Sec. 16.7] INTERNAL DOSIMETRY 435 



where n = linear-absorption coefficient, cm 



R = distance of point from volume element dV 



In practice the integral leads to excessively complicated expressions for 

 all but the simplest geometrical shapes of the volume. For the same reason 

 the point in the organ or animal for which the dosage rate is computed cannot 

 always be chosen arbitrarily. Furthermore, it is sometimes convenient 

 to neglect absorption in order to simplify the calculations. This is usually 

 justified when the dimensions of the organ are very much smaller than 

 \/n, where fx is the linear-absorption coefficient of tissue for a gamma ray of 

 energy E y . 



Formulas for g are given below for various geometries that can be used to 

 approximate organs and tissue masses. It is assumed that both the tissue 

 and radioactive substance are uniform in density and composition throughout 

 the volume. 



a. Geometrical Factor for the Center of Sphere. For a sphere of radius a, 

 the value of g at the center is 



Air < 



g = — (1 — e-" a ) cm 



M 



~ 4ra cm 



b. Arbitrary Point in Sphere. Neglecting absorption, the value of g for 

 any point at a distance c cm from the center of a sphere of radius a cm is [14] 



x ( 2c H log — — '■ I 



\ c a — c) 



g = t [ 2a H log I cm 



\ c a — cf 



It is seen that at the surface c = a, and g is just one-half its value at the 

 center. 



c. Disk. Considering the disk to be flat with radius a and thickness /, 

 then neglecting absorption, the value of g at any point located a distance c 

 from the plane of the disk and a distance b from its axis is [15] 



, . a- - b- + c? + V(a 2 -b* + c 2 ) 2 + 4a-b 2 

 g = *t log ^ cm 



d. Cylinder. The value of g at the mid-point of the axis of a cylinder of 

 length 2L and radius R is approximately [13] 



8 = 



2tt (l log (l + ??\ + 2R tan- 1 (^ - M { L V& + U 



- U- + R- [log (Z + VR- + L~) - log A'] | J c 



m 



e. Graphical evaluation of g is possible for any arbitrary point whether 

 inside or outside the tissue mass containing active material and may be 



