6 We take the GT to Fermi ratio from Ref. [11], where $^{it was determined to be 0.044}$±0.002. Adding this value to the Fermi matrix element and taking into account the ratio between the squares of the vector and the axial- vector coupling constants of 1.2695(29) [17], we derive a total f t value for the decay to the IAS of 1962(5) s. As we have neglected the corrections mentioned above, we add an additional uncertainty of 1% for this number which yields the final f t value for the IAS of 1962(20) s. TABLE III: Gamma-ray energies and their relative branching ratios from the present work and the work of Borge et al. [8]. Averages are given only for γ rays following the decay of $^{33}$Ar. For the γ ray at 2230 keV, the relative branching ratio in our experiment indicated by the star is too high, when it is cal- culated with respect to the 810 keV line. The former γ ray is always preceded by a proton which triggers the DSSSDs, while for the latter the β particles have to trigger. Evidently, the β trigger probability is much smaller than the proton trigger efficiency which then yields higher relative branching ratios for β p γ events. The literature value for the last γ -ray energy is 2867.72(2) keV. FIG. 5: (Color online) Gamma-ray spectrum registered with the three germanium clover detectors. The peaks labeled belong directly or indirectly to the decay of $^{33}$Ar. The in- set shows the region around the 1541 keV and 1548 keV γ rays. The 1548 keV peak from the decay of the second ex- cited state in $^{32}$S is very weak and only visible as a shoulder of the stronger 1541 keV peak from the decay of the sec- ond excited state of $^{33}$Cl. The relative intensities of all rel- evant peaks can be found in table III. Background lines are from $^{60}$Co (1173 keV, 1332 keV), from a contamination of the beam with $^{35}$Ar (1220 keV, 1764 keV, 2694 keV), from $^{40}$K (1461 keV), and from the decay of the first excited state of $^{208}$Pb (2615 keV). To determine the absolute branching ratio to the IAS, we now need the statistical rate function or Fermi function calculated from the β -decay Q EC value (11.6193(6) MeV [18]) from which we subtract the excita- tion energy of the IAS (5.5478(9) MeV) [14] and the half- life of $^{33}$Ar. For the half-life, we use the average of differ- ent literature values [4–8] for which we find 173.9(9) ms. The statistical rate function is calculated to be 3501(4). With these numbers, we determine a branching ratio to the IAS of 31.0(14)%. The branching ratio to the ground state of $^{33}$Cl could not be determined in our experiment. We therefore as- sume that mirror symmetry is a good approximation and calculate its feeding from the f t value of the mirror de- cay. $^{33}$P decays with a 100% branch to the ground state of $^{33}$S. The half-life (25.34(12) d) and the Q E C value (248.5(11) keV) [18] enables us to determine the f t value to be 107280(2250) s ( logf t = 5.03(1)). Using this f t value for the decay to the ground state of $^{33}$Cl, we deter- mine a branching ratio of 18.7(4)%. The difficulty is now to convert the branching ratios for the feeding of bound levels in $^{33}$Cl to absolute branch- ing ratios. We will test two ways of determining these branching ratios. In the first procedure, we use the to- tal proton branching ratio and the branching ratio to the ground state to deduce the feeding of bound excited lev- els as the three contributions should add up to 100%, as long as γ decay of proton-unbound levels is negligible. In the second, we use the decay of $^{33}$Cl and the relative intensities of the γ transition in $^{33}$Cl to determine the feeding of bound levels. For the first procedure, we can obtain the total pro- ton branching ratio in two ways: i) by summing all pro- ton branching ratios in table II, ii) by integrating the β -gated proton spectrum assuming that it contains all proton events. However, in second this case, one has to cut the β particles by means of a threshold which we chose, somewhat arbitrarily, to be 1000 keV. We note that the final result changes by 0.8%, if we integrate the proton spectra starting at 900 keV. We include this in the final error. The total proton rate can then be nor- malized by means of the known absolute branching ratio of the IAS of 31.0(14)%. We determine a ratio between the number of counts for the IAS proton line and the to- tal proton intensity of 78(2)%. In the former procedure, where we sum the branching ratios from table II, we ob- tain a total proton branching ratio of 36.9(17)%. The latter procedure gives a value of 39.7(12)%. We adopt a final value of 38.8(13)% for this first procedure. With the branching ratio to the ground state of $^{33}$Cl of 18.7(4)% and the total proton branching ratio of 38.8(13)%, we derive a branching ratio to bound excited states in $^{33}$Cl of 42.5(17)%. From this number and the relative γ branching ratios (see figure 5 and table III), one can determine the absolute branching ratios for the feeding of the 810 keV level of 40.5(16) % and for the 2352 keV level of 2.0(3)%. this work Borge et al. [8] average E$_{γ}$ (keV) BR (%) E$_{γ}$ (keV) BR (%) BR (%) $^{33}$Cl 810.6(2) 100(1) 810.3(5) 100(3) 100 $^{33}$Cl 1541.4(6) 3.6(2) 1541.5(5) 2.4(5) 3.4(4) $^{32}$S 2230.3(5) 6.1(2) ∗ 2230.6(9) 1.7(5) - $^{33}$Cl 2352.5(6) 1.3(2) 2352.2(9) 1.7(5) 1.4(2) $^{33}$S 2866.2(9) 0.6(1) 2867.7(9) 1.3(1) - 811 keV,  33 Ar -  33 Cl 1541 keV,  33 Ar -  33 Cl 2230 keV,  33 Ar -  32 S 2353 keV,  33 Ar -  33 Cl 2866 keV,  33 Cl -  33 S Energy (keV) Counts 10 4 10 5 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 7000 8000 9000 1500 1525 1550 1575 1600