## 3. The pair yieldThe differential yield of produced pairs is calculated as where The differential cross section has been evaluated by Jauch & Rohrlich (1959): where We may express the solid angle element . Using Eq. (2), we find This enables us to carry out the with we find where with and we used the integrals and the identity which follows from Eqs. (5), (6) and (14). Now, inserting Eq. (15)
into Eq. (8) yields the exact expression for the differential pair
injection rate. Using Eq. (1) we transform the which can be calculated analytically. The integration limits follow from and the condition which yields where Using the integrals 2.271.4, 2.271.5, 2.272.3, 2.272.4, and 2.275.9, of Gradshteyn & Ryzhik (1980), we find as final result for the differential pair yield where for we have and For we find © European Southern Observatory (ESO) 1997 Online publication: April 28, 1998 |