4 FIG. 4: (Color online) The figure shows the β -gated proton spectrum as obtained from the strips on the front side of de- tectors 1, 3, 5, and 6 overlaid with the spectrum obtained from the 2230 keV γ -ray coincidence spectrum. The normal- ization of the second spectrum is such that the intensities of the 1317 keV peak, being to 100% due to the 2230 keV γ co- incidence, match. To generate the γ -coincident spectrum, a spectrum was first generated with a 20 keV wide condition on the 2230 keV γ line. From this spectrum, we subtract then a similar spectrum conditioned by a gate left and right of the γ line. FIG. 3: (Color online) (a,b) The figure shows the β -gated proton spectrum as obtained from the strips on the front side of detectors 1, 3, 5, and 6. The peak numbers correspond to those of table II. Numbers below the curve are for protons decaying to the first excited state, but visible in the uncon- ditioned spectrum. The decay from the IAS in $^{33}$Cl to the ground state of $^{32}$S is by far the most prominent peak. (c) The spectrum is generated from the same detectors, how- ever, with a condition that the 2230 keV γ ray is observed in the germanium detectors. (d) The spectrum is obtained in a similar manner with a condition of the 1548 keV γ ray. No subtraction is operated in the sense that spectrum (a,b) contains also proton groups decaying to the first excited state (e.g. the 1317 keV protons), whereas spectrum (c) contains also events in coincidence with the 1548 keV γ line, as this 2230 keV γ ray always follows the 1548 keV γ ray. The area of the proton peak at 3173 keV observed in the coincidence spectra with the 2230 and 1548 keV γ lines gives the level of random coincidences of about 2 × 10 − $^{4}$. For spectra (c) and (d) we indicate the reminder of this 3173 keV peak number 21. To determine proton and γ -ray intensities, we used Gaussians for the peaks and straight-line fits for the 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. Energy (keV) Counts 1317 keV 1 10 10 2 10 3 10 4 10 5 10 6 2500 5000 7500 10000 Energy (keV) Counts singles spectrum (a) Energy (keV) Counts singles spectrum (b) Energy (keV) Counts E  = 2230 keV (c) Energy (keV) Counts E  = 1548 keV (d) 1 10 2 10 4 10 6 10 8 2000 4000 1 10 10 2 10 3 10 4 6000 8000 10000 1 10 10 2 10 3 1000 2000 3000 4000 5000 1 10 10 2 1000 2000 3000 4000 5000