nucteonics DATA SHEET no. 17 
Dosimetry 
Gamma Dose Rates in Cylindrical Sources 
By DONALD R. SMITH 
Air Force Institute of Technology, Dayton, Ohio 
WHAT GAMMA-RAY exposure dose rate* 
will you find at the center of a given 
cylindrical Co® source? How should 
you design such a source for a required 
flux in a given volume? Figures 1 and 
2 are designed to answer such ques- 
tions. By appropriate conversion they 
can be used for other gamma emitters. 
The computations are an extension of 
earlier work (1, 2). 
Figure 1 is a plot showing the gamma 
dose rate to be expected at the centers 
of cylindrical sources of various sizes 
and activities. Self-absorption and 
backscatter are neglected. To use 
the graph for other gamma-emitters 
one must multiply the ordinates by 
M/14.7, where M is the exposure dose 
rate in r/hr 1 ft from a 1-c point source 
of the other isotope. 
The following useful rules will be 
found to follow from this method of 
source design: 
1. For a specified total activity, an 
increase in the flux by a factor of 10 
will decrease the useful volume by a 
factor of 31.6 (1,000%) if the same rela- 
tionship between the average radius 
and height is maintained. 
2. For a specified central dose rate 
an increase in the total activity by a 
factor of 10 will increase the useful in- 
* The International Committee on Radi- 
ation Units has recommended introduction 
of the terms ‘‘exposure dose’’ (measured in 
roentgens) and ‘‘absorbed dose’”’ (measured 
in rads) to reduce the confusion between the 
radiation field and the energy absorbed in 
any exposure. 
». '400 
1200 
Volume (in 
1000 
! 2 3 4 5 
Ratio of Height to Average Radius 
FIG. 2. Volume of 10,000-c cobalt source 
with central flux of 5 X 10° r/hr as a func- 
tion of ratio of height to average radius 
MARVIN C. ATKINS 
and 
Central Flux / Total Activity (r/hr/c) 
FIG. 1. 
of activity, height, and radius. 
ternal volume by a factor of 31.6 if the 
radius-height ratio is maintained. 
Example. ‘‘Select dimensions to 
give maximum interior volume of a 
10,000-c cobalt source if the central 
flux is to be 5 X 10° r/hr.” Since 
5 X 105/10,000 = 50, we follow the 
50-r/hr/c line across the graph to find 
appropriate combinations of dimen- 
sions. Usable values are h = 24, 
b = 4.4, etc. In Fig. 2 we plot the 
volume as a function of h/b. The 
maximal volume is found to be 1,440 
Wright Air Development Center, Dayton, Ohio 
8 10 2 
Radius (in.) 
Exposure dose rate at center of cylindrical cobalt source is a function 
Ordinate gives flux per total activity 
in.? for h/b = 3.6. The closest inte- 
gral values that correspond to this vol- 
ume and ratio areh = 18 and b = 5in. 
From Fig. 1 the central dose rate in a 
10,000-c source of these dimensions 
would be 5.02 X 10° r/hr. 
BIBLIOGRAPHY 
1. D. L. Loughborough, A. E. Juve, J. R. Beatty, 
J. W. Born. A study of the effects of nuclear 
radiation on elastomeric compounds and com- 
pounding materials, Wright Air Development 
Center Technical) Report 55-58, pp. 6, 76 
(1955) 
2. J. G. Lewis, J. V. Nehemias, D. E. Harmer, 
J. J. Martin, Nucueonics 12. No. 1, 40 (1954) 
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