Asymptotic Behavior of theSMatrix for High Angular Momentum

The behavior of the partial-wave transition matrix is discussed for large values of the angular momentum. For physical values of the angular momentum, it is shown that the $N$-channel $T$ matrix vanishes in the high angular momentum limit. The validity of the optical model is discussed. In the Gelfand-Levitan formalism, it is shown that the two Jost functions coincide as the angular momentum goes to infinity along the real axis. For the Yukawa-type potentials, it is shown that the transition matrix reduces to its Born term as the real part of the complex angular momentum variable goes to infinity.