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Half-life and branching ratio measurement of 23Mg and 27Si - 2013

last update: january 2016

Half-lives and branching ratio measurements of 23Mg and 23Si

Date: november 2013


  1. CEN Bordeaux Gradignan, F-33175 Gradignan, France
  2. JYFL, FI-40014 Jyväskylä, Finland
  3. Max-Plank-Institut für Kernphysik, D-69029 Heidelberg, Germany

contact@CENBG: B. Blank, J. Giovinazzo, C. Magron

Participants: P. Alfaurt, B. Blank, L. Daudin, T. Eronen, M. Gerbaux, J. Giovinazzo, D. Gorelov, S. Grévy, H. Guérin, J. Hakala, V. Kolhinen, J. Koponen, T. Kurtukian-Nieto, C. Magron, I. Moore, H. Penttilä, I. Pohjalainen, J. Reinikainen, M. Reponen, S. Rinta-Antila, M. Roche, A. de Roubin, B. Thomas, A. Voss


Half-lives and branching ratios of 23Mg and 23Si have been measured very precisely, better than 0,1% of precision each. These different values are in good agreement with previous ones [1]. More important, each new value helps to improve on the precision of the average value given in the literature. The experiment has been performed at the University of Jyväskylä, with the IGISOL facility.


Beta decays are a fantastic tool to study the weak interaction described by the standard model. This model and the physics beyond can be tested by precise measurements of nuclear beta decays. Among these tests, the conserved vector current (CVC) hypothesis and the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix are of great interest. The CVC hypothesis assumes that the vector coupling constant, G_V, is a universal constant. Regarding the unitarity condition of the CKM matrix, the quadratic sum of the elements of the first row should add up to unity:

\Sigma_{i=d,s,b} V_{ui} = 1.

In this equation, V_{ud} is the main term, V_{ud}^2 = \left(\frac{G_V}{G_{\mu}}\right)^2.

In order to test these two properties, superallowed Fermi beta decays have yielded the highest precision [2]. However, there are three other possibilities to make these tests: neutron decay, pion decay and mirror beta decays. This last one has not been used for long due to the difficulty of determining corrected ft values, Ft0, and Gamow-Teller to Fermi mixing ratios [1].

ft = \frac{f(Q_{EC}) \cdot (1+P_{EC}) \cdot T_{1/2}}{BR}

Ft=ft \cdot (1+\delta_{R}' )(1+\delta_{NS}^{V}-\delta_{C}^{V})

Ft_{0}=Ft \cdot G_{V}^{2} \left| M_F^0 \right|^{2} \left[1+(f_A/f_v)^{2} \right] = \frac{cst}{G_V^2 (1+\Delta_R^V )}

With the expression of ft, we can see that accurate determinations of half-lives and gamma-ray branching ratios (and the energy of the transition) are needed (figure 1). Because the reaction takes place in the nucleus, some theoretical corrections have to be added. These terms correct the Strong and Electromagnetic interactions effects. This new value is called corrected Ft, and it is a constant for super-allowed Fermi transitions with a fixed isospin, but not for mirror beta decays because there are mixed Fermi and Gamow-Teller transitions.

For those, the value Ft_0 is constant. It takes into account the \rho parameter which is the parameter for the mixing of Fermi and Gamow-Teller transitions. With this expression, we can verify that G_V is a constant. And then we can calculate V_{ud}.

Only 5 mirror transitions are available to calculate Ft_0 and V_{ud}. The precisions are 0.4% and 0.2% respectively. Compared to super-allowed Fermi decays which provide the most accurate values, 0.02% for each coefficient, these precisions are not good enough. To get better precision, we need to improve on those nuclei or add other nuclei to the 5 already used.

We have chosen to add 2 nuclei to the 5 already used: 23Mg and 23Si.

Figure 1: The precise determination of Ft_0 requires the measurement of the decay Q_{EC} value (from masses) and the super-allowed transition partial half-life, which implies the beta decay half-life and the branching ratio.


Experimental setup

A proton beam was produced by a cyclotron at an energy of 15 MeV, and then it was transferred to a target chamber. The targets were 23Na or 27Al depending on the nucleus we wanted to study, 23Mg or 23Si respectively. The secondary beam was transported to the yield station where our device was set-up (figure 2). There, we observed our nuclei decay by positron emission to its daughter. If in an excited state, the daughter nuclei decay emitting a gamma ray to its ground state. Our device consisted in a plastic scintillator, a tape transport system and a germanium detector very precisely calibrated in efficiency (10-3) (figure 2). It’s one of the two most precisely calibrated germanium detector in the world. The plastic scintillator and 2 photomultipliers were used to measure the ?+ particles and have access to the half-lives, the germanium detector was used to record the gamma rays needed to determine the branching ratios. The tape was used to implant the nuclei and transport them from the collection point to the measurement point between the plastic scintillator and the germanium detector. During the experiment, we used 2 acquisitions to record the data: a list mode type and a scaler one. These two acquisitions were both triggered by the beta particles.

Figure 2: Experimental setup.



The analyses for 23Mg and 23Si are very similar, so we will focus on 23Mg.

Half-life: We measured cycles with different phases (figure 3), these cycles were grouped into 28 runs. Each decay phase of each run was fitted by a decreasing exponential function plus a constant (for the background). Figure 4 presents the different half-lives determined versus the number of the run. The blue full point is the average of the 28 values. The errors are only statistical.

Figure 3: Measurement cycles.


Figure 4: Half-lifes measured for the experimental runs concerning the decay of 23Mg.


To look for systematic dependence we tested different parameters of the analysis: the beginning and the end of the fit of the decay phase, and parameters of the experiment: the number of nuclei in the decay part, the level of background, and the high voltages of the 2 photomultipliers.

None of these parameters induces a systematic error. So our final value for the half-life of 23Mg is: 11.3028 (43) s with a precision of 0.04%.

Branching ratio: We want to determine BRgs, but we can only measure very precisely BRexc through the gamma ray at 440 keV (figure 5). 52 runs were dedicated to the determination of the branching ratio. Each run lead to a gamma spectrum (figure 6), with the peak at 440 keV. This peak was fitted by a Gaussian function with a linear background. The results of these fits are presented on figure 7. The errors are only statistical.

To test systematic dependences we fitted the peak with different backgrounds (quadratic, stepping-linear and linear left-right), and different limits around the peak. None of these parameters induces a systematic dependence, so the final value for the branching ratio is 92.195 (79)% with a precision of 0.09%.

Figure 5: The measurement of the decay branching ratio to the ground state requires to estimate the branching ratio to the excited states, through gamma de-excitation measurement.


Figure 6: Gamma energy distribution measured in the decay of 23Mg.


Figure 7: Branching ratio estimated for the runs concerning the decay of 23Mg.




- 23Mg: Including this work’s value, the new average is 3 times more precise than the previous one: 11,3085 (133) s \rightarrow 0.12% precision.
- 23Si: Including this work’s value, the new average is twice more precise than the previous one: 4,1166 (74) s \rightarrow 0.18% precision.

Branching ratios:

- 23Mg: Including this work’s value, the new average is twice more precise than the previous one: 92,10 (14) % \rightarrow 0.15% precision.
- 23Si: Including this work’s value, the new average isn’t more precise than the previous one, but is in perfect agreement: 99,820 (17) % \rightarrow 0.02% precision.

The last figure (figure 8) presents uncertainties for different parameters needed to calculate Ft_0. The 5 mirror nuclei used to calculate Ft_0 and V_{ud} are pictured; in addition there are 23Mg and 23Si. For all these 7 nuclei, the most limiting parameter is the \rho coefficient, this parameter is very difficult to determine.

Concerning the 2 nuclei we have studied, we can see that our measurements have allowed to improve on the precision for the half-lives of 23Si and 23Mg and on the branching ratio for 23Mg. We can also see that the precision on the energy of the transition for 23Mg could be improved.

Figure 8: Improvement of the overall data for the mirror transitions.



[1] N. Severijns et al., Phys. Rev. C 78, 055501 (2008)
[2] J.C. Hardy and I.S. Towner, Phys. Rev. C 91, 025501 (2015)