6 Electrons -5 0 5 10 15 6 10 × Counts 1 10 2 10$^{3}$ 10$^{4}$ 10 Single p.e. spectrum 6 10 ×  0.01)  ± Gain: (1.58  FIG. 8: Single photoelectron spectrum of a XENON10 top PMT, acquired during a routine LED calibration. Clearly visible is also the noise peak. FIG. 7: (Color online) XENON10 top PMT array, with the cathode HV feedthrough and liquid level meter also visible. Negative HV was applied to the cathode of each PMT, via unshielded Kapton wire. The average HV was about 750 V, with a maximum of 900 V. The signal was carried out with 50 Ω teflon cables (RG178U), stripped of their shielding, to avoid trapped air which would impact the liquid purity. PMTs signal and HV cables were carried outside by 48 pin Burndy feedthroughs [34]. The radioac- tivity of these feedthroughs was reduced by replacing the ceramic plugs holding the pins with plugs made out of polyether ether ketone (PEEK). The 89 PMTs were routinely calibrated with the goal of equalizing the gain and to correct for differences in the quantum efficiency. The gain equalization was per- formed using light emitting diodes (LEDs). Two LEDs were used: one was mounted close to the top array, to equalize the bottom PMTs; the other was mounted close to the bottom array, to equalize the top PMTs. Both LEDs were covered with a PTFE cap acting as a dif- fuser to ensure a uniform illumination of all the PMTs in each array. The LEDs were driven by a pulse generator, which synchronously activated also the main DAQ trig- ger: the pulse duration was 6 µ s, but the charge on each channel was integrated only in a 1 µ s window, 4 µ s after the activation of the LED, to minimize electronics noise generated when the LED was switched on. The gain measurement was performed in single photo- electron (p.e.) regime. Under the assumption that the p.e. spectrum is the sum of a Gaussian noise peak and a Gaussian single p.e. peak, each with a Poisson-like dis- tribution, and with a single photoelectron to noise ratio of 1/5, less than 2% of the events had 2 or more pho- toelectrons (a typical single p.e. spectrum is shown in figure 8). To ensure that the single p.e. condition was met for all the PMTs, the calibration data were acquired under different illumination conditions. The spectra for each PMT were fitted with a function which included the noise Gaussian, the single p.e. Gaussian and a third Gaussian accounting for the multiple p.e. contribution. After measuring the gain for each channel, the ampli- fication factor was equalized for all PMTs, by adjusting the single PMT operating voltage. After the equaliza- tion, the gains were measured again and the resulting amplification factors were then fed to the XENON10 data analysis programs (see Sec. V) and used as a conversion factor between the measured charge and the actual p.e. number. During normal operation, such a gain measure- ment was repeated at least once a week, to ensure the stability of the PMTs gain. The time evolution of the gain, measured during the WIMP search data taking, is shown in Fig. 9 for two typical PMTs. The variation in PMT gain was < 2%. A reliable and stable cryogenics system was an es- sential requirement for the XENON10 experiment since both PMTs gain and the proportional light yield vary with temperature. The XENON10 TPC vessel contain- ing the 25 kg of LXe, made of stainless steel (SS), was FIG. 9: Stability of the gain of two typical XENON10 PMTs during the WIMP search data taking period. D. Cryogenic System Time 2006 08/17 2006 10/01 2006 11/15 2006 12/29 2007 02/12 2007 03/29 Normalized PMT Gain 0 0.2 0.4 0.6 0.8 1 1.2