-values of super-allowed Fermi transitions.

The half-life of 14O and the ft value of the superallowed Fermi decay

A series of experiments has been carried out to measure the half-life for 14O decay, using different reactions and a variety of techniques, in two laboratories. Considerable care has been taken in the experiments, and in the data analyses, to reduce the possibility of systematic errors. The final result obtained is 70.588 ± 0.028 s, where the error is the statistical standard deviation (external error) of the weighted mean. This leads to an ft value for the 0 + → 0 + superallowed 14O Fermi decay of 3050 ± 11 s, excluding electromagnetic radiative corrections; the corresponding “effective” ft value is 3090 ± 11 s, allowing for the first-order outer radiative correction. The error quoted for the ft value is determined very largely by the error in the f-value. This result for the 14O Fermi decay is consistent with the ft values for the 26mAl and 34Cl decays.

Half-Lives ofV46,Mn50, andCo54

The nuclides $^{46}\mathrm{V}$, $^{50}\mathrm{Mn}$, and $^{54}\mathrm{Co}$ were formed via the ($p, n$) reaction at ${E}_{p}=10$ MeV and half-lives were measured by observing $\ensuremath{\beta}$ rays in a plastic scintillator. Values obtained were 425.3\ifmmode\pm\else\textpm\fi{}2.0, 285.1\ifmmode\pm\else\textpm\fi{}0.9, and 193.1\ifmmode\pm\else\textpm\fi{}0.8 msec, respectively. The results agree with previous work within errors and thus confirm the systematic behavior of these ${0}^{+}$\ensuremath{\rightarrow}${0}^{+}$ superallowed Fermi $\ensuremath{\beta}$ decays.

The superallowed Fermi decay of 34Cl and the vector weak interaction

The half-life for the superallowed Fermi decay of 34 Cl has been measured to be 1.526 ± 0.002 s, and the beta end-point energy, 4467.4 ± 1.9 keV. The deduced ft value is in good agreement with that for 26 Al m . The result provides no evidence for mirror asymmetry in mass 34 Fermi decays.

Questions Pertaining to Charge Dependence of Radiative Corrections to Superallowed Fermi Transitions

We consider the problem posed by the near equality of the $\mathrm{ft}$ values for the nine ${0}^{P}\ensuremath{\rightarrow}{0}^{P}$ ($P=+ or \ensuremath{-}$) superallowed Fermi transitions. So long as one is oblivious to radiative effects, this near equality of $\mathrm{ft}$ values may be (as, indeed, it has been) regarded as a triumph of the CVC (conserved-vector-current) hypothesis. However, if one takes note of the fact that CVC, which guarantees the equality of the "bare" $\mathrm{ft}$ values, is broken by electromagnetism and that the charge of the decaying nuclei varies from $Z=1$ (for ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$) to $Z=27$ (for ${\mathrm{Co}}^{54}$), the relationship between CVC and the physical $\mathrm{ft}$ values becomes obscure; CVC can be upheld only if one can establish that the renormalization effects are small. In a previous contribution we used a combination of general theorems and model-dependent arguments to show that, in the limit of vanishing lepton momenta, $Z$-dependent renormalization effects arise only in order ${Z}^{2}{\ensuremath{\alpha}}^{2}$ (3.9% for ${\mathrm{Co}}^{54}$). The present paper contains a fuller explanation of the aforementioned theorems as well as amplified and improved proofs. Also, topics not treated in our earlier work (corrections for finite lepton momenta, effects of real photon emission, etc.) are discussed and the model-dependent part of the argument is reviewed.

Is the detailed shape of the nuclear charge distribution relevant to the ft values of superallowed Fermi transitions?

Abstract The uniform nuclear charge distribution remains a satisfactory model for calculating electron radial wave functions and nuclear matrix elements even in the case of the superallowed Fermi transitions of light nuclei up to 54 Co, where high accuracy is needed to determine the vector coupling constant of nuclear β-decay. The modifications due to the deviation of the realistic charge distribution from this simple model are found to be smaller than previously thought and therefore are negligible, provided that the nuclear radius, which is the most important shape parameter, has its correct value (i.e. the r.m.s. radii of the realistic and the model distribution are the same). Moreover, the dependence on the nuclear radius is fairly small for the light nuclei under consideration.

The 26Al m problem

A precision measurement of the 26Al m 26Mg mass difference brings the anomalously low ft value for the super-allowed pure Fermi transition 26 Al m (β +) 26 Mg closer to the average of the ft values of six similar β + transitions. The anomaly, however, is still significant.

The ft value of the superallowed fermi beta decay 26mAl( β+) 26Mg

The threshold for the reaction 26Mg(p, n) 26mAl has been measured in terms of the accurately known energies of the α-particle groups from a ThC source. The result E th = 5208.5 ± 1.7 keV corresponds to a Q-value of −5013.5 ± 1.6 keV. The weighted mean of this and an earlier independent Q-value measurement gives for the end-point in the beta decay 26mAl( β +) 26Mg the result 3208.6±1.3 keV. The half-life for the beta decay has been measured as 6.346±0.005 sec. The ft value for the transition is thus found to be 3081±7 sec, including radiative corrections. This result is lower than those for other superallowed Fermi decays. It corresponds to a value for the vector coupling constant G β v = (1.4129±0.0016) x 10 −49 erg · cm 3. The value inferred for the Cabibbo angle is cos θ β v = 0.985±0.001, excluding uncertainties in the radiative corrections. This result appears to differ appreciably from the value inferred from the rate of K + → π 0e + v decay.

Screening Corrections to the Fermi Function for AllowedβDecay

The influence of electron screening on the Fermi function $F(W,Z)$ for allowed $\ensuremath{\beta}$ decay is reconsidered. Numerical values for $F(W,Z)$ are obtained by integrating the radial Dirac equations for the decay electrons (positrons) in a self-consistent atomic potential. Relativistic Hartree-Fock-Slater equations are used to construct the atomic potential. The Fermi function is tabulated for various nuclei and energies, and comparisons are made with $F(W,Z)$ for a pure Coulomb field. Detailed comparisons are also made with the WKB screening formula of Rose as well as with the previous numerical results of Reitz and of B\uhring. It is found that the Rose formula provides an accurate approximation to $F(W,Z)$ over the dominant portion of the $\ensuremath{\beta}$ spectrum provided the endpoint energy is sufficiently high and provided further that an appropriate value of the potential at the nucleus ${V}_{0}$ is used. An empirical formula for ${V}_{0}$ from the Hartree-Fock-Slater calculations is provided. The numerical results of Reitz appear to be badly in error, especially for large electron momenta. The predictions of B\uhring for a screened-potential model are in good agreement with the present work. Corrections to the $\mathrm{ft}$ value of several superallowed Fermi transitions are recomputed and found to be negligibly different from the predictions made using the Rose approximation.