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Experimental verification of theoretical uncertainties in non-linear least-squares analysis of gamma spectra

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Abstract

Typically, gamma spectra are analyzed by fitting individual peaks. In an entirely different approach to analysis of gamma spectra, non-linear least-squares methods have been applied in a program known as VRF to fitting gamma spectra taken as single, self-consistent sets of data. According to theory, uncertainties from non-linear least-squares fitting are obtained directly from the inverse of the second-derivative matrix. There remains a need to independently verify theoretical uncertainties as implemented in VRF. We report results of a numerical experiment in which uncertainties derived from analysis of a large number of spectra are compared to theortical uncertainties from VRF.

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References

  1. Levenberg K (1944) A Method for the Solution of Certain Non-Linear Problems in Least Squares. Q Appl Math 2:164–168

    Article  Google Scholar 

  2. Marquardt D (1963) An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J Soc Ind Appl Math 11:431–441

    Article  Google Scholar 

  3. Bevington P, Robinson K (2003) Data Reduction and Error Analysis for the Physical Sciences, 3rd edn. McGraw-Hill, New York

    Google Scholar 

  4. Coldwell R, Bamford G (1991) The theory and operation of spectral analysis using ROBFlT. American Institute of Physics, New York

    Google Scholar 

  5. Currie A (1968) Limits for Qualitative Detection and Quantitative Determination: Application to Radiochemistry. Anal Chem 40:586–593

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Snakedance Scientific, 13509 Quaking Aspen Pl, 87111, Albuquerque, NM, USA

    George P. Lasché

  2. Radiation Safety Engineering, 3245 N Washington St, 85225, Chandler, AZ, USA

    Robert L. Metzger

Authors
  1. George P. Lasché
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  2. Robert L. Metzger
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Correspondence to George P. Lasché.

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Lasché, G.P., Metzger, R.L. Experimental verification of theoretical uncertainties in non-linear least-squares analysis of gamma spectra. J Radioanal Nucl Chem 331, 5047–5051 (2022). https://doi.org/10.1007/s10967-022-08459-y

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  • DOI: https://doi.org/10.1007/s10967-022-08459-y

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