By R. K. Osborn
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Extra resources for Foundations of Neutron Transport Theory
New York , 1960. IS. H. , 1959. 16. Uhknbeck an d G. W. , 196). lo\/ un Hove, PAysira,11 : 517 (1955); 1. Kohn, Phys_ R~r •• 109 : 189:! ( 1958). 18. O. P incs, Th~ Many-Body Prob/~m, Benjami n, New York, 1962. ill Neutron-nuclear Interactions: Mainly Nuclear Considerations In this cha pter we will undertake an investigation into the effects of neutron-nuclear collisions upon the balance relation (2 56). Many kinds of nuclear reaction s may be initiated by such collisio ns. However, we shalt concentrate our atten tio n on only a few of them.
1. 1 it is necessary to evaluate the co mmutator, IT'" ,(X. K)] - ~1 L 2mL x (a'(X',K', x') a(X" ,K" , x')• • ,(X, K») , X·. ll· '. (lt"-K·)[E(X" , x) K" . 57) On e ca n readily show, using the commutation relations given in Eq. 2. 14, th:1t [a+(X ' , K ', x') a(X", K" , s'J, a+(X, K , x) a(X, K, x)] ;: (a +(X', K', s) a(X, K.. " - a+(X, K, s) a(X " , K", s) 6xX' 6"d 6... 58) T hus Eq. 57 assumes the form, (r, . J ... s)o(X. s)J d1x E(X, x)EtX' ,x) c'· ·''' -ln x X ·. (x,-x; - ~)] - X;('(XI- x, + ~) - '(XI- x, - ~)]} L (±)(X, + XJ) x ", x ((a+(X, + L.
Represents the energy of a photon with moment um Ale, and the contribut ions from sta tes like the intermediate sla te as On accoun t of t heir denominators. ANS PORT T H EOR Y gible contribution. They describe an increase in the width and shift function due to a scattering interaction (elasti c if E~+ I is equal to E:' :-') between the compound nucleus and the neutron field. We expect the effects of this type of collision broadening to be relatively small, and will ignore such term s in t he following.
Foundations of Neutron Transport Theory by R. K. Osborn