FIG. 7: (Color online) Summed Gamow-Teller strength distri- bution for the decay of $^{33}$Ar. The experimental distribution is compared to shell-model calculation by B.A. Brown [19] with the universal sd shell interaction USD and two updated ver- sions of the same interaction [28]. For these calculations, we used a quenching factor of 0.5, the generally accepted value. The experimental data correspond only to resolved proton groups obtained from the average values of Table IV . FIG. 6: (Color online) Comparison of the GT strength be- tween experiment and shell-model calculations for eight in- dividual transitions of $^{33}$Ar for which a correspondence be- tween the shell-model calculations with the USD interaction and experiment was established in table IV. The fit yields a quenching factor of 0.49(4). teractions for the sd model space: the USD interac- tion [21] and two newly determined interactions USDa and USDb [28]. For this purpose, we convert the exper- imental branching ratio into a B(GT) strength for each individual level observed. As a function of the excita- tion energy, this strength is then summed. The result is shown in figure 7. At low excitation energies, almost perfect agreement of the experimental data with all three interactions is obtained. At higher excitation energy, the new interactions USDa and USDb seem to slightly better fit the data. Nonetheless, for all three interactions, the agreement is remarkable. The procedure just described has one drawback: Only decay strength identified as a peak usually is taken into account. Very weak decay branches are omitted. There- fore, we developed a procedure which uses all strength present in the proton spectra. For this purpose, we take the total charged-particle spectrum as obtained by means of the silicon detectors and subtract first the β back- ground by a fit of the low-energy part of this spectrum. In a second step, we subtract the decay strength to the first and second excited state. These contributions are obtained from the proton spectrum conditionned by the detection of these γ rays renormalized by the gamma ef- ficiency. This yields the proton decay strength to the ground state. Now we have to convert this spectrum bin by bin to a center-of-mass (CM) spectrum. To this we add the decay spectrum (again converted to the center- of-mass) to the first excited state shifted by the excita- tion energy of this state. Similarly, we treat the spec- trum for decays to the second excited state. After a correction for the proton separation energy, this yields the excitation energy spectrum to which we have added the decay to bound states (see figure 8a). After calcu- lating the statistical rate function f for each energy bin, we can determine the B(GT) value for each energy bin (figure 8b). This spectrum can be compared to the theo- retical B(GT) values for individual transitions (figure 8c) and the summed B(GT) distribution (figure 8d). At high excitation energies, the summed experimental B(GT) dis- tribution exceeds the theoretical one with a quenching of 0.5. If we integrate the B(GT) up to 11 MeV we get 5.3 which correspond to a quenching of 0.59. To discuss the contribution at very high excitation energy is always del- icate, enough to say that if we integrate in the full Q E C window of 11.6193 MeV the cumulated B(GT) grows to 41.2. A possible explanation for this large B(GT) sum is that we shift too much strength to high excitation ener- gies by attributing too much decay strength to decays to excited states, in particular to the second excited state. To test this assumption, we calculated the GT strength distribution also by omitting the second excited state and both excited states. However, even when omitting both excited states, we still exceed the quenched theoretical B(GT) values. Another possible explanation could be that we deal to some extent with forbidden transitions. In the latest analysis of Singh et al. [29], the log(ft) values of allowed transitions are distributed over a large range from 3 to 7, whereas forbidden transitions start with values of about 5. As can be seen in figure 9, we determined indeed high log(ft) values which could be due to forbidden tran- sitions. However, as we have no means to distinguish between allowed and forbidden transitions, we assume that all transitions are allowed, but we give their spins in parenthesis to indicate this uncertainty. Finally, background is of course also a concern. Proton-proton pile up might create high-energy events which get an important weight due to the larger space phase factor. However, we do not have any means to distinguish such possible background counts from real counts. The good agreement between experimental and theo- retical B(GT) strength up to rather high excitation ener- 9