The absorption coefficient uy in Equation 1.2 is applicable for narrow~beam geometry, and a correction should be made for field conditions where the detector is approximately a 27 sensing element. This is done by adding a buildup factor B to Equation 1.2 to account for the scattered radiation that will be detected. Buildup factors for different energies and distances have been calculated (Reference 6), and some values are shown in Table 1.2. For omni-directional detectors, the expression is: Ip = Ip Bet /anv? (1.3) 1.3.4 Hydrodynamic Effect. As shown in Section 1.3.3, the attenuation of gamma radiation is highly dependent on the amount of absorber between the source and the detector. For devices of less than 100-kt yield, essentially all of the initial-gamma radiation is emitted before the shock front can produce an appreciable change in the effective TABLE 1.2 CALCULATED BUILDUP FACTORS The buildup factor (B) given here is the factor B, (uy D, Eq) as computed by Nuclear Development Associates for AFSWP (Reference 6). Energy (&o) 900 500 3,000 Mev yds yds yds 1 3 4 10 16.2 3.85 2.97 1.70 29.3 5.35 4.00 2.01 85.0 10.2 7.00 2.90 absorption of the air between source and detector. For high-yield devices, the velocity of the shock front is sufficiently high to produce a strong enhancement of a large percentage of the initial-gamma radiation (Reference 7). The higher the yield, the larger is this percentage. A simplified treatment of the hydrodynamic effect follows. Assume a sphere that has a volume V, and radius R, and is filled with a gas of density Py and mass M. Then, M = Vo pp = 47R° p,/3 (1.4) Let the gas be compressed into a shell with thickness AR (R remaining constant). The new gas volume is expressed as V; (V; = 4rR? OR) with a density of p;. The mass has not changed; thus, M = Vo0o = 41R? AR, (AR «R) 47R%p,/3 = 47R? ARP, (1.5) ARp, = Rpo/3 (1.6) 16