2 II. EXPERIMENTAL DETAILS the same spin quantum number. According to pertur- bation theory, the mixing gets larger with decreasing en- ergy difference between the two states. Of course, mixing is possible not only with one state, but with any state, however, with rapidly decreasing amplitude as the energy difference increases. The decay of $^{33}$Ar, the subject of the present work, was studied several times in the past (see [4–11]). Our experimental data are compared to the most recent work from these authors and experimental averages are con- fronted to theoretical shell-model calculations using dif- ferent effective interactions optimized for the 2s1d nu- clear shell-model space. In particular, we will determine the Gamow-Teller strength distribution and investigate the possibility to identify the state(s) responsible for isospin mixing in $^{33}$Cl. The isospin mixing of the IAS was suggested to be as much as 20% for $^{33}$Cl [7], a huge value compared to ”today” standards. Hardy et al. [7] and Borge et al. [8] studied the decay of $^{33}$Ar in detail in order to extract the GT strength distribution. Schardt et al. [9] and Garcia et al. [11] also determined limits of possible scalar contributions to β decay and the Fermi-to-Gamow-Teller ratio of the decay of $^{33}$Ar. We will in particular use this ratio in our analysis and comparison to theory. In the present work, the use of high-resolution sil- icon surface-barrier detectors and of a high-efficiency γ -detection array permitted to determine the proton branches to the ground as well as to the first and second excited states in the proton daughter. In particular, the GT distribution in the full Q EC window was established and a detailed comparison to shell-model calculations was performed. The isotopes of interest were produced by pro- jectile fragmentation of a $^{36}$Ar18+ primary beam at 95 MeV/nucleon with intensities between 4 µ A and 8 µ A provided by the coupled cyclotrons of GANIL. This beam was fragmented in the SPIRAL carbon target. The SPI- RAL ECR source then produced a low-energy beam of $^{33}$Ar$^{3+}$, which was directed to the SPIRAL identifica- tion station, where the experimental setup was mounted. The beam line to this detection station was regularly op- timized by means of a stable $^{40}$Ar3+ beam produced with the ECR source. Secondary beam intensities of 1200 pps on average were obtained for $^{33}$Ar$^{3+}$. The $^{33}$Ar beam was contaminated by small amounts of $^{35}$Ar possibly trans- mitted as a gas to the detection setup. Beam profilers and Faraday cups close to the detection setup allowed to optimize the beam position in the exper- imental setup and to monitor the beam intensity (mainly stable isotopes or molecules). The secondary beam was finally intercepted in the center of the experimental setup by means of a 0.9 µ m thick aluminized Mylar foil (1 cm × 2 cm) mounted on a thin metallic frame. FIG. 1: (Color online) Schematic view of the Silicon Cube consisting of 6 DSSSDs backed by 6 PIPS detectors. The position of the mylar foil catcher and the entrance of the sec- ondary beam are also shown. The standard detection setup of the SPIRAL identi- fication station was replaced by the Silicon Cube detec- tor [12] and three high-efficiency germanium detectors from the EXOGAM array [13]. The Silicon Cube con- sists of six double-sided silicon strip detectors (DSSSDs) $^{with 16}$×16 strips and a pitch of 3 mm forming a cube surrounding the mylar catcher foil. These DSSSDs were backed by six large-area (50x50 mm $^{2}$) Passivated Im- planted Planar Silicon (PIPS) detectors used to detect β particles. The thicknesses of the different detectors are given in Table I. The arrangement of the different de- tectors can be seen on figure 1. A photo of the setup installed at the low-energy identification station of SPI- RAL at GANIL is shown in figure 2. The 192 signal channels from the DSSSDs were read- out via a printed circuit board incorporated in the de- tector housing. The 16-channel pre-amplifier cards were mounted directly on the detector chamber enabling thus a rather compact configuration. The six channels of the PIPS detectors were connected to their pre-amplifiers via standard LEMO connectors. This setup reaches a geo- metrical efficiency for proton detection of 54% [12]. The Silicon Cube was surrounded by three EXOGAM clover detectors. These detectors were calibrated in ef- ficiency and energy by means of standard calibration sources and yielded a total efficiency of about 3.2% at 1332 keV. Due to technical problems, DSSSD 2 did not function TABLE I: Thicknesses of the different silicon detectors used in the present study. The arrangement of the detectors can be seen in figure 1. DSSSD - PIPS position 1 2 3 4 5 6 DSSSD thickness ( µ m) 300 287 270 64 1000 288 PIPS thickness ( µ m) 300 300 500 1473 150 1498