An Approximation for the Doppler Broadening Function and Interference Term Using Fourier Series

Affiliation(s)

Department Nuclear Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.

Brazilian Nuclear Energy Commission, Rio de Janeiro, Brazil.

Department Nuclear Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.

Brazilian Nuclear Energy Commission, Rio de Janeiro, Brazil.

ABSTRACT

The calculation of the Doppler broadening function and of the interference term are important in the generation of nuclear data. In a recent paper, Goncalves and Martinez proposed an analytical approximation for the calculation of both functions based in sine and cosine Fourier transforms. This paper presents new approximations for these functions, and , using expansions in Fourier series, generating expressions that are simple, fast and precise. Numerical tests applied to the calculation of scattering average cross section provided satisfactory accu- racy.

The calculation of the Doppler broadening function and of the interference term are important in the generation of nuclear data. In a recent paper, Goncalves and Martinez proposed an analytical approximation for the calculation of both functions based in sine and cosine Fourier transforms. This paper presents new approximations for these functions, and , using expansions in Fourier series, generating expressions that are simple, fast and precise. Numerical tests applied to the calculation of scattering average cross section provided satisfactory accu- racy.

Cite this paper

A. Goncalves, D. Palma and A. Martinez, "An Approximation for the Doppler Broadening Function and Interference Term Using Fourier Series,"*World Journal of Nuclear Science and Technology*, Vol. 2 No. 4, 2012, pp. 144-149. doi: 10.4236/wjnst.2012.24021.

A. Goncalves, D. Palma and A. Martinez, "An Approximation for the Doppler Broadening Function and Interference Term Using Fourier Series,"

References

[1] D. A. P. Palma and A. S Martinez, “A Faster Procedure for the Calculation of the ,” Annals of Nuclear Energy, Vol. 36, No. 10, 2009, pp. 1516-1520. doi:10.1016/j.anucene.2009.07.019

[2] A. Talamo, “Analytical Calculation of the Fuel Temperature Reactivity Coefficient for Pebble Bed and Prismatic High Temperature Reactors for Plutonium and UraniumThorium Fuels,” Annals of Nuclear Energy, Vol. 34, No. 1-2, 2007, pp. 68-82. doi:10.1016/j.anucene.2006.11.003

[3] S. G. Hong and K. S. Kim, “Iterative Resonance SelfShielding Methods Using Resonance Integral Table in Heterogeneous Transport Lattice Calculations,” Annals of Nuclear Energy, Vol. 38 No. 1, 2011, pp. 32-43. doi:10.1016/j.anucene.2010.08.022

[4] D. A. Palma, A. Z. Mesquita, R. M. G. P. Souza and A. S. Martinez, “Real-Time Monitoring of Power and Neutron Capture cross Section of Nuclear Research Reactor,” In: International Conference on Research Reactors: Safe Management and Effective Utilization, International Atomic Energy Agency, Vienna, 2011.

[5] W. M. Stacey, “Nuclear Reactor Physics,” Wiley, New York, 2001.

[6] A. C. Gon?alves, A. S. Martinez and F. C. Silva, “Solution of the Doppler Broadening Function Based on the Fourier Cosine Transform,” Annals of Nuclear Energy, Vol. 35, No. 10, 2008, pp. 1878-1881. doi:10.1016/j.anucene.2008.04.003

[7] G. Arfken and H. Weber, “Mathematical Method for Physicists,” Academic Press Inc., London, 2001.

[8] C. M. Amaral and A. S. Martinez, “The Effect of Scattering Interference Term on Pratical Width,” Annals of Nuclear Energy, Vol. 28, No. 11, 2001, pp. 1133-1143. doi:10.1016/S0306-4549(00)00112-2

[9] R. S. Keshavamurthy and R. Harish, “Use of Padé Approximations in the Analytical Evaluation of the Function and Its Temperature Derivative,” Nuclear Science and Engineering, Vol. 115, No. 1, 1993, pp. 81-88.

[10] D. A. Palma, A. C. Gon?alves and A. S. Martinez, “An Alternative Analytical Formulation for the Voigt Function Applied to Resonant Effects in Nuclear Processes,” Nuclear Instruments & Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 654, No. 1, 2011, pp. 406411. doi:10.1016/j.nima.2011.07.029

[1] D. A. P. Palma and A. S Martinez, “A Faster Procedure for the Calculation of the ,” Annals of Nuclear Energy, Vol. 36, No. 10, 2009, pp. 1516-1520. doi:10.1016/j.anucene.2009.07.019

[2] A. Talamo, “Analytical Calculation of the Fuel Temperature Reactivity Coefficient for Pebble Bed and Prismatic High Temperature Reactors for Plutonium and UraniumThorium Fuels,” Annals of Nuclear Energy, Vol. 34, No. 1-2, 2007, pp. 68-82. doi:10.1016/j.anucene.2006.11.003

[3] S. G. Hong and K. S. Kim, “Iterative Resonance SelfShielding Methods Using Resonance Integral Table in Heterogeneous Transport Lattice Calculations,” Annals of Nuclear Energy, Vol. 38 No. 1, 2011, pp. 32-43. doi:10.1016/j.anucene.2010.08.022

[4] D. A. Palma, A. Z. Mesquita, R. M. G. P. Souza and A. S. Martinez, “Real-Time Monitoring of Power and Neutron Capture cross Section of Nuclear Research Reactor,” In: International Conference on Research Reactors: Safe Management and Effective Utilization, International Atomic Energy Agency, Vienna, 2011.

[5] W. M. Stacey, “Nuclear Reactor Physics,” Wiley, New York, 2001.

[6] A. C. Gon?alves, A. S. Martinez and F. C. Silva, “Solution of the Doppler Broadening Function Based on the Fourier Cosine Transform,” Annals of Nuclear Energy, Vol. 35, No. 10, 2008, pp. 1878-1881. doi:10.1016/j.anucene.2008.04.003

[7] G. Arfken and H. Weber, “Mathematical Method for Physicists,” Academic Press Inc., London, 2001.

[8] C. M. Amaral and A. S. Martinez, “The Effect of Scattering Interference Term on Pratical Width,” Annals of Nuclear Energy, Vol. 28, No. 11, 2001, pp. 1133-1143. doi:10.1016/S0306-4549(00)00112-2

[9] R. S. Keshavamurthy and R. Harish, “Use of Padé Approximations in the Analytical Evaluation of the Function and Its Temperature Derivative,” Nuclear Science and Engineering, Vol. 115, No. 1, 1993, pp. 81-88.

[10] D. A. Palma, A. C. Gon?alves and A. S. Martinez, “An Alternative Analytical Formulation for the Voigt Function Applied to Resonant Effects in Nuclear Processes,” Nuclear Instruments & Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 654, No. 1, 2011, pp. 406411. doi:10.1016/j.nima.2011.07.029