MEASUREMENT OF IONIZING RADIATIONS 169 



whole question must be kept in abeyance." It is felt, however, that, 

 although probably not very precise, the published calculations remain 

 very valuable in estimating doses under certain conditions. These 

 limitations have been amply discussed by the various authors. 



For the convenience of the reader some geometries will be illustrated 

 by examples in which the variation of /3-ray ionization with distance is 

 assumed to be a function of distance and an "absorption coefficient." 



Spherical geometries have been considered extensively by Bush (1949), 

 Rossi and ElHs (1950), and Oddie (1951). The results of their computa- 

 tion can be summarized concisely by considering a sphere of radius a and 

 a point at a distance b from the center. If the sphere of unit density 

 material, of radius a, contains a concentration of C fic per gram of radio- 

 element, the radiation of which is absorbed exponentially according to a 

 coefficient /i, then the dose 8^ at a distance from the center can be calcu- 

 lated as 



d, = Dff- g^ (19) 



where 



f M~'"' 

 <" = j. 4^-- ''" 



which is the integral of the contributions of elements dv in the sphere 

 located at a distance r from the point of interest. The factor g may be 

 considered as the geometrical factor of the distribution itself for the 

 point in question and retains its meaning in any configuration. Whenever 

 the dose rates per hour or per minute are desired, the values of d^ in 

 Eqs. (16), (17), and (18) are substituted for D^ directly into Eq. (19). 

 Values of g for spheres can be computed by means of Table 2-3 (Oddie, 

 1951) if the absorption coefficient /x of the radiation is known. The table 

 is of general use since the distance ^ = b/a is expressed as a fraction of 

 sphere radius and the radius is in units of the "relaxation length," l//x. 

 By relaxation length is meant the distance within which a parallel beam 

 of radiation is reduced to 1/e of its former value. Values of l/n, as 

 given by Rossi and Ellis (1950), are shown by the dotted fine in Fig. 2-9. 

 For the case of irradiation of chemical compounds or microorganisms, the 

 average energy absorbed within the sphere becomes a parameter of special 

 importance. In this case the geometrical factor becomes (Bush, 1949) 



11 Analysis by Loevinger (l050) of the ionization resulting at different distances from 

 uniform plane distributions of fi emitters shows that, to about one-half of the maximum 

 range, the ionization from a /3-emitting point source can be expressed as 



/(r) ex r-2 for < r < 1 

 and 



f(r) oc r-igi"'' for r > 1 



where r is the distance from the source in relaxation lengths (1/m) for the radiation in 

 question. Values of l//x pertaining to this type of variation are expressed as a func- 



