IB Nuclear Physics 3.264 (1976) 173-178; (~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher GENERAL THREE-PARTICLE SCATTERING THEORY K. L. KOWALSKIt Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106 Received 1 March 1976 Abstract: A unified treatment of three-particle scattering theory with a three-body force in addition to the usual pair interactions is developed. The relationship of the generalized AGS and Faddeev formalisms to each other as well as distinct versions of each corresponding to the two most natural techniques for handling the three-body potential are established. It is found, just os in the case without the three-particle force, that the AGS formalism appears to be more practical for considering elastic and rearrangement scattering in two-body channels. On the other hand, for scattering amplitudes with at least one three-body channel (breakup and the 3-to-3) the Faddeev version of the theory is preferable. Other advantages of each formalism depending upon the treatment of the three-body interaction are noted. I. Introduction Brayshaw i) has recently proven the physical equivalence of his nonrelativistic boundary-condition formalism for three-particle scattering 2) to the characterization of this problem in terms of two- and three-particle potentials. Although the particular potential scattering formalism employed in ref. 1) is introduced merely as a technical adjunct, its appearance does emphasize the fact that all of the various formalisms for general three-particle potential scattering introduced thus far 1,3-6) bear a rather disjointed relationship to each other as well as to the conventional theories without three-body forces. The reasons for this seem to be two-fold. The first derives from the circumstance that the three-body potential, V,, does not by itself generate an observable scattering amplitude in contrast to the pair interactions 1,~, ~ = 1, 2, 3, except in the case where the latter all vanish. This has given rise to a variety of formalisms depending upon whether or not 1"4 is handled in a fashion distinct from the V~ for ~ :# 4. The second reason has to do with the fact that, whether or not 1" 4 = 0, the usual Faddeev formalism is much more convenient than that of Alt, Grassberger, and Sandhas (AGS) 7) for considering those amplitudes with three free particles in the initial and/or final states, whereas for elastic and rearrangement scattering in two particle channels the opposite is true. The convenience of the Faddeev type of theory in the former instance with 1", # 0 is illustrated by the work of refs. 1,6) in contrast to that of ref. s). * This work was supported in part by the National Science Foundation. 173 June 1976