Yazar "Oztekin, E." seçeneğine göre listele

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    Asymptotic behavior of Clebsch-Gordan coefficients
    (Springer, 2024) Akdemir, S.; Ozay, S.; Oztekin, E.
    In this study, the Clebsch-Gordan coefficients are expressed using the generalized hypergeometric functions of unit argument and binomial coefficients, and their behavior as a function of quantum numbers is examined. The Clebsch-Gordan coefficients are also numerically computed for integer and non-integer quantum numbers. Subsequently, the convergence between the Clebsch-Gordan and asymptotic Clebsch-Gordan coefficients is investigated based on the orbital angular momentum quantum numbers.
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    Calculation of electric multipole moment integrals with the different screening parameters via the Fourier transform method
    (Wiley, 2012) Yukcu, N.; Senlik, I.; Oztekin, E.
    Three-center electric multipole moment integrals over Slater-type orbitals (STOs) can be evaluated by translating the orbitals on one center to the other and reducing the system to an expansion of two-center integrals. These are then evaluated using Fourier transforms. The resulting expression depends on the overlap integrals that can be evaluated with the greatest ease. They involve expressions for STO with different screening parameters that are known analytically. This work gives the overall expressions analytically in a compact form, based on Gegenbauer polynomials. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 112: 414-425, 2012
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    Generating function for rotation matrix elements
    (Wiley-Blackwell, 2012) Akdemir, S. O.; Oztekin, E.
    The rotation matrix elements are expressed in terms of the Jacobi, Hypergeometric, and Legendre polynomials in the literature. In this study, the generating function is presented for rotation matrix elements by using properties of Jacobi polynomials. In addition, some special values and Rodrigues' formula of rotation matrix elements are obtained by using the generating function. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012
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    New analytical expressions, symmetry relations and numerical solutions for the rotational overlap integrals
    (Wiley, 2012) Akdemir, S. O.; Eryilmaz, S. D.; Oztekin, E.
    In this article, extremely simple analytical formulas are obtained for rotational overlap integrals which occur in integrals over two reduced rotation matrix elements. The analytical derivations are based on the properties of the Jacobi polynomials and beta functions. Numerical results and special values for rotational overlap integrals are obtained by using symmetry properties and recurrence relationships for reduced rotation matrix elements. The final results are of surprisingly simple structures and very useful for practical applications. (c) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012
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    New orthogonality relationships of the Gaunt coefficients
    (Elsevier, 2024) Ozay, S.; Akdemir, S.; Oztekin, E.
    A new analytical formula for the Gaunt coefficients is derived using expressions of Clebsch Gordan coefficients in terms of the generalized hypergeometric functions of unit argument and binomial coefficients. In addition, new sum expressions and orthogonality relations containing the Gaunt coefficients are written. These expressions are used to test the accuracy of the numerical calculation for the Gaunt coefficients. These formulae are coded in the Mathematica programming language, and the Gaunt coefficients are calculated numerically and compared with the values from the literature.
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    Reducing and Solving Electric Multipole Moment Integrals
    (Elsevier Academic Press Inc, 2013) Yukcu, N.; Oztekin, E.
    Electric multipole moment integrals with the same screening parameters are calculated using Slater type orbitals (STOs) translation formulae and the Fourier transform method. First, multipole moment operators which appear in the three-center electric multipole moment integrals are translated from the 0-center to the b-center. After the translation procedure and using Fourier transform convolution theorem, three-center electric multipole moment integrals were reduced to two-center molecular integrals. Then, the analytical expressions obtained were written in terms of overlap integrals. The numerical values for electric multiple moment integrals are useful especially for high quantum numbers and atomic parameters.