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Gaussian Broadening of MCNP Pulse Height Spectra

Article  in  Transactions of the American Nuclear Society · January 2004

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North Carolina State University

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Gaussian Broadening of MCNP Pulse Height Spectra

W.A. Metwally1, R.P. Gardner1, and Avneet Sood2

1Center for Engineering Applications of Radioisotopes, North Carolina State University,

Raleigh, NC 27695-7909, gardner@ncsu.edu 2Los Alamos National Laboratory, X-5, Diagnostics Applications, Los Alamos, NM 87545,sooda@lanl.gov

A comparison of Monte Carlo calculated and laboratory measured gamma-ray spectra is complicated by the fact that physical radiation detectors have finite resolution. The measured spectra for a mono-energetic photon source will appear as a broadened peak at the source energy. The shape of this peak is approximately Gaussian with the center at the source energy and a width characteristic of the specific detector. A typical example of this is the spectrum resulting from the mono-energetic Cs-137 radioactive source that emits a gamma ray with an energy of 0.662 MeV. Such a spectrum is shown in figure (1) for a 3”x3” NaI detector [1]. For simulated spectra, the calculated peak will also appear at the source energy, but a single value will be calculated and placed in a tally bin without any broadening. This complication extends to the rest of the photon spectra with considerable statistical fluctuation exhibited in the rest of the spectrum. A solution to this is to modify the calculated spectra to account for the peak broadening.

Figure 1: A typical Cs-137 spectrum [1]

One of the most commonly used radiation transport codes is MCNP. In MCNP [2], the peak broadening is dealt with by changing the energy of the particle during the Monte Carlo simulation just before it is tallied by randomly sampling an energy to be deposited from a Gaussian distribution centered at the original particle energy. The user includes the width of the

Gaussian distribution as an input to the Monte Carlo code. This procedure produces a Gaussian distribution of energies for monoenergetic particles and is included as a special treatment for tallies in MCNP. The tallied energy is broadened by sampling from a Gaussian distribution. The desired Full Width at Half Maximum (FWHM) is specified as follows:

FWHM = a + b (E + c E2)(1/2) (1)

where E is the gamma-ray energy in MeV, and a, b, and c are user-provided constants. The FWHM is related to the Gaussian standard deviation σ by: FWHM = 2.35 σ (2) This approach, while accurate in the limit of a large number of histories, does not take full advantage of the natural smoothing effect of Gaussian broadening. The authors were aware that considerable improvement in the resulting broadened spectrum can be achieved if the broadening process is performed at the end of the simulation [3] as opposed to performing it history by history, which is the current procedure in MCNP. The detector resolution would be specified in terms of the standard deviation of a Gaussian distribution. The standard deviation is given by the power-law form:

σ = d Ee (3) Where σ is the standard deviation in MeV, E is the gamma-ray energy in MeV, and d and e are empirical constants. The broadened spectrum is obtained by spreading the detector response function model with a Gaussian distribution that has this form of the standard deviation. To compare these two approaches, a Cs-137 source was placed 10 cm away from the face of a bare 3”x3” NaI detector. Three cases were run using MCNP, two of which were with MCNP Gaussian broadening for 100 and 1 million histories. The third case was without the

MCNP Gaussian broadening for 1 million histories. The resulting spectrum from the third case was then broadened at the end of the simulation using a Gaussian distribution that has a standard deviation of the form in equation (3). The constants used in equations 2 and 3 were a=0.0, b=0.05086, c=0.30486, d=0.02529, and e=0.65934. The resulting three spectra are shown in the upper part of figure (2). When performing a least squares fitting between the MCNP 100 million histories and our 1 million histories spectra, the reduced chi-square was 2.5. When performing the same fitting between the MCNP broadened spectra the reduced chi-square was 99. The lower part of figure (2) shows the normalized residuals. The horizontal lines in the middle and lower part of figure (2) correspond to the 3σ limits, between which 97% and 29% of the points fall, respectively.

Figure 2: Comparison of the MCNP and our

broadened spectrum.

To conclude, an approach has been presented to replace the commonly used MCNP pulse height spectral broadening approach [4]. This approach can reduce the total number of histories of the simulation by up to two orders of magnitude. This has the effect of tremendously reducing computation time while still yielding essentially the same results as the broadened pulse height spectra using the MCNP approach.

REFERENCES 1. Heath, R.L., 1964, ``Scintillation

Spectrometry Gamma-Ray Spectrum Catalogue,'' IDO-16880-1. AEC Research and Development Report, Physics, TID-4500.

2. 'MCNP - A General Monte Carlo N-Particle Transport Code, Version 5, Volume I: Overview and Theory, ‘Vol. 1 LA-UR-03-1987 (2003).

3. Gardner, Robin P. and Avneet Sood, “A Monte Carlo Simulation Approach for Generating NaI Detector Response Functions (DRF's) that Accounts for Nonlinearity and Variable Flat Continua", Nuclear Instruments and Methods B, 213 pp. 87-99, 2004.

4. Chen, Jianwei, Ayman I. Hawari, Zhongxiang Zhao, and Bingjing Su, “Gamma-ray Spectrometry Analysis of Pebble Bed Reactor Fuel Using Monte Carlo Simulation”, Nuclear Instruments and Methods A, 505 pp. 393-396, 2003.

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