TDCRPy 0.0.27

TDCR model

TDCRPy

TDCRPy is a Python code to calculate detection efficiency of a liquide scintillation counter using 3-photomultiplier tubes. The calculation is based on the photo-physical model called of the Triple-to-Double-Coincidence-Ratio method (TDCR) [1] and a Monte-Carlo sampling allowing to adress complexe decay schemes and radionuclide mixtures. The process is summarized in the figure below.

Nuclear decay

The code directly reads decay data from the Decay Data Evaluation Project (DDEP) web interface [2] that is recommanded to be used by the radionuclide metrology community. The PenNuc format [3] is used to simulate decays and the $\beta$ spectra from the BetaShape code [4] are used. The BetaShape code estimates accurate $\beta$ spectra by taking the atomic exchange effect and also simulate accurately electron capture decay [5]. It has been demonstrated to offer significant improvement in the context of liquid scintillation counting [6].

Atomic relaxation

The atomic relaxation from missing electrons in the inner-shell following electron capture and internal conversion is simulated by ENSDF data on the DDEP web interface.

Interaction

The interaction of $\gamma$ rays, electrons and positrons are simulated using response kernels calculated by the Monte-Carlo code MCNP6 developped by Los Alamos [13].

Scintillation

The stopping power of electrons between 20 keV and 1000 keV is a mixture of a radiative loss model [7] and a collision model [8] that has been validated agaisnt the NIST model ESTAR [9] recommanded by the ICRU Report 37 [10]. At low energy - between 10 eV and 20 keV - the model from Tan and Xia [11] is implemented.

The stopping power of $\alpha$ particles of energy comprises between 1 keV and 8 MeV comes from the NIST code ASTAR [9] recommanded in the ICRU Report 49 [12]. For energy below 1 keV, an extrapolation is made.

Statistical model

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References

[1] Ryszard Broda, Krzysztof Pochwalski, Tomasz Radoszewski, Calculation of liquid-scintillation detector efficiency, Applied Radiation and Isotopes 39:2, 1988, 159-164, https://doi.org/10.1016/0883-2889(88)90161-X

[2] http://www.lnhb.fr/ddep_wg/

[3] E. García-Toraño, V. Peyres, F. Salvat, PenNuc: Monte Carlo simulation of the decay of radionuclides, Computer Physics Communications 245, 2019, 106849 https://doi.org/10.1016/j.cpc.2019.08.002

[4] X. Mougeot, Erratum: Reliability of usual assumptions in the calculation of $\beta$ and $\bar{\mu}$ spectra, Physical Review C 91, 2015, 055504, https://doi.org/10.1103/PhysRevC.92.059902

[5] X. Mougeot, Towards high-precision calculation of electron capture decays, Applied Radiation and Isotopes 154, 2019, 108884, https://doi.org/10.1016/j.apradiso.2019.108884

[6] K. Kossert, X. Mougeot, Improved activity standardization of ⁹⁰Sr/⁹⁰Y by means of liquid scintillation counting, Applied Radiation and Isotopes 168, 2021, 109478, https://doi.org/10.1016/j.apradiso.2020.109478

[7] S.M. Seltzer, M.R. Berger, M. R., Evaluation of the collision stopping power of elements and compounds for electrons and positrons, Applied Radiation and Isotopes 33:11, 1982, 1189-1218, https://doi.org/10.1016/0020-708x(82)90244-7

[8] M.O. El-Ghossain, Calculations Of Stopping Power, And Range Of Electrons Interaction With Different Material And Human Body Parts, International Journal of Scientific & Technology Research 6:1 2017. https://www.ijstr.org/final-print/jan2017/Calculations-Of-Stopping-Power-And-Range-Of-Electrons-Interaction-With-Different-Material-And-Human-Body-Parts.pdf

[9] M.J. Berger, J.S. Coursey, M.A. Zucker and J. Chang,Stopping-Power & Range Tables for Electrons, Protons, and Helium Ions, NIST Standard Reference Database 124, 2017, https://dx.doi.org/10.18434/T4NC7P

[10] ICRU Report 37, Stopping Powers for Electrons and Positrons

[11] Z. Tan, Y. Xia, Stopping power and mean free path for low-energy electrons in ten scintillators over energy range of 20–20,000 eV, Applied Radiation and Isotopes 70, 2012, 296-300, https://doi.org/10.1016/j.apradiso.2011.08.012

[12] ICRU Report 49, Stopping Power and Ranges for Protons and Alpha Particles, https://www.icru.org/report/stopping-power-and-ranges-for-protons-and-alpha-particles-report-49/

[13] https://mcnp.lanl.gov/