NEUTRON INTERACTIONS WITH HYDROGEN AND TISSUE 41 



Let us examine these processes in some detail in order to derive a few 

 relationships which may help our understanding of the biological action 

 resulting from neutron irradiation. Collision of a neutron with another 

 nucleus results in deflection of the incident particle, along with a transfer 

 of part of the energy of the neutron to the struck nucleus. When the 

 process follows the simple billiard ball laws of classical particle physics 

 and does not raise the nuclear energy levels of the struck nucleus, it is 

 called elastic scattering. 



The loss of energy by elastic scattering with other nuclei is dependent 

 on the size of the colliding nucleus and the kind of collision, whether 

 glancing or head-on. The neutron will transmit the maximum amount 

 of its energy if it collides head-on with a proton, far less if it just bounces 

 off a heavy nucleus; the exact equations can be derived from the laws 

 of conservation of energy and momentum. On the average, the following 

 simple approximate expression gives the mean ratio of the energy of a 

 neutron after collision (£"2) to its energy before collision (-E'l): E2 = 

 ^^g-[2/(3f +1)1 ^ -^yhere M is the mass of the struck nucleus. Each collision 

 with a hydrogen atom reduces the average energy of the neutron by the 

 factor 1/e, or roughly 3^. On the other hand, collision with a carbon or 

 nitrogen atom reduces the average energy of the neutron by only about 

 15 per cent, and collision with oxygen, phosphorus, and sulfur by even 

 smaller amounts. For a 1-mev neutron, 18 collisions with protons are 

 needed to slow the neutron down to thermal energy, a figure which can 

 be compared with 110 collisions required with carbon. 



Neutron Interactions with Hydrogen and Tissue 



It is helpful to examine the scattering process in detail from the point 

 of view of collisions of a neutron with a proton, because of both the 

 predominance of hydrogen in tissue and the importance of neutron- 

 proton forces in nuclear theory. It is customary to consider the relative 

 importance of several competing nuclear reactions in terms of their 

 cross section, the apparent cross-sectional area that the target nucleus 

 offers to the impinging particle, in this case the neutron. The accepted 

 unit of cross section, 10"""* cm^, is called, in physics jargon, a barn. The 

 radius of the hydrogen nucleus is about 1.5 X 10""^^ cm, and it should, 

 therefore, have a cross section on geometrical grounds alone of 0.07 barn 

 for fast neutrons. For neutrons of energies of 10-20 mev, the cross section 

 has been experimentally determined to be about 0.5 barn. From this 

 low value the cross section rises to a plateau of about 20 barns which is 

 maintained in the region from 10,000 ev to 1 ev. At energies below 1 ev, 

 the cross section rises again and reaches a value of about 75 barns at the 



