date: Mai 2006 / mai 2007
Due to its inherent simplicity, the super-allowed nuclear decay between nuclear states with (J,T) = (0+,1) is a very powerful tool to test the present theory of weak interaction at low energies. The corrected Ft value, determined from the experimental comparative life-time, ft, is :
and directly related to the vector coupling constant, gV.
The matrix element, MF, equals 2 for T=1 nuclei. ft is determined from the mass difference between the initial and final analogue states, QEC, the half-life of the parent nucleus, T1/2, and the branching ratio (BR) for the super-allowed decay, while C, NS, ’R and R are correction factors that must be determined by models. From the corrected Ft value, one can determine the vector coupling constant, gV, and test the validity of the Conserved Vector Current (CVC) hypothesis of the weak interaction stating that the vector part of the weak interaction is not influenced by the strong interaction. Furthermore, the gV value combined with the weak vector coupling constant determined from the purely leptonic decay, gV yields the up-quark down-quark element Vud of the Cabibbo - Kobayashi - Maskawa (CKM) quark-mixing matrix.
In order to perform such tests of the electroweak part of the Standard Model one needs high precision measurements of QEC, T1/2 and BR. 38Ca is a T=1, TZ= -1 nucleus that decays with a probability of about 75 % by a super allowed 0+ to 0+ transition. The aim was the measurement of the decay half-life with a relative precision of 1 ‰.
Production and purification
The experiment was performed at ISOLDE, CERN. Pure samples of 38Ca were produced by spallation reaction of proton beam on a titanium target. A fluorine leak in the ion source allowed the formation of CaF+ ions which were separated by the ISOLDE high-resolution separator as mass 57 molecules and collected by REXtrap. Decays of 38Ca in the trap and other contaminants were rejected by a time-of-flight analysis during ejection of the ion bunch from REXtrap where a beam shutter allowed only mass 57 ions to pass to a Mylar tape, which then transported the activity into the detection setup.
The thus purified samples of 38Ca were implanted on a 0.5 inch wide movable tape placed at the end of the extraction beam line. The tape transported the activity to the center of a 4 gas counter working in the Geiger regime. In 2006, the Geiger counter was surrounded by 4 NaI -ray detectors. For the 2007 experiment, the NaI detectors were replaced by two high-purity coaxial germanium detectors in the horizontal plane in order to provide - coincidence data. The aim of the detection was to measure the super-allowed BR and to monitor the background.
Figure 1: Photo of the experimental setup used in 2007. The tape system, the two Germanium detectors as well as the Geiger counter in the center are visible.
For the data taking we have used two independent data acquisition (DAQ) systems. The trigger for both DAQ systems was the signal from one of the two halves of the Geiger counter. The first system, simple but fast, DAQ A, was running in a cycle-by-cycle mode and had two predefined dead times - 2 (Data1) and 8 (Data2) s. The second system, DAQ B, providing event-by-event data, had a predefined dead time of 100 s (Data3). For both DAQ systems, the dead times were chosen to be longer than any possible event treatment by the electronics or data processing. The dead-time window was generated with a module having a precision better than 10 ns. DAQ A registered only the time difference between the trap extraction signal and the subsequent event triggers. With the DAQ B we could register also the energy signals from the germanium detectors in coincidence with the trigger signal.
Results from 2007
During the 2007 data taking we have accumulated more than 1.7 millions 38Ca ions. A typical spectrum for the decay of 38Ca is presented in figure 2 below where the contributions from daughter decays (38K) and the background are specifically shown.
Figure 2: Result from a typical run for the half-life of 38Ca. The different contributions to the total decay curve are presented separately as determined by a likelihood fit.
The life-time measurements provided by one of the data sets as a function of run number are presented in figure 3 below. A preliminary half-life value is 445.81(96) ms.
Figure 3: The half-life as determined from the different runs is presented as a function of the run number. The preliminary average value is 445.81(96) ms.
Branching ratio (BR):
The BR for the super-allowed decay was never measured before on a absolute scale. The main purpose of the present experiment being the half-life measurement, we were not aiming to achieve the required precision on the BR. Nevertheless, we have analyzed the spectra of the two germanium detectors. Figure 4 shows the spectrum of one of the two Germanium detectors. We determine the absolute BR for the 1568 keV ray to be 20.3(7)% (preliminary value). Using the relative ray intensities from Anderson et al. , we determine the super-allowed branching ratio to be 75.6(29) %.
Figure 4: Gamma-ray spectrum as registered by one of the two Germanium detectors. The rays belonging to the decay of 38Ca are labeled.
Conclusion and perspectives
Using the new values for the correction factors and the statistical rate function, f, as given in [2,3] along with our results as well as the literature values  for the half-life and the Q value, the ft value of 38Ca becomes 3140(120) s and the corrected Ft value 3154(120) s. This value has to be compared to the accepted value of Ft from the most precise 13 measured transitions that is 3072.08(79) s .
In order to include 38Ca in the high precision measurements of super-allowed decays, one needs to improve in particular the precision of the super-allowed BR. The QEC has already been remeasured at MSU  and at ISOLDE .
 J.C. Hardy and I. S. Towner, Phys. Rev. C (2009), to be published
 J.C. Hardy and I. S. Towner, Phys. Rev. C71, 055501 (2005)
 I. S. Towner and J.C. Hardy, Phys. Rev. C77, 025501 (2008)
 B.D. Anderson et al., Phys. Rev. C54, 602 (1996)
 G. Bollen et al., Phys. Rev. Lett. 96, 152501 (2006)
 S. George et al., Phys. Rev. Lett. 98, 162901 (2007)