Comparison of exact and approximate time developing functions in the statistical theory of nuclear reactions

In this paper we study the time developing function in compound nucleus reactions. This function can be evaluated exactly using recent results for the average of two S-matrix elements. The exact result is compared to the approximate one obtained previously. We find that for large values of the sum of the transmission coefficients the approximate result deviates from the exact one. The discrepancies are most pronounced for small times. In all other cases they are very close.