We have seen that for narrow resonance approximation the flux is given by (7.4)

2Po. + 2,i 1

2,o + 2,i + 2o E

2„ 1

2,i + 2o E

If the resonance is neither narrow nor wide one can use the intermediate form, first proposed by Goldstein and Cohen,<2>

(7.8)

where

When A = 1, eqn. (7.8) gives the NR expression and when A = 0 eqn. (7.8) gives the NRIM approximation.

With NR approximation for the moderator eqn. (7.3) takes the form

where the integral operator Кф is defined by

From eqn. (7.9) it is possible to define the iterative sequence

(7.10)

where фт, фа . . ., ф(п) are successively closer approximations to the correct solution. The first guess can be taken from the NR or NRIM approximation and the iteration can be repeated until ф(а> converges to the solution of eqn. (7.9). However, these iterations become quite laborious. The intermediate resonance (IR) method consists of inserting a

given by фт is equal to I<2) given by ф(2