Analysis of Gamma-Ray Spectra Using Levenberg-Marquardt Method

Levenberg-Marquardt method (LM) was proposed to be applied as a non-linear least-square fitting in the analysis of a natural gamma-ray spectrum that was taken by the Hp (Ge) detector. The Gaussian function that composed of three components, main Gaussian, a step background function and tailing function in the lowenergy side, has been suggested to describe each of the y-ray lines mathematically in the spectrum. The whole spectrum has been analyzed by determining the energy and relative intensity for the strong y-ray lines.

Authors:

• A. H. Fatah
• A. H. Ahmed

Keywords:

• Gamma-Ray
• Spectrum analysis
• Non-linear leastsquare fitting.

References:

[1] G. S. Zahn, Frederico A. Genezini, MaurícioMoralles,, 2009
International Nuclear Atlantic Conference - INAC 2009 Rio de
Janeiro,RJ, Brazil, September27 to October 2, 2009.
[2] R. E. Abdel-Aal, IEEE TRANSACTIONS ON NUCLEAR SCIENCE,
VOL. 45, NO. 1, (1998)1.
[3] P.H.G.M. Hendriks, J. Limburg, R.J. de Meijer, Journal of
Environmental Radioactivity, 53 (2001) 365.
[4] M.A. Mariscotti ,Nucl.Inst.and Methods, 50(1967) 309-320.
[5] R.G. Helmer, R.I. Heath, M. Putnam and D.H. Gipson, Nucl.Inst.and
Methods, 57(1967) 46-57.
[6] J.T. Routti and S.G. Prussin, Nucl.Inst.and Methods, 72(1969) 125-142.
[7] M. Blaauw, Nucl.Inst.and Methods, A333 (1993) 548-552.
[8] A. H. Fattah, JZS, 11(1), Part A( 2008 )9.
[9] Philip R. Bevington, Data Reduction and Error Analysis for the Physical
Sciences, (McGraw-Hill,2003).
[10] P. C. Gregory, Bayesian Logical Data Analysis for the Physical
Sciences, Cambridge University Press (2005).
[11] E. Philip Gill and Walter Murray , Siam J. Numer. Anal., 15,2,(1979)
[12] M. A. Bhatti, Practical Optimization Methods, Springer-Verlag New
York (2000).
[13] W. Murray, Numerical Methods for Unconstrained Optimization,(New
York,1972).
[14] T.A.E.C.Pratt.,Luther.M.L.,Nucl.Inst.andMethods,92(1971)141-157.
[15] Wang Liyu, Appl.Radiat.Isot.,Vol.40,No.7,(1989)575-579.
[16] Ciftcioglu özer, Nucl.Inst.and Methods, 174(1980) 209-220.
[17] Camberra, Technical Refference Mannual 1088, (1988).
[18] K.S. Toth, Nucl.Inst.and Methods, Vol.21, No.4, August (1977).
[19] M.J. Martin, Nucl.Inst.and Methods, Vol.27, No.4, August (1979).
[20] M.R. Schmorak, Nucl.Inst.and Methods, Vol.40, No.1,
September(1983).
[21] M.J. Martin, Nucl.Inst.and Methods, Vol.47, No.4, April (1986).
[22] M.J. Martin, Nucl.Inst.and Methods, Vol.49, No.1, September (1986).