56 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 



3.7. Nuclear Excitation. Energy loss by nuclear excitation and capture is 

 negligibly small in terms of absorption of beta-particle beams for all energies 

 that have been observed. Its principal importance is in the determination of 

 nuclear energy levels. Theoretical as well as experimental values of the cross 

 section for nuclear excitation are of the order of 10 -7 barn. 



3 8. Absorption of Beta Particles of Homogeneous Energy. A well-defined 

 range does not exist for beta particles because of the great variation in energy 

 loss per collision and, . to an even greater degree, because of scattering. 

 Nevertheless, a useful experimental range can be found since the absorption 

 curve for a beam of initially monoenergetic beta particles such as conversion 

 electrons is roughly linear for energies greater than 0.5 mev. Hence an extra- 

 polated range may be determined by plotting the number of particles against 

 thickness of absorber and extending the linear portion of the curve to the axis 

 (or background count). Experimental determination of the range of parti- 

 cles with energies smaller than 0.5 mev by the absorption method is somewhat 

 more difficult and less certain in its results than at higher energies. The 

 absorption curve becomes more concave with decreasing energy and may, at 

 low energies, be approximated by an exponential function over a considerable 

 portion of the range. Estimation of the termination of the curve, however, 

 is subject to considerable uncertainty, particularly if the background activity 

 is appreciable. More accurate measurements of energy in this range are 

 obtained with the beta spectrograph. 



The relationship of energy to maximum range is also found to be linear for 

 energies greater than 0.7 mev and at least as high as 3.0 mev. In this 

 respect the range-energy relation for monoenergetic particles is almost 

 identical to that for heteroenergetic beams, differing by only a few per cent 

 for corresponding maximum energies. Figure 11 gives the observed extra- 

 polated ranges of beta particles determined with the aid of the monoenergetic 

 electrons provided by line spectra of various radioisotopes. An empirical 

 relation for the extrapolated range in aluminum, fitting these data within 

 ±5 per cent over the energy range from 0.5 to 3 mev, is [4] 



R = 0.52£ - 0.9 mg/cm 2 



where E = energy, mev 



The range in aluminum for energies less than 0.2 mev is given approximately 



by the relation proposed by Libby [26]. 



R = K5o£ 5/ * gm/cm 2 



3.9. Absorption of Inhomogeneous Beta-particle Beams. The absorption 

 curve for beta particles of inhomogeneous energy decreases more rapidly than 

 the curve observed for monoenergetic beams of the same maximum energy. 

 The shape and range of such curves is of particular importance in its applica- 



