By R. K. Osborn
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Extra info for Foundations of Neutron Transport Theory
Example text
Y. _{ . Th e transition probability is independent of .. See Ueitler, rd. 3. 70- t See S:hiff. rd C1'C'fK'C II, p. I98. ) as one might expect in N U CL EA I. A TlONS 37 the present situation. To develop exp licit cross-section formulas for the vari ous reactions, it is now necessary t o consider in more detail the states (In ) } and the matrix elements of th e interaction , V. 1 simply as a diagonalizing representation for the kinetic energy of free neu trons in cells and for the t otal energy of the " system" with which the neutrons interacted acco rding to a potential V.
58. The direct matrix elements. u •• ca n be est imated in ter ms of II specific model ora neutron-nuclear interactio n. It is to be emphasized that this use of a model does not affect th e other matrix elements of VN, those describing resonance scattering. Th is will become evident in the fo llowing, for the parameters of the model arc to be determ ined acco rding to co mparisons with data fro m low-energy pote ntial scattering. , th e Born ap p roximation o r firstorde r pert urba tio n theory as presented here, it is not clear that such a model should he employed in general theor etical a nalyses whieh are not restr icted to these ap proxi mations.
Clcmcms ~)r r" an d V/II. c and will be considered first . :.. A (r~) . C where the I »pccitics the nuc leus and L specifics the nucleon. 01 manner wholly similar to the qcunuzatio n of t he neutron field in Cha pter II. :.. (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.