Analytical cross section formula for inelastic Coulomb excitation in direct reactions induced by heavy ion collisions

An analytical formula for inelastic Coulomb excitation induced by the collision of heavy ions has been developed within the framework of the Distorted Wave Born Approximation (DWBA). The formula was derived by using a generalized semiclassical method whose results agree closely over a wide range of Q-values with those obtained using fully quantal DWBA calculations. Through this method, an analytical expression has been obtained for the Coulomb inelastic amplitude which is exact for partial waves corresponding to non-overlap of the colliding heavy ions. In this paper, the contributions from the partial waves are summed analytically resulting in a closed form expression for the inelastic Coulomb excitation differential cross section. This formula is in good agreement with numerically-obtained cross section. The role of the various terms in the formula is discussed. (author). 14 refs., 1 fig