Where: ¥p intensity at distance D I, = source intensity ft = linear absorption coefficient (this varies with gamma energy, and is generally lower for higher energies). D = distance The absorption coefficient »p in Equation 1.2 is applicable for narrow-beam geometry, and a correction should be madefor field cgnditions 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 11), and some values are shown in Table 1.2, For omni-directional detectors, the expression is: _ Io Be7 HD ID = —“TgDe 0.3) 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 TABLE 1.2 CALCULATED BUILDUP FACTORS The buildup factor B given here is the factor By (49D, Ey) as computed by Nuclear Development Associates for AFSWP (Reference9). Energy (Ep) Mev 1 1,000 yds 16.2 B 1,500 yds 29.3 3,000 yds 85.0 3 4 3.85 2.97 5.35 4.00 10.2 7.00 10 1.70 2.01 2.90 less than 100-kt yield, essentially all the initial-gammaradiation is emitted before the shock front can produce an appreciable change in the effective 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 enhancementof a large percentage of the initial-gammaradiation (Reference 10). The higher the yield, the larger is this percentage. A simplified treatment of the hydrodynamic effect follows. Assume a sphere that has a volume Vj, and radius R, andis filled with a gas of density py and mass M. Then, (1.4) Let the gas be compressed into a shell with thickness A R (R remaining constant), The new gas volume is expressed as V, with a density of py(Vy = 47 R?AR). The mass has not changed; thus M = VoPy = 407 R?A Rp, (AR <<R) AaB Po s an Ra Roy 3 (1.5) (1.6) ARR, = “ps 12