Classical and quantal atomic form factors for nlm→n′l′m transitions -: art. no. 022703

An analytical expression for the classical form factor or impulsive probability P-if(q) for nlm-->n'l' m transitions is derived directly from the "phase-space distribution" method [Phys. Rev. A 60, 1053 (1999)] and is compared with quantal results. Exact universal scaling laws are derived for the classical probability for any i-->f transition. As n is increased, convergence of the quantal to classical results is obtained and it becomes even more rapid upon averaging in succession over the in and then the l substates. The classical results reveal the basic reason for the underlying structure in the variation of P-if with momentum transfer q. Classical form factors can operate as an effective averaged version of the exact quantal counterpart.