Where:
Fp _ intensity at distance D
I, = source intensity
y = linear absorption coefficient (this varies with gamma energy, and is generally
lower for higher energies).
D = distance
The absorption coefficient yp in Equation 1.2 is applicable for narrow-beam geometry, and a
correction should be made for field cqnditions 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 de~
tectors, the expression is:
_
To pe-UD
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.
TABLE 1.2
For devices of
CALCULATED BUILDUP FACTORS
The buildup factor B given here is the factor B, (uD, Ey) as computed by Nuclear Development Associates for AFSWP (Reference 9).
Energy (Eg)
Mev
B
1,000 yds
1,500 yds
3,000 yds
l
3
16.2
3.85
29.3
5.35
85.0
10.2
4
10
2.97
1.70
4.00
2.01
7.00
2.90
less than 100-kt yield, essentially all the initial-gamma radiation 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 enhancement of 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 V, and radius R, andis filled with a gas of density py and
mass M. Then,
M =
VoPo = TT
(1.4)
Let the gas be compressed into a shell with thickness A R (R remaining constant).
gas volume is expressed as V, with a density of p,(V, = 47R’4R).
thus
The new
The mass has not changed;
M = Vobo = 407 R?A Rp (AR <<R)
3
ant
Po + 47 R7ARPy
(1.5)
ARP, = Ps
(1.6)
12