Analytical accurate Regge-trajectory calculation for singular potentials -art. no. 022719

An entirely analytical method for computing Regge-pole trajectories for sin gular potentials (potentials diverging faster than r(-2) at the origin) is presented. Explicit results an presented for polarization (1/r(4)) and Lenn ard-Jones (6,12) potentials. Numerical precision of the calculations is ful ly controlled and often better than the state of the art numerical methods. The present method combines two different analytical approaches, The first one obtains a perturbation expansion of the Regge trajectories in terms of an appropriate parameter. Then the convergence of the resulting asymptotic series is improved through Pade approximations. Highly accurate results ar e then possible within a wide range of energies. For typical parameters use d in the literature, the two-term expansion, for which explicit formulas ar e presented, gives at least five digits of accuracy, while higher approxima tions give up to 14 digits of accuracy.