Sec. 10.11] GEIGER-MULLER COUNTERS 317 



Neutron counters with boron-coated cathodes are usually filled with con- 

 ventional argon-alcohol mixtures and operated at voltages within the pro- 

 portional region for the particular counter. The thickness of the boron 

 layer on the cathode should not be made greater than the range of the alpha 

 particle ejected from a boron nucleus by a slow neutron capture, i.e., about 

 0.1 mm. Greater thicknesses will not increase the efficiency but, rather, 

 lead to excessive absorption of neutrons since a larger fraction of ejected 

 alpha particles will not reach the sensitive volume of the counter. The 

 maximum efficiency of such counters is given [6] by the formula 



paRN 

 6 ~ A 

 where p = boron density 



N — Avogadro's number 

 A = atomic weight 

 R = alpha-particle range in boron 

 <7 = boron cross section for neutrons^of energy E 

 In a similar way, a very thin layer of uranium may be used instead of 

 boron. The fission products resulting from the absorption of slow neutrons 

 produce extremely heavy ionization. However if most of the range of a frag- 

 ment lies within the uranium layer, it cannot be distinguished from the alpha 

 particles due to the natural uranium decay and must, therefore, be treated by 

 the usual statistical methods for background counts. The normal fractional 

 concentration of the effective isotope is 0.007 and has a cross section ^550 

 barns for 0.025 ev neutrons. The use of enhanced U 235 mixtures will increase 

 the efficiency correspondingly. 



10.11. Fast Neutron Counters. Detection of fast neutrons with counters 

 is accomplished most effectively by the recoil of light nuclei from elastic 

 collisions with neutrons. The maximum energy transferred from the neutron 

 to the struck nucleus is 



„ AM 



(M + l)^ 



= Ea mev 



where M = mass of nucleus in units of neutron mass 



E = neutron energy 



E r = recoil kinetic energy of nucleus 

 and the average energy is approximately 



E = E 2M 



(M + 1)= 



If hydrogen is used for the filling gas, the maximum recoil proton energy, due 

 to a head-on collision, is equal to the full neutron energy. 



If, for a gas of atomic mass M, the smallest detectable pulse is produced by 

 a recoil energy B , referred to as the bias energy, the lowest neutron energy 



