Narrow resonance approximation (NR)

If the resonance width is small compared to the maximum energy loss per collision with an absorber atom, one can assume that any collision, even with heavy absorber atoms, slows down the neutron outside the resonance. It is then possible to replace ф(Е’) on the right-hand side of (7.3) by its asymptotic ЦЕ’ solution. This equation can

tThe reader is reminded that in the past some authors (e. g. Wigner-Weinberg, Nordheim) used a different definition of a, so that instead of a in every formula appears 1-а.

then be easily integrated if we assume 2,о and 2,i to be independent of energy. This is generally true for 2,i while 2,о consists of a constant part Spot and a resonance part. In the NR approximation we can set 2,о = Spo. in (7.3) because the collisions in the resonance range do not contribute to the resonance flux. Considering that

1 fE/° 1 dE’ 2 1-а JE Е’г E’ E

Подпись: we can obtain

<ME)S,(E) = —

Подпись: (7.4)і / n 2pot+ 2s,

Ф(Е)‘~ЁШ)

image145

(7.5)

 

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