Getachew, Elias2018-06-212023-11-092018-06-212023-11-091996-06http://10.90.10.223:4000/handle/123456789/2627Numerical values of waw functions. calculated from Hartree-fock method. are nowadays available for many atoms and ions. Analytical forms of these functions are important in some cases. By studying Pron~"s method of representing numerical results analytically into sums of exponentials. it is shown that it is possible to apply the technique for approximating the numerically given radial part of atomic \va\'e functions into sums of exponentials analytically. for each important step in Prony's method computer program is developed. The integrated program of the Prony's method is applied to the numerical radial self consistent field (SCf) wave functions of a closed-shell Cd++ ion and the exponents and coefficients for the exponentials of the approximated analytical functions are determined, Comparison between the analytical functions and the numerical functions show good agreement for \\'a\'e functions with smaller principal quantum number value, ,\ new algorithm for approximating tabulated numerical radial SCf atomic waw functions analytically into sums of exponentials is introduced, ,\ computer program is developed for the proposed new algorithm and the technique is applied to ,Id function of cadmium ion. Cd++. and to 2s and 2p functions of floride ion .f-. Exponents and coefficients of the exponentials of the approximating functions are determined. The approximated analytical forms of the numerical radial wave functions are used to reproduce numerical values of the function. The analytical and numerical functions are found to be in good agreement. These techniques can also be applied to analytically approximate nllll1erical SCF functions of other ionsenNumerical values of wave functionsThesis