REGGE-POLE DESCRIPTION OF RAINBOW SCATTERING BY MEANS OF THE PHASE-INTEGRAL METHOD

In the present paper we study the effects in the rainbow differential cross sections of using higher-order phase-integral residues in the po le sum of the scattering amplitude. We have recently found that alread y in the first-order approximation the uniform residue formula, derive d by Froman and Froman, provides an important means for an accurate ca lculation of the rainbow differential cross section where reliable num erical quantum methods are not available. From the present investigati on it is clear that the use of higher-order approximations is not the crucial step to further reveal the rainbow structures in the cross sec tion. For that purpose, it is instead essential to increase the purely numerical precision (in any order) of the uniform phase-integral resi due calculations.