Transition form factor of the hydrogen Rydberg atom

Abstract

The form factor for the transition between the hydrogenic states with parabolic quantum numbers n{sub 1}n{sub 2}m and n{sub 1}{sup {prime}}n{sub 2}{sup {prime}}m{sup {prime}} is obtained in a closed analytic form. The asymptotic limit of the transition form factor at large parabolic quantum numbers is derived, and a comparison with exact quantum calculations shows that the asymptotic limit is accurate in a wide region of parabolic quantum numbers and the momentum p transferred to electrons. A simple quasiclassical formula for the transition probability is given, and the range of quantum numbers corresponding to quasiclassically forbidden transitions are defined. {copyright} {ital 1997} {ital The American Physical Society}