11 E. Decay scheme of $^{33}$Ar D. Search for candidate states for isospin mixing V. SUMMARY Acknowledgment excited states for both spins are then compared to the ratio of the experimental branching ratios. If we believe that the situation is relatively clear and one spin assign- ment gives a much closer agreement than the other spin, we propose a spin. The procedure used is tested with and works well for the state at 7292 keV, for which we find a spin of 3/2 + in agreement with the literature [20]. For the state at 9152 keV which decays to the three lowest states of $^{32}$S, we determine that for a 3/2+ emit- ting state the decay to the first excited state is indeed the fastest transition thus receiving the highest branch- ing ratio. For a spin 1/2 $^{+}$, the decay to the ground state is calculated to be a factor of ten faster than the de- cay to the other two states, opposite to the experimental observation. We therefore attribute a spin 3/2 + to this state. We underline again that the present spin assignments have to be confirmed by other means before they should be accepted. Therefore, they appear in parenthesis in figure 9. Proton emission from the T=3/2 IAS in $^{33}$Cl can only take place due to isospin impurity either in the proton emitting state or in the proton daughter state. Therefore, Honkanen et al. [10] searched for states in the vicinity of the IAS with which the IAS can mix. We identified three of the four states discussed by Honkanen et al. There is one state about 230 keV below the IAS and two other states 180 keV and 310 keV above the IAS. However, we do not have evidence for a state about 100 keV below the IAS which would be the best candidate for mixing between such a state (T=1/2, I $^{π}$=1/2 $^{+}$) and the IAS (T=3/2, I $^{π}$=1/2 $^{+}$). The proton group identified by Honkanen et al. [10] at 3073 keV corresponds to our peak at 3066 keV. However, we clearly identify the proton group to decay to the first excited state and not to the ground state as suggested by Honkanen et al. Therefore, the emitting state is no longer in the vicinity of the IAS. We do not completely exclude the possibility of such a close-by state, as our resolution is maybe not good enough to resolve several small peaks in the close vicinity of the strong IAS. However, if such a state is absent, the mixing has to take place with states further away from the IAS. A better resolution experiment with higher statistics is certainly needed to answer this question. A state with (T=1/2, I $^{π}$=1/2 $^{+}$) about 100 keV be- low the IAS was also observed in proton scattering ex- periments on $^{32}$S [25]. This would of course be a good candidate for isospin mixing with the IAS. As mentioned above, we do not observe such a state. However, we can- not exclude that our proton peak at 3066 keV contains also a small branch to the ground state of $^{32}$S. It is interesting to note that the shell model using the three different USD interactions [2, 28] does not predict any (T=1/2, I $^{π}$=1/2 $^{+}$) state close to the IAS. The states close to the IAS have all a spin of I $^{π}$=3/2 $^{+}$. The clos- est I $^{π}$=1/2 + state is at about 400 keV above the IAS for the USD interaction, 550 keV above for the USDa in- teraction, and 450 keV above the IAS for USDb. Below the IAS, the first (T=1/2, I $^{π}$=1/2 $^{+}$) state is typically 800-900 keV away from the IAS. The information accumulated in the present paper to- gether with the results from previous work enables us to establish a rather complete decay scheme of $^{33}$Ar with decays to bound states and proton unbound states which then decay to the three lowest states of $^{32}$S by proton emission. Figure 9 gives this decay scheme. We remind the reader that the branching ratios for the three proton- bound states are based on the assumption of mirror sym- metry of the ground states of $^{33}$Ar and $^{33}$P. Using a novel experimental setup of high granularity and high efficiency for charged-particle detection com- bined with a high-efficiency γ array allowed a complete study of the decay of $^{33}$Ar to be performed. The experi- mental results are to a large extent in agreement with pre- vious experimental studies of this nucleus. They enabled us to establish a quasi complete decay scheme of $^{33}$Ar and to compare the experimental results with shell-model cal- culations using different effective interactions optimized for the sd shell-model space. The excellent agreement obtained testifies of the high quality of the shell model in this region of the chart of nuclei. The comparison of experimental B(GT) strength to well identified levels and theoretical calculations yields a quenching factor of 0.49(4), in excellent agreement with the accepted value. States in close vicinity of the isobaric analog state of the $^{33}$Ar ground state in $^{33}$Cl are searched for and discussed in terms of isospin mixing. However, a state identified before could not be observed in the present work. We would like to thank the whole GANIL and, in par- ticular, the accelerator staff for their support during the experiment. We express our gratitude to the EXOGAM collaboration for providing us with the germanium detec- tors. This work was partly funded by the Conseil r´egional d’Aquitaine and the EU through the Human Capital and Mobility program. We acknowledge support from CI- CYT via contract FPA2007-62179. RDR was supported via a FPI grant. We are in debt of B.A. Brown for pro- viding us with the shell-model calculations.