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The main source of neutrons in XENON10 are ( α ,n) and spontaneous fission reactions from $^{238}$U and $^{232}$Th in the detector and shield material. Another source of neutrons are spallation and photo-nuclear reactions of cosmic ray muons in the rock and shield. As explained in Section III, the neutrons from outside the shield are stopped or thermalized by the polyethylene. 

Using the $^{238}$U and $^{232}$Th activities as given in Ta- ble III, the energy spectra and number of expected neu- trons from ( α ,n) and spontaneous fission reactions in each material has been calculated with the modified SOURCES4A code [58]. These are given in Table IV (second column). 

The neutrons are then propagated into the sensitive region using the GEANT4 code and detector geometry. In figure 45 the predicted single scattering nuclear recoil energy spectrum from the neutrons from all the mate- rial considered in the simulation is shown, together with the individual contributions from all the material. The number of predicted single nuclear recoils in the WIMP search region is shown in Table IV (third column), along with the total number of single nuclear recoils (fourth column). 

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The total rate of single nuclear recoils in the energy region from 2 to 12 keV ee is expected to be 1.67 × 10 − 3 event/kg/day, i.e. for an exposure of 5.4 kg × 58.6 days, the total number of nuclear recoils expected from the contamination of the XENON10 detector material is less than 0.53 events [11]. 

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Delayed coincidence analyses to determine the Radon, Thoron, U/Th and $^{85}$Kr concentration in the LXe have been carried out by looking at the specific decay signa- tures. For Radon, the consecutive beta-alpha decays oc- curring in the decay of $^{214}$Bi (shown in Eq. A2) are required to occur within the same waveform, in the same time order as in the decay scheme and with the proper en- ergies ( E$_{β}$ < 3000 keV and E$_{α}$ > 6500 keV). With these cuts, the residual accidental coincidences are negligible and the events surviving the cuts are taken as real $^{214}$Bi decays. The resulting Rn concentration in LXe, consid- ering the detection efficiency and the efficiency of above cuts, is (59 ± 2) µ Bq/kg. For $^{220}$Rn arising from the $^{232}$Th 

## 2. Intrinsic backgrounds in LXe 

