**ELECTRON IMPACT IONIZATION OF I**^{(50+)} USING R-MATRIX METHOD_{}

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**E. Chahid**^{1}**, K. Laghdas**^{1}*, R.H.G. Reid^{2}

^{1 }*Département de Physique, Faculté des sciences, Université Chouaïb Doukkali, BP 20, 24000 El Jadida, Maroc*

^{2}* Department of Applied Mathematics and Theoretical Physics, Queen’s University Belfast, BT7 1NN, UK*

** Corresponding author: E-mail: khalid_laghdas@yahoo.fr*

*Received: 25 March 2011; revised version accepted: 26 July 2011*

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**Abstract**

We present a theoretical study of electron-impact single ionization of I^{50+ }(1s^{2}2s) ^{2}S^{e} using a method that combines the distorted wave born approximation and non-relativistic R-matrix method. In this method, the incident/scattered electron is described by the distorted- wave born approximation, while both the initial ground state and the final continuum states (I^{51+}+ e^{- })_{ }are calculated by using the non-relativistic *R*-matrix method. With an initial state of the target ion, we have included only the 2^{4}- pole components of the interaction with ionizing electron, and produce five accessible continuum states with symmetries:^{ 2}S^{e}, ^{2}P^{o}, ^{2}D^{e}, ^{2}F^{o} and ^{2}G^{e}. We have calculated single differential cross sections for each residual ion states namely (^{ }1s^{2} ) ^{2}S^{e}, (1s 2s) ^{3}S^{e} (1s2p) ^{3}P^{o} , (1s2s) ^{1}S^{e} and (1s2p) ^{1}P^{o}.

Total cross sections for production of I^{51+}, in each of the five states, are calculated and presented for impact energies which is varies from threshold energy at 330.289au to 1700au . The contribution of excitation-autoionization processes for the total cross section, while not negligible, is not very significant, being of the order of a few percent. Good agreement was found between our theoretical results and the semi-empirical Lotz formula for the total cross section.

**Keywords:** *R*-matrix theory; Coulomb distorted wave; Born approximation; Continuum; Autoionization.