NEUTRON LIFE CYCLE DOE-HDBK-1019/2-93 Reactor Theory (Nuclear Parameters) Infinite  Multiplication  Factor,  k ¥ Not  all  of  the  neutrons  produced  by  fission  will  have  the  opportunity  to  cause  new  fissions because some neutrons  will be absorbed by non-fissionable  material.   Some will  be absorbed parasitically in fissionable  material and will not cause  fission, and others  will leak  out of the reactor.  For the maintenance of a self-sustaining chain reaction, however, it is not necessary that every neutron produced in fission initiate another fission.   The minimum condition is  for each  nucleus  undergoing  fission  to  produce,  on  the  average,  at  least  one  neutron  that  causes fission of another nucleus.  This condition is conveniently expressed in terms of a multiplication factor. The number of neutrons absorbed or leaking out of the reactor will determine the value of this multiplication factor, and  will also determine  whether a  new generation of  neutrons  is  larger, smaller,  or  the  same size  as  the  preceding generation.   Any  reactor  of a  finite  size  will have neutrons  leak  out  of  it.    Generally,  the  larger  the  reactor,  the  lower  the  fraction  of  neutron leakage.  For simplicity, we will first consider a reactor that is infinitely large, and therefore has  no  neutron leakage.   A  measure of the increase  or decrease in neutron flux  in an infinite reactor is the infinite multiplication factor, k ¥ .   The infinite multiplication factor is the ratio of the  neutrons  produced  by  fission  in  one  generation  to  the  number  of  neutrons  lost  through absorption in the preceding generation.  This can be expressed mathematically as shown below. k_¥   neutron  production  from  fission  in  one  generation neutron  absorption  in  the  preceding  generation Four  Factor  Formula A group of fast neutrons produced by fission can enter into several reactions.   Some of these reactions reduce the size of the neutron group while other reactions allow the group to increase in size or produce a second generation.   There are four factors that are completely independent of the size and shape of the reactor that give the inherent multiplication ability of the fuel and moderator materials without regard to leakage.  This four factor formula accurately represents the infinite multiplication factor as shown in the equation below. k ¥ =      p f h where: = fast fission factor p   = resonance escape probability f   = thermal utilization factor h  = reproduction factor Each of these four factors, which are explained in the following subsections, represents a process that adds to or subtracts from the initial neutron group produced in a generation by fission. NP-03 Rev. 0 Page 2