Sec. 3.11] BETA PARTICLES 63 



approximately 2/jl (0.54 mg per cm 2 ). In a more recent study of scattering, 

 Williams [27] gives as the criterion for multiple scattering the expression 



1 « nn Z t 



2ir(3mlc 2 



where / is in centimeters. 



Single deflections of low-energy beta particles through large angles (> 90 

 deg) may be expected with a finite but very small probability in "thin" foils 

 but in "thick" layers where multiple scattering is important an appreciable 

 fraction of an incident beam of particles is back-scattered, or deflected, 

 through more than 90 deg. The coefficient of reflection R e may be defined by 

 the ratio I r /I where I Q is the incident beta intensity and I r is the back- 

 scatter intensity. For most substances the reflection coefficient has a value 

 between 0.1 and 0.5 depending upon the atomic number and density. 



This effect is particularly important in measurements of radioactive 

 samples and in the preparation of standards. The observed activity or 

 counting rate is profoundly affected by the backing material. The back- 

 scatter from platinum and lead, for example, is found to be 20 to 50 per cent 

 greater than from aluminum, depending to some extent upon the counter 

 geometry and beta-particle energy. 



3.11. Beta Decay. The emission of beta particles (negatrons and posi- 

 trons) occurs only during the decay of an unstable nucleus and is a slow 

 process compared with the primary process in which an excited nucleus is 

 formed by bombardment. The -latter process takes place in less than 10 -10 

 sec, whereas the probable time for beta-particle emission is usually a second 

 or longer. When an excited nucleus is formed by bombardment with heavy 

 particles, it contains an excess of either protons or neutrons as compared with 

 a stable nucleus of the same mass number. If the replacement of a proton 

 with a neutron leads to a smaller atomic weight (greater binding energy), the 

 transformation will occur according to the scheme 



P -> « -f (P + ) + n° 



Conversely, if the replacement of a neutron with a proton results in a more 

 stable nucleus, the transformation is 



A 7 -> P + 08") + n° 



In both cases the excess energy (mass) is carried off by the neutrino n° and 

 beta particle. If a negatron is emitted, the nuclear charge increases by one 

 unit; if a positron is emitted, the charge decreases by one unit. In calculating 

 the exact mass reduction by these processes, the exact atomic weights (neutral 

 atom) can be used in negatron emission since the loss of the rest mass of the 

 beta particle is exactly compensated by the gain of an orbital electron. In 



