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Energy of a Particles on passing through Matter* 683 



where j/ { is given by 



2j _ 2 2EV 



and 



2irEVN 



A 



w 



„ AT An,. Pl * + a 2 



Hence ^.= —log/ - r 



= W lo « Q- • 

 Summing for all types of electrons, 



AT A v . 2mY* 



— y2 [ /4 lo » 2mV 2 — 2 s n«log Q,] 



is the rate of loss of energy due to ionization potentials. 



To take into account the effect of resonance potentials, 

 consider, first, the n x electrons with the ionization potential 

 Q t . Let there be resonance potentials Q/, Q/' . . ., all less 

 than Q 1? and let the corresponding upper limits, given by (1), 

 for them's be pi } pi" .... We assume that for values of p 

 lying between p 1 and />/ (i. <?., when the energy available, 

 according to (1), lies between the ionization and resonance 

 potentials) the energy transferred to the electron is constant 

 and equal to Q/. Similarly, for all values of p between p/ 

 and /)/', the energy transferred is constant and equal to Q/\ 



Then the total loss of energy by the a particle passing 

 through a distance A.r, which is due to the presence of 

 resonance potentials, will be 



AT = 27rN,iAr [<iApdp + Q 1 "Ldp + . . .], 



U=7rNn 1 [Q 1 '(^-^)+Q 1 "(W' 2 ^ 1 ' 2 )+. . .], 



AT_ 2ttNEV/i 1 

 A.r~ m\ 2 



[ Q ''(i-i) +Q '"(^-^) + -] 



1 Qi <() 1 



An , 0,<' +1 >' 



V * 



