Calculations Of First-Order Born Approximation And BBK Theory In (e,2e) Reaction Of Hydrogen

In this paper,firstly we introduce the quantum-mechanically analytical methods of scattering theory:the basically analytical progress of scattering problem, triple differential cross sections,Lippman-Schwinger equation,the concept of Green function,first-order Born approximation and second-order Born approximation;Then,present the basic theories of (e,2e) reaction:the origin and development of (e,2e) reaction, geometric conditions and some approximate theories of (e,2e) reaction,include plane wave Born approximation,distorted wave Born approximation, Coulomb wave Born approximation,CCC theory,CDW-EIS theory,BBK theory and DS3C theory.In the (e,2e) reaction of hydrogen, we adopt distorted wave, plane wave and Coulomb wave in the Born approximation theory to calculate the triple differential cross sections (TDCS) at incident energies of 250,150 and 54.4 eV, respectively. And the theoretical results are compared with experiments. We find that there is little difference between the results from the two models, one uses the description of plane wave and the other of distorted wave. However, if the interaction between the scattered electron and the nucleus is considered, the result of the calculation coincides of the experiments better than the calculation result from the description of distorted wave. at incident energy of 54.4 eV,the calculation results from the DWBA theory and the DWBA-CW theory are all very different from the experimental results.Because in the two theories the interaction between the scattered electron and the ion and the dynamic screening effect of the third particle to any two-body Coulomb interaction are not considered.The triple differential cross sections for electron impact ionization of atomic hydrogen at low incident energies in the coplanar asymmetric geometry are calculated by first-order Born approximate theory,3C theory and DS3C theory.And the calculated results are compared with experimental results.It is found that high-order effects occupy an important place in the process at low incident energies.In the final state of the process,the dynamic screening effects of the third particle on the coulomb interaction of any two particles can not be neglected.However,the exchange effects are not very significant as expected.