الفهرس 
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Abstract
The calculation of different reactor cell par inters for the thermal neutron group represent one of the important steps needed for the physics design of nuclear reactors. The collision probability theory is one of the useful UI o rios used for these calculations In this thesis, a collision probability Otho proposed for calculation of cell consideration is given to tle developm it and the application of one of the most powerful tools of applied viz the variational calcul is, to the Irol3e of deterina¬tion of neutron collision DrObabilities A generpa variational method for calculation of improved initial self and intial collision probabilities in a rialtire icn reactor cell of a general geometry is resentod Tile basic equation, used for the formulation of tjicsn probabilities, is tile one reap integrl-1 Boltzran transport equation.A suitable variational functional is choose and an optimization procedure is adopted to get the best estimate fcr tile average virgin flux in each region of the cell The main advantages of the proposed rariational procedure are the dispense with the usual flat birth and flat collision density distribution assumptions and the adoption of other realistic assumptions for these distributions. Ai o the r advantage is that it is possible to deduce direct expressions for those probabilities, thus avoiding the necessity of the Luse of other indirect algorithms such as those of Bonalix .