8 IV. DISCUSSION OF THE RESULTS A. Comparison with previous experimental work B. Comparison with shell-model calculations and the GT strength distribution In the second procedure to determine the total branch- ing ratio for decays to bound states in $^{33}$Cl, we calculate these branching ratios from the observation of the decay of $^{33}$Cl. The γ ray at 2868 keV from this decay has a branching ratio of 0.44(6)% [22]. If we use the observed relative branching ratio for this γ ray from table III and the possible branches populating the ground state of $^{33}$Cl, we determine a branching ratio of the 810 keV γ ray of $^{33}$Cl of 51.4(120)% and of 2.6(6)% for the branching ra- tio to the 2352 keV level. These values agree with those determined with the first procedure, but they are signif- icantly less precise. We therefore adopt the values ob- tained with the first procedure. The procedures just laid out assume that there is no γ decay of proton decaying levels. In addition, forbid- den transitions could falsify the GT strength distribu- tion calculated in the following. The possible presence of forbidden transitions is shortly discussed below. With these absolute branching ratios for the feeding of the ground state of $^{33}$Cl as well as of the bound and unbound excited states of $^{33}$Cl, one can determine the feeding of all states in the decay of $^{33}$Ar, the Gamow- Teller strength B(GT) and its sum. These data are given in Table IV. For the 762 keV and 2941 keV proton lines, we adopted the level energy calculated only from the 2941 keV protons, as the low-energy protons are much stronger affected by the energy loss in the silicon dead layer and in the mylar foil of the catcher than the high- energy protons. For all other decays, we use average val- ues from decays to the ground and first (second) excited states. In addition, we determine the log(ft) values for all observed transitions which are given in figure 9. In the work of Borge et al. [8], the energy calibration of the silicon detector at higher energies suffers from the fact that the calibration was performed with α particles and that the pulse height defect [23] was not corrected for. Therefore, with increasing energy above the IAS, the proton energies determined become smaller and smaller. In order to find the proton lines in Borge et al. corre- sponding to proton lines of the present work, we corrected for this effect of the Borge et al. data. Compared to previous work [8–10], we observe all the proton lines identified in the work of Borge et al. [8]. However, eight of them are now attributed to proton emission to the first excited state rather than to the ground state (see table II). Generally, the branching ra- tios of Borge et al. are higher than our values. As for Schardt et al. [9], the proton group at 1750 keV corre- sponds most likely to our proton energy of 1764(5) keV observed in coincidence with the 2230 keV γ ray. The lines at 2121 keV and 2096 keV observed by Schardt et al. are not resolved in the present work. They corre- spond to our line at 2100(3) keV. The 1665 keV line is assigned to the decay to the second excited state, as ob- served in the present work. Honkanen et al. [10] identified two weak lines at 3485 keV and 5658 keV. The first one corresponds probably to our line at 3469(6) keV which we observe in coincidence with the γ ray at 2230 keV (see below). For the higher-energy line, we can not exclude that it corresponds to our proton line at 5623(3) keV. Table II gives the proton group energies, their absolute intensities from the different experiments and the average intensities. The branching ratios of the previous work were updated with respect to the branching ratio to the IAS as determined above. For the experimental proton energies, we give only our energies. In table IV, we compare the levels observed in the present work with those found in the latest review of properties of the mass A=33 chain by Endt [20]. The levels given in this compilation come both from β -decay studies [8] and from reaction work [24–27]. For levels de- termined by different experimental approaches, we find reasonable agreement. For higher-energy levels, we just compare with those deduced from reaction work as the comparison with β -decay work has already been done in table II. Therefore, in table IV, we only compare with previously established states deduced from work other than β decay. Similarly, the spin values shown come only from reaction studies. If we compare our results to shell-model calcula- tions [19] (see table IV), we find that below the IAS only one predicted state at 3.863 MeV with a branching ratio of 0.0747% is not observed experimentally. All other pre- dicted states are observed experimentally with branching ratios in most cases close to the predicted ones. For a comparison of the experimental GT strength distribution with theoretical predictions, the theoretical strength has to be quenched. The origin of this quenching is not completely clear, but excitations of sub-nucleonic degrees of freedom, notably of the Δ resonance, and, probably to a much larger degree, contributions from outside the considered model space are most often sus- pected (see e.g. [3]). A typical quenching factor for the sd shell is q 2 = 0.5. With our data, we can check this quenching factor. We will use experimental B(GT) val- ues deduced for individual transitions below the IAS and compare them to the B(GT) strength for the equivalent transitions (see table IV) as predicted by theory. This comparison is shown in figure 6. A fit of these theoreti- cal data as a function of the experimental data yields a quenching factor of 0.49(4). This is in perfect agreement with the generally accepted quenching in the sd shell. Using this quenching factor, we can compare the sum- med experimental B(GT) strength with the prediction from the shell model. For this comparison, we use cal- culations with three different effective shell-model in-