Foundations of Neutron Transport Theory by R. K. Osborn

By R. K. Osborn

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The co llision terms, Eqs . 62, ca n be entered into Eq . S6. Keeping in mind th at time and spatial derivatives are act ua lly finite differences, we may exhibit the resulting eq uation , in the absence of quantum effects, as (~at + ~m K· V, + W)F(X, K,t) - L F(X, KJ, ' )[WiJ-K+ L ",~,4 IK"" t IlJ J. ] " + -I' , V + - I , (P) f{X. I,. ~(P'} ' (P' - P) - !!!.. (P ' r - P) The frequency Jf. is introduced such that S:(P', P) d 'P is the probability tha t a fission induced by a neutron at P' will prod uceexactly J neuIron s, /\ of whieh have mo menta in d'P about P.

K·) · p~ lk .. ,·.... I\.. :.. L " ' •. l·) e-'··f a" (K)' pI. 55) The label 0 i.. : uf the nucleus. u the above factorizati on we have introduced the cente r-ofmass position vecto r, R, and the relati ve displacement , p, so t ha t = R, • These coord inates, however, a rc not independen t. T he mom entum p:. is co njuga te to r~ , an d t here fore consists of co ntribution s From center-of-mass motions as well as from relative motion s. But bccau-c the nuclear momentum is very small compared to the nucleonic momen t um we have neglected t he former and set p~ :::: p'-.

J However, it is no t clear that che mica l binding effects ca n be conveniently grafted onto this elegant and rigorous theory of binary nucl ear reactions. •• Althou gh such an a pproach enables easy incorpo ration of the medi um effects. this extreme must also be avoided since it a ppears that only po tential scatt ering can be readily and usefully weiss- 29 30 TH E FOUNDATIONS Of NEUTRO N TRANSPORT THEORY tr eated in this manner. 56), conventional perturbation methods are therefore not adequate.

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