94 



ISOTOPIC TRACERS AND NUCLEAR RADIATIONS 



[Chap. 4 



Zero coulomb energy 



where z = alpha-particle charge 

 Z = atomic number 

 R = nuclear radius 

 The field in the nucleus therefore may be represented by a cylindrical 

 potential well, as shown in Fig. 20, extending an unknown distance E below 

 the zero coulomb energy and a distance Eb above. Outside the potential 



well only the coulomb field is effective. 

 In the nucleus, an alpha particle in 

 an energy state above the zero cou- 

 lomb energy has a finite probability 

 of leaving by penetration through 

 the barrier even though its energy is 

 considerably smaller than the barrier 

 height. If the alpha particle is raised 

 to a level equal to the barrier, or into 

 the continuum of states above the 

 barrier by external excitation, it is 

 emitted in a time of the order of 10 -21 

 sec. When the alpha particle is 

 excited to a quantum state lying 

 below the top of the barrier, the 

 probability of emission per unit time by penetration through the barrier is 

 greatly reduced. The mean life r for alpha emission under this condition 

 (alpha decay) is given by the expression 



r = T e f 



where t ^ 10 -21 sec and the function / depends on the charge and mass of 

 the nucleus. If the observed kinetic energy of the alpha particle is small 

 compared to 2e 2 Z/R, the function / is given approximately by 



Sir 2 e 2 Z STe(4ZmR)V> 



»- Radius -J 



Fig. 20. Diagram of potential fields of 

 nucleus showing "square" potential well 

 and coulomb barrier. 



/ = 



hv 



h 



where E a = energy of alpha particle above zero coulomb energy, or the 

 observed kinetic energy of the alpha particle plus the recoil 

 nucleus (Fig. 20) 

 m = mass of alpha particle 

 R = nuclear radius, « 1.47 X 10r l3 A^ cm 

 v = alpha-particle velocity 

 h = Planck's constant 

 The factor t is the mean life for emission in the absence of a barrier and may 

 be thought of as the period of vibration of the alpha particle in the nucleus. 

 The reciprocal of e f is the transmission coefficient, or penetrability, and 



