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To determine proton and γ -ray intensities, we used Gaussians for the peaks and straight-line fits for the 

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background. All intensities were first normalized with respect to the most intense peak (the 3173 keV proton line and the 810 keV γ line, respectively) to obtain rela- tive branching ratios. 

The relative intensities of the proton groups can eas- ily be converted into absolute intensities by assuming that the absolute intensity of the feeding of the IAS at 5549 keV can be reliably determined. For this purpose, one usually assumes that the Fermi strength can be cal- culated more or less model independently by neglecting Coulomb and radiative corrections (see e.g. [16]). In the case of $^{33}$Ar as for other odd-mass nuclei, the additional problem of a GT contribution to the decay to the IAS arises. This contribution can either be determined ex- perimentally (see e.g. [9, 11]), be neglected assuming its contribution to be small, or taken from theoretical pre- dictions. We will calculate the Fermi part neglecting the corrections mentioned above and take the GT contribu- tion from Ref. [11]. 

The Fermi strength can be calculated from the relation between the ft value and the Fermi matrix element M F : ft = K/ ( g ’ 2 v ∗ M 2 $_{F}$), where K is a constant and g ’ v is the effective vector coupling constant of the weak interaction. For K/g ’ 2 $_{v}$, we use a value of 6144.2(13) s deduced from the super-allowed 0 + → 0 + decays [16]. The matrix ele- ment for nuclei with an isospin quantum number T = 3 / 2 is √$_{3. This allows the Fermi}$ ft value to be calculated to be 2048 s. 

