Sec. 3.10] 



BETA PARTICLES 



61 



for any beta absorption curve which is measured with the same counting 

 arrangement and plotted on the same kind of graph paper. The rest of the 

 procedure is followed as before. 



The Feather analysis can be extended to complex spectra provided that the 

 difference in the maximum energies of the components is sufficiently great 

 to allow the absorption curve to be 

 broken down into components. 



The relation between range and 

 maximum energy of beta particles 

 emitted from radioisotopes is linear 

 within experimental errors for ener- 

 gies greater than 0.8 mev and at least 

 as high as 3.0 mev. On the basis of 

 range measurements made by the 

 method above and corresponding 

 energies determined with the beta 

 spectrograph, Feather [5] proposed 

 as the range-energy relation for beta 

 particles in aluminum the expression 



.2 .3 .4 .5 .6 .7 



FRACTIONAL RANGE 



- — A 



10 



R = 543£ - 160 mg/cm 5 



Fig. 14. Beta-particle range determina- 

 tion by the Feather method. The curve of 

 partial ranges is extrapolated to full range 

 (1.0) to obtain the actual beta-particle 



range given by the ordinate A. 

 where E — energy, mev, > 0./ 



The constants were redetermined by Glendenin and Coryell [25] with more 

 extensive data, and they give the relation as 



R = 542£ - 133 mg/cm 2 



For energies less than 0.8 mev the range-energy curve bends toward the 

 origin in a way that cannot be represented accurately with a single function. 

 For energies less than 0.2 mev, Libby [26] finds that the range is accurately 

 represented by the formula 



R 



Hso- 



?tt 



In the range from 0.15 to 0.8 mev, the range is given by [12] 



R = 407£ 138 



mg/cm 2 



mg/cm 2 



The portion of the curve for energies less than about 0.7 mev is essentially 

 the same for monoenergetic and heteroenergetic beta-particle beams with the 

 same maximum energy. The formulas above therefore can be used in either 



case. 



3.10. Scattering of Beta Particles by Nuclei. The elastic scattering of 

 beta particles has presented a difficult problem both in theory and in measure- 

 ment. Because of the small mass of the electron compared to a nucleus, 



