Authors
Abstract
A second-order approximation to the Faddeev-Watson-Lovelace treatment of the rearrangement channel is used in a three-body scattering cross sections. In this formalism, the Three-body wave function is expressed by three coupled integral equations, the Faddeev equations, which contian the two-body (off-shell) transition amplitudes, and proved the uniqueness of their solutions. This amplitude corresponds to the summing of infinite numbers of terms involving the electron-projectile and electron-target nuclear potentials in a Born expansion of the transition operator. It thus represents a considerable improvement over a treatment involving only the second-order Born approximation. Application of this method is tedious because of a difficulty arising from the complicated nature of the two-body off-shell Coulomb T-matrix, which is the basic dynamical ingredient in the formalism. The difficulty arises from the fact that the Coulomb T-matrix does not have a well-defined on-shell limit. Expressions are derived for projectile scattering angles in the extreme forward directions and for angles centered about the local maximum of the differential cross section [at (mc/Mp < /sub>) Sin600, where mc is the electron mass and Mp < /sub> is the projectile mass] known as the Thomas peak. A mixture of analytical and numerical methods have been used to calculate the transition amplitudes for state to state [H+ +H(nIm)→H (n´I´m´) + H+] reaction and therefore the corresponding cross sections. Many numerical and analytical calculations are available within a near-the-shell limit for 1s-1s transition of electron-capture process in proton hydrogen collision, but no calculation was performed for the state (nlm) to state (n’l’m’). We have compared the calculated differential cross sections for electron capture of different states and also with the available measured cross sections in the literature.
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