Fragmentation and Energy Conservation - Ci in the Eikonal - Regge Model

We have studied the effect of fragmentation and energy conservation in the Eikonal-Regge model. A generalized eikonal representation involving multiimpact-parameters is given for the elastic and inelastic amplitudes when fragmentation takes place. The generalized eikonal function depends on more than one impact parameter which describes a many-body potential. In the strong absorption model and at high energy, however, the elastic amplitude can be approximated by a single impact parameter representation with an effective eikonal function. As a result of the fragmentation, we find that although ~~ and oT still increase as Qn2 s, their ratio is no longer l/2. Instead, it is the sum of the elastic and diffractive cross sections which remains to be one half of the total cross section. To enforce the energy conservation, we propose a thermodynamic approach by introducing an impact-parameter-dependent temperature. Using well-known thermodynamics relations, we obtain various corrections to the naive Eikonal-Regge model predictions due to energy conservation. Experimental consequences are discussed. *Work supported in part by the U. S. Atomic Energy Commission and in part by the National Science Foundation under Grant No. NSF GP40908X. ‘fAlfred P. Sloan Foundation Research Fellow, 1972-1974. t?On leave of absence from Cornell University, Ithaca, New York 14850. (Submitted to Phys. Rev.)