a minimum value of as when the exponent equals unity:

 ('sP + ,eO) 1[8]
which can be written in a simpler form:

 x* [9]
 SpP + ^9O
where x* represents the optimum thickness of the soil sample. Thus not
only does the optimum thickness of the soil sample depend upon the
variables of bulk density (p) and water content (0) but also upon the
mass attenuation coefficients for water and the soil. The mass attenua-
tion coefficients .o and /k, are greatly dependent upon the primary
energy of the gamma photons and upon the chemical composition of the
absorber material.
 For a given soil the optimum thickness of the column or core tends
S to be greater for high energy photons such as 662 KeV than for lower
energy photons such as 60 KeV. With increasing energy of the photons,
the magnitude of t, and g, have been observed to decrease (Fig. 2).
For example, the value of A, is much greater for 60 KeV gamma pho-
tons than for 662 KeV. Therefore the optimum thickness of the soil
sample is influenced by the energy of the gamma photons and the chem-
ical composition of the soil and the water in the soil. Using equation
[Cviii] in Appendix C, error in the water content determination was
plotted in Figure 3 as a function of the soil sample thickness, x,- for sev-
eral different soils using 60 and 662 KeV photons. For low energy pho-
Stons such as the 60 KeV, the chemical composition of the soil is ob-
served to strongly affect the magnitude of the mass attenuation coefficient,
A. In Figure 3 curves relating ca with x are presented for 60 KeV pho-
tons with a mineral soil high in iron content (A), with the same soil
when compacted to a higher bulk density (B), and with an organic soil
(C). A fourth curve (D) is given for any soil using 662 KeV photons.
The minima values for the curves represent the optimum thickness, x*,
for the soil samples, and these values were approximately 1.5, 1.8, 3.0,
and a range from 6 to 13 cm for curves A, B, C, and D. Thus the opti-
mum thickness of the soil sample is an important consideration when low
ene .i ga:nmn. photons are used in the gamma attenuation method for
determining the soil water content. For higher energy photons such as
662 KeV, variations in the sample thickness may not cause appreciable
error in the determination of 0. Thus the optimum thickness of the soil
sample will vary with the primary energy of the gamma radiation used
in the method. Generally for soil columns less than 10 cm thick, 60 KeV
photons from 241Am provide best determinations for either 0 or p, but
for columns 10-25 cm thick, 662 KeV photons from 137Cs provide best
results.