Classical and quantal atomic form factors for arbitrary transitions

The classical form factor is deduced from exact correspondence with a phase -space representation of the quantal form factor. Analytical expressions ar e provided for nl-->n'l', nl-->n', and n-->n' transitions in hydrogenic sys tems and for n-->n' in the one-dimensional harmonic oscillator. An efficien t procedure for calculation of quantal form factors as analytical functions of momentum transfer, for arbitrary quantum numbers, is presented. The cla ssical approach has the ability to explain quite succinctly interesting tre nds and various important aspects which remain hidden within the quantal tr eatment of form factors; The classical quantal comparison ranges from being qualitatively good for nl-->n'l' transitions to close agreement for nl-->n ' and n-->n' transitions. Excellent agreement is obtained for the integrate d form factor for all transitions. [S1050-2947(99)09107-6].