DIMENSIONAL PERTURBATION-THEORY FOR REGGE-POLES

We apply dimensional perturbation theory to the calculation of Regge p ole positions, providing a systematic improvement to earlier analytic first-order results. We consider the orbital angular momentum l as a f unction of spatial dimension D for a given energy E, and expand l in i nverse powers of kappa=(D-1)/2. It is demonstrated for both bound and resonance states that the resulting perturbation series often converge s quite rapidly, so that accurate quantum results can be obtained via simple analytic expressions given here through third order. For the qu artic oscillator potential, the rapid convergence of the present l(D;E ) series is in marked contrast with the divergence of the more traditi onal E(D;l) dimensional perturbation series, thus offering an attracti ve alternative for bound state problems. (C) 1997 American Institute o f Physics.