FT values measured to ±0.1% for superallowed beta transitions: Metrology at sub-second time scales
Introduction
Superallowed beta decay between nuclear analogue states1 with isospin, T=1, and spin-parity, Jπ=0+, occurs only via the vector current of the weak interaction: angular momentum conservation completely rules out the axial-vector component, which must carry off a spin of one and cannot connect two states that both have spin zero. Furthermore, the strength of such a transition – its ft value – is affected only by the small difference between the analogue parent and daughter configurations resulting from isospin symmetry breaking, not by the dominant nuclear structure common to them both.
As a result, the measured ft value can be related directly to the vector coupling constant, GV, with the intervention of only a few small (~1%) calculated terms to account for radiative and isospin-symmetry-breaking effects. These corrections can be calculated with 10% relative precision or better; so, with sufficient experimental precision, GV can be determined from a single superallowed transition to ±0.1%. If many such transitions can be measured with similar precision, the constancy of GV can be demonstrated and an average value extracted with still better precision. Once a reliable value for GV has been determined, it is only a short step to obtain from it the value of Vud, the largest element in the quark-mixing matrix known as the Cabibbo–Kobayashi–Maskawa (CKM) matrix; and only another short step to the most demanding available test of the unitarity of that matrix (Hardy and Towner, 2009). Since the unitary CKM matrix is a central pillar of the three-generation Standard Model of particle physics, any experimentally determined deviation from CKM unitarity would be a signature of new physics beyond the Model; and even uncertainty limits on a result that agrees with unitarity can serve as a constraint on possible candidates for new physics.
These are important goals that probe fundamental physics, but they can only be met if the transition ft values have been measured to better than ±0.1%.
Section snippets
The experimental challenge
The ft value that characterizes any β transition depends on three measured quantities: the total transition energy, QEC; the half-life, t1/2, of the parent state; and the branching ratio, R, for the particular transition of interest. The QEC value is required as a measure of the available phase space in the computation of the statistical rate function, f, while the half-life and branching ratio combine to yield the partial half-life, t. Since our goal is to achieve ±0.1% uncertainty on the ft
The experimental arrangement
Our experimental arrangement combines: (1) a production facility that can provide a pure (typically >99.8%) source of a selected short-lived activity; (2) a rapid tape-transport system that can periodically move the collected source to a shielded counting location in under 200 ms; and (3) two possible counting configurations at that location depending on whether a branching ratio or a half-life is being measured. For the former we use a combination of a thin scintillator and an HPGe detector for
Measurement methods
We determine β-decay branching ratios from the corresponding intensities of the β-delayed γ-ray peaks, which predominantly correspond to γ-transitions to the isomeric 0+ state at 130 keV in 38K (see Fig. 1). If the γ ray de-exciting state i in the daughter is denoted by γi, then the β-branching ratio, Ri, for the β-transition populating that state can be written:where Nβγi is the total number of β–γ coincidences measured in the γi peak, Nβ is the total number of β singles, εγi is
Current status of results
Measurements of the ft values for superallowed 0+→0+ β transitions have been going on for more than half a century with ever increasing precision. The most recent survey of world data was published by Hardy and Towner in 2009. It lists the ft values for 13 transitions, which were precisely determined from more than 150 independent measurements – including many of ours – which have contributed to the three input quantities, QEC, t1/2 and R, for each superallowed transition. On average, each
Conclusions
We have established a metrology facility for short-lived activities that are produced with an accelerator. With it, we have measured half-lives and β branching ratios to high precision (0.03% for half-lives and ~0.1% for branching ratios). Our methods have been described briefly and their capabilities illustrated with measurements on the superallowed β decay of 38Ca.
Acknowledgements
This work is supported by the U.S. Department of Energy under Grant No. DE-FG02-93ER40773 and by the Robert A. Welch Foundation under Grant no. A-1397.
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