3 FIG. 2: (Color online) Photo of the setup as installed at the low-energy identification station of SPIRAL at GANIL. The silicon cube detector is seen in the center of the photo. On the left, the vacuum pipe to insert the catcher is visible. Two out of the three EXOGAM clover detectors are mounted and displayed on the bottom and right-hand side of the photo. III. ANALYSIS PROCEDURE AND EXPERIMENTAL RESULTS correctly and was excluded from the present analysis. The thickness of detector 4 limited its use to low-energy protons. Therefore, it was also excluded from the anal- ysis. Due to its large thickness, DSSSD 5 yields a quite high β tail thus worsening its energy resolution. We used this detector only for the high-energy part of the spec- trum (above 6 MeV) where the other detectors did no longer fully stop the protons. Therefore, we used detec- tors 1, 3, and 6 to determine proton energies and branch- ing ratios for proton lines below 6 MeV and detector 5 above. The spectrum above 6 MeV was corrected for the geometrical efficiency of detector 5 with respect to de- tectors 1, 3, and 6. The β signal in the PIPS detectors was used in the analysis to reduce the β -p summing by requiring to have the β signal in any of the other back detectors of the cube. This condition permitted to sig- nificantly reduce the β tails in the proton spectra. All silicon detectors were first calibrated by means of a triple α source ( $^{239}$Pu, $^{241}$Am, $^{244}$Cm). The final energy calibration of the DSSSDs was performed using the β - delayed proton peaks to the ground state of $^{32}$S from the IAS recently remeasured [14] to be at 5547.8(9) keV and the 3/2 + state at 3971.9(12) keV [15] excitation energy in $^{33}$Cl, respectively. An energy resolution of 50 keV was obtained for the DSSSD sum spectrum from detectors 1, 3, and 6. Events in the DSSSDs were accepted only if the signals in the front and back side were within ± 100 keV of each other. Different runs optimized for $^{33}$Ar were performed yield- ing a total of 28 h for this isotope. Several runs were also performed for $^{31}$Ar. These latter settings were strongly contaminated by $^{33}$Ar and yielded rather low production rates for $^{31}$Ar. These data were thus only used to study the performance of the Silicon Cube [12]. For the data taking with the different argon isotopes, only the DSSSDs were allowed to trigger the data ac- quisition. After a trigger, all channels were readout by means of the GANIL data acquisition system via VXI and VME modules. The experimental data were analyzed as singles and coincidence data. The different peaks were fitted and in- tegrated by means of the PAW package from the CERN library. Most of these peaks are due to β -delayed pro- ton emission from states in the β -decay daughter nucleus $^{33}$Cl to the ground states of $^{32}$S. Decays to excited states were identified by means of proton- γ coincidences with the 2230 keV and the 1548 keV γ lines from the decay of excited states in $^{32}$S. Figure 3 shows the $^{33}$Ar β -gated proton spectrum and the proton spectra coincident with the γ lines at 2230 keV and the 1548 keV, respectively. At several instances, peaks due to proton emission to the ground state and to the excited states overlay. To ensure correct identification due to the different decay branches, the γ -gated proton spectrum for the 2230 keV γ line was normalized to the β -gated spectrum by means of the proton peak at 1317 keV which is assumed to be only due to emission to the first excited state [9]. As this line is seen in the β -gated spectrum and, of course, in the spectrum gated with the 2230 keV γ line, both spectra can be normalized with respect to each other and a common relative normalization can be established. A fit of the 1317 keV peak in both spectra, γ gated and singles, yielded a factor of 56 with which the γ -gated spectrum has to be multiplied to match both spectra. As the error of this number does not influence the final result in any significant way, it was not included. Figure 3c and the shaded part of figure 4 show this spectrum dominated by this proton peak. For the proton spectrum gated by the 1548 keV γ line, we normalized the proton spectrum with the same factor as the spectrum in coincidence with the 2230 keV line and the ratio of the γ detection efficiencies of the 1548 keV line and the 2230 keV line. This exploits the idea that in such an analysis the probability to observe protons in co- incidence with the 1548 keV line is only modulated with respect to the spectrum gated by the 2230 keV line by the γ -detection efficiency. The ratio of the two γ -ray efficien- cies was ϵ$_{1548}$ / ϵ$_{2230}$ = 2.44%/1.89%. Thus, the spectrum generated with a γ coincidence of the 1548 keV line was multiplied by this factor and the factor determined be- tween the β -gated spectrum and the spectrum produced with the 2230 keV coincidence in order to match the rel- ative proton intensities for the ground state transitions, the transitions to the 2230 keV state and to the 3778 keV state in $^{32}$S.