22 reactions in the detector materials. 1. Gamma and Neutron Backgrounds from Data and MC Simulations Gamma and neutron backgrounds from the environ- ment were studied to optimize the shield, and have been discussed in section III. After shielding, the dominant backgrounds in XENON10 result from radioactive con- taminants in the detector and shield materials. These in- ternal backgrounds were studied with material screening, using gamma-ray spectroscopy in a low count rate facil- ity, with Monte Carlo simulations, and with the analysis of delayed coincidences in decay chains of radio-nuclides inside LXe. Simulations were based on the GEANT4 simulation toolkit [56], where the complete geometry of the detector and surrounding material was included. As detailed in Table I, the shielding material and many detector construction components were screened with HPGe gamma spectrometers at the LNGS and SOLO screening facility [57]. The radioactive contamination of the screened material are listed in Table I (for the shield) and in the first row of table III (for the PMTs + bases). However, since XENON10 was a prototype experiment, the radioactivity of some detector components was not known. We used the minimum χ 2 method to extract the individual activities, by comparing the measured energy spectrum with the sum of the energy spectra for each radioactive decay chain within each material: where n and N are the first and last bin of the energy spectra, defining the fit range. Here we use a bin width of 3.75 keV, n = 50, and N = 450. d$_{i}$ is the rate in the i th bin of the measured energy spectrum, and F$_{ij}$ is the cor- responding expected rate from simulated backgrounds in material j ; m = 41 is the total number of simulated ma- terials; u$_{j}$ , th$_{j}$ , k$_{j}$ , co$_{j}$ and cs$_{j}$ are the scaling parameters related to nominal activities of material j in $^{238}$U ( U$_{j}$ ), $^{232}$Th ( Th$_{j}$ ), $^{40}$K ( K$_{j}$ ), $^{60}$Co ( Co$_{j}$ ), and $^{137}$Cs ( Cs$_{j}$ ), respectively. The minimization is done by the MINUIT routines in ROOT [45]. The results of this fit procedure are summarized in table III. The main component to the background energy spectrum of XENON10 originates from a $^{137}$Cs peak at 662 keV. Fig. 44 shows the 662 keV peak decreasing at smaller radii, a clear indication that it is not diluted in the LXe. A study of the spacial distribution of events in this peak shows that the $^{137}$Cs source is all around the detector edges. Thus a surface contamination of the anthropogenic $^{137}$Cs has to be assumed, either on the inner cryostat can or on the Teflon. The best fit results localize the $^{137}$Cs on the Teflon, with a total activity of 5.73 ± 0.57 Bq. nal. Unless they are detected as multiple interactions in the sensitive volume, neutrons constitute an unre- jectable background in the nuclear recoil band. Gamma and beta rays mostly populate the electron recoil band and constitute the most prominent background of the experiment. Alphas can contribute to background in the WIMP search region as they give rise to neutrons via α -n χ 2 = N ∑ i = n d$_{i}$ − ∑ m j $_{=1}$F$_{ij}$ ( u$_{j}$U$_{j}$, th$_{j}$Th$_{j}$, k$_{j}$K$_{j}$, co$_{j}$Co$_{j}$, cs$_{j}$Cs$_{j}$ ) d$_{i}$ (A1) FIG. 43: (Color online) Cuts based on p$_{RMSb}$ for the bottom PMTs, as defined in the text. The crosses indicate the events that “leak” into the nuclear recoil acceptance region, as shown in Fig 40. The two vertical lines are the energy window of WIMP search. Red circles indicate the remaining events after all software cuts. The solid black curve is pre-defined, which varies from 99% at 2 keVee and 90% at 20 keVee cut efficiency and fitted by the third-order polynomial function. It removes 9 out of 22 “leakage events” in the energy window of interest (2-12 keVee). FIG. 42: (Color online) A cut based on the asymmetry of the S1 signal, p$_{asy}$ , as discussed in the text. The crosses indicate the events that “leak” into the nuclear recoil acceptance re- gion, as shown in Fig 40. The two vertical lines are the energy window of WIMP search. Red circles indicate the remaining events after all software cuts. The solid black curve is pre- defined to keep 98% electron recoil events. It removes 3 out of 22 “leakage events” in the energy window of interest (2-12 keVee). S1/2.2 [keVee] 0 2 4 6 8 10 12 14 16 18 20 S1Asy -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 S1/2.2 [keVee] 0 2 4 6 8 10 12 14 16 18 20 S1RMS Bottom 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2