Final State Interactions in Weak Three-Body Decays Calculated in the Impulse Approximation

1123 An exactly soluble model of the weak three-body decay of a Q+ particle to three daugh ter O+ particles which interact strongly has been studied by Amado and Noble. The same problem with identical input data is studied in the impulse approximation. The two sets of results are compared to examine the accuracy of the impulse model. The question is stud ied of how accurately the two-body parameters can be extracted from the weak-decay data using the impulse approximation. An increase in our fundamental knowledge of the three-body decay mechanism has been made by Amado and Noble1l' 2 ) who have studied the non-relativistic weak decay of a o+ particle (the G's or Gedanken) into three o+ particles (the H's) which interact strongly. The problem was facilitated by the choice of a separable two-body interaction between the final state H's. This choice of the two-body potential ensured that the Faddeev equations for the three-body T matrix could be solved exactly. The numerical solutions of the Faddeev equations showed that the three-body data were very strongly dependent upon the volume of the weak-decay vertex (3-t, making the extraction of two-body parameters risky and unpredictable. In this paper the calculations of Amado and Noble are repeated with identical input data but using the impulse approximation. The two sets of results are compared to examine the accuracy of the impulse model and to examine how accurately two-body parameters can be extracted by fitting the impulse model to the data (taken to be the exact calculations of Amado and Noble). Of the three commonly used models for resonant three-body decay-the Born approximation, the Breit-Wigner model and the impulse model-the last is the most accurate as it includes the effects of interference between the break-up and the :first scatter ing terms. This model is a non-relativistic analogue of the dispersion treatment of Khuri and Treiman. 8l