Following the work of Berakdar Phys. Rev. A 53 2316, momentum correlation in the three-body Coulomb continuum problem is considered by the introduction of effective Sommerfeld parameters for both the symmetric and the asymmetric geometry. The triple differential cross sections for electron impact ionization of atomic helium at incident energies of 50 eV in the asymmetric geometry are calculated. Results of this approach are compared with the absolute measurements, the results of the BBK model without modification, the convergent close-coupling calculations and the results of our earlier model.

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The BBK model is modified by the introduction of effective Sommerfeld parameters for both symmetric and asymmetric geometries on an empirical basis, while still maintaining the philosophy that all three Coulomb interactions are included on an equal footing. The triple differential cross sections for electron-impact ionization of atomic helium at an incident energy of 40 eV in an asymmetric geometry are calculated. Results of this approach are compared with the absolute measurements and the only existing theoretical results of the convergent close-coupling method.

The triple differential cross sections for electron impact ionization of helium in the special geometry of coplanar large energy loss are calculated by using the BBK model and the modified BBK model. The calculated results are compared with the experimental results of Catoire and the present experimental results of Stevenson. The previous theoretical deduction is proved and the exchange effects are analyzed and discussed.

Based on the modified three-body Sommerfeld parameters,the effective shield of the residual electron in the final state of He+ is further modified for (e,2e) processes- Such a modification represents a dynamic screening of the four bodies in the final state- The triple differential cross sections for electron impact ionization of atomic helium at an incident energy of 50eV in the asymmetric geometry are calculated by use of the modified Sommerfeld parameters-The results were compared with those of the absolute measurements and the only existing theoretical results of the convergent colse-coupling method-It was found that the present results give a better description for the experimental data at fixed ejected energy of 10eV-