Sec. 4.111 



PROTONS, DEUTERONS, AND ALPHA PARTICLES 



91 



expression, provided that the beam of particles was monoenergetic initially 

 [27]: 



PdR = -i- e -( R »- RWa * dR 



where P = probability that a particle has a range lying in the interval R to 

 R + dR 

 a = range straggling parameter 

 R = mean range 

 The 'parameter a is the half-width of the differential distribution curve at 

 1/e of its maximum height. It increases with energy, and its order of magni- 

 tude may be illustrated by the observed value of approximately a = 0.13 cm 

 for 10-mev alpha particles stopped in air. 



DIFFERENTIAL 

 CURVE, THIN 

 SOURCE 



EXTRAPOLATED 

 RANGES 



DISTANCE FROM SOURCE 



R -.MEAN RANGE 



Fig. 19. Integral and differential number-range curves for heavy charged particles. 



The mean range R u is the distance from the source to the maximum of the 

 differential number-range (Gaussian) curve, or alternatively it may be 

 defined as the distance at which the initial number of particles is reduced to 

 one-half. In practice the extrapolated number-distance range is the most 

 readily determined quantity. This is the range indicated by the intercept of 

 a line extended along the straight portion of the slope of steepest descent of 

 the integral range curve. The mean and the extrapolated ranges are then 

 related by the expression 



i?es — R = 



ir -a 



These definitions are exact only for strictly monoenergetic particles such as 

 those emitted from a source that is infinitesimal in thickness. In practice, 

 sources and targets are often "thick" in that their thickness is comparable to 

 or greater than the range of the particles. In this case the beam is not 



