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Superallowed Fermi transitions

Last update: February 2016

Weak interaction studies with nuclear beta decay

Three of the four fundamental interactions are important to describe correctly the behaviour of the atomic nucleus: the strong interaction between protons and neutrons, the weak interaction which transforms a proton into a neutron and vice versa, and the electromagnetic interaction which acts between charged particles. Therefore, the atomic nucleus is an ideal "laboratory" to study these interactions.

In our group, we use nuclear beta decay to study the properties of the electro-weak interaction, a unification of the weak and electromagnetic forces. The strength, i.e. the velocity of certain beta-decay channels, so called Fermi 0+ —> 0+ decays, allow to determine a fundamental constant in the quark sector (protons and neutrons are made of three quarks), the "vector coupling constant" of the electro-weak interaction.

By measuring with high precision properties of atomic nuclei which decay by this super-allowed 0+ —> 0+ \beta+ decay branch, the half-life T1/2, the super-allowed branching ratio BR, and the mass difference between the parent nucleus and the daughter nucleus, one can determine the decay strength, the ft value. This value has to be corrected by theoretical corrections (of the order of 1%) to arrive at a nucleus independent Ft value which then allows to extract the vector coupling constant gv.

Schematic view of the \beta+ decay of an atomic nucleus. At the nuclear level, a proton is transformed into a neutron with the emission of a positron and a neutrino. At the quark level, an up quark is transformed into a down quark. The experimental observables are the half-life T1/2, the branching ratio BR, and the parent-daughter mass difference called Q value


This coupling constant is directly related to the mixing of different quark flavours as described initially by N. Cabibbo and by the Nobel Prize winners M. Kobayashi and T. Maskawa in the Cabibbo, Kobayashi, Maskawa (CKM) quark-mixing matrix.

The CKM matrix mixes different flavour of quarks. "Theoretical quarks" are thus transformed into "real quarks"


Experimental program

In our group, we started a program of high-precision measurements with experiments mainly at the Accelerator Laboratory of the University of Jyväskylä ands at ISOLDE/CERN. The first experiments were devoted to the decay of 62Ga for which we measured the half-life (also during an experiment at the GSI online separator) and the branching ratio with sufficiently high precision. The figure below shows a photo of the experimental setup used in this experiment. In the following experiments, we determine the half-lives of 26Si, 30S, and 42Ti. The half-life of 38Ca was measured in an experiment conducted at the ISOLDE laboratory at CERN.

Photo of the setup used during one of the first experiments at Jyväskylä showing in the left-hand part 3 germanium detectors for gamma-ray detection and the photomultipliers to read-out the plastic scintillators detecting the beta particles. The Penning trap on the right-hand side is used to purify the samples measured from contaminants and to measure the mass difference between the parent and the daughter nuclei, the Q value


The figure below shows a typical result from the half-life measurements. The measured spectrum has to be "unfolded" into the contribution from background, daughter decay and the decay of interest. A global fit yields the half-life needed.

Example of a decay curve as measured during our experiments. The data from the nucleus of interest, 38Ca, are “mixed” with the daughter decay, 38mK, and background counts.


Beyond the high-precision measurement of the half-life, the branching ratio and the decay Q value have to be determined with the same precision. The precision on the Q values can be reached relatively easily with Penning-trap mass spectroscopy. These experiments are performed by instruments like ISOLTRAP at CERN, JYLFTRAP in Jyväskylä or similar installations. A typical result from one of our measurements at JYFLTRAP is shown in the figure below.

Mass determination of 62Ga and 62Zn via a measurement of their "cyclotron frequency" to deduce the mass difference, the Q value.


Future measurements

The most difficult part today is the measurement with high precision of the branching ratio. To perform the measurements in the future, we have a program running to calibrate with the necessary precision ( 0.2%) the efficiency of a germanium detector (more details, in french). This program being under way, we have already performed branching ratio measurement of18Ne, 38Ca and 10C. Future measurements will deal with 26Si, 30S, and 42Ti.


Photo of the setup used during one the 2015 experiment at ISOLDE-CERN for measuring the branching ratio of 10C. The branching ratio is measured by means of our precisely calibrated germanium detector. The activity is accumulated on a fixed catcher with a slight angle such that the catcher faces the germanium detector at 0°. A DSSD dectector is used for monitoring the beam implantation profile.


These types of measurements are performed all over the world and evaluated regularly. The outcome, the "world data" on Ft values determined with high precision, is shown in the following figure. From these data, the vector coupling constant of the electro-weak interaction is determined and, with a measurement of the muon decay, the CKM matrix element Vud is deduced.

The figure below shows a summary of such measurements. The red isotopes are the most precisely measured ones. In green are candidates for future experiments. This type of measurement yields today the highest precision on the vector coupling constant and on the CKM matrix element, about an order of magnitude more precise than any other method.

The plot shows a summary of the "world data" on super-allowed 0+ —> 0+ beta decays. The inset shows the nuclides where high-precision data are already available. The green nuclides are presently addressed or will be addressed in future measurements.


Mirror beta decays

Another possible approach are mirror beta decays. These decays are a mixture of Fermi (vector) and Gamow-Teller (axial-vector) decays and can serve the same purpose. However, in addition to the half-life, the branching ratios and the Q value, the Fermi-to-Gamow-Teller mixing in the decay has to be measured e.g. via a beta-neutrino angular correlation measurement, a rather difficult experiment. Nonetheless, a recent analysis of the available data showed the potential of this approach and new measurements have recently started. The figure below compares the different results on Vud as obtained through the different approaches.

Comparison of the precision obtained on 0+ —> 0+ decays, the neutron decay, nuclear mirror decays and the pion decay to determine the Vud CKM matrix element.


This program being under way, we have already performed the measurement of half-lives and branching ratios of 31S, 23Mg, 27Si, and 37K. Future measurements will deal with 17F and 29P.