3.2.5 System Calibration Flux Calculation, The unscattered flux of gamma rays of energy E at a height h above a smooth air-ground interface due to an emitter distributed in the soil is given by (see Figure 3-2): > -| | 0 0 Agr? ur a) dx dz exp [-(h/p), Pg Tal exP (n/p), ps tgl ° 20 x where S, = the activity per unit volume . r= rtr, (cm), Y/sec cm , 2 (h/p),4. (4/p), = the air and soil mass attenuation coefficients (5 ) and Da Ps = the air and soil density (g/em), z = depthin soil below the surface This expression assumes a source distribution which varies only with depth. A uniform distribution in the horizontal plane is assumed, which leads to results expressed in terms of an area average over the field-of-view of the detector. For fallout activity subject only to environmental weathering, the distribution after a period of time can be reasonably approximated by an exponential distribution given by: = §9—°%7 (2) sy = the activity per unit volume at the surface (vee) and cm & = the reciprocal of the relaxation length (em=!). Detector h Air Soil rs Zz . x Source Element FIGURE 3-2. GEOMETRY USED IN THE DERIVATION OF CONVERSION FACTORS RELATINGIN SITU PHOTOPEAK COUNT RATE DATA TO SOURCE CONCENTRATION IN THE GROUND 88