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On the Measurability of True Coincidence Summing in Gamma-Ray Spectroscopy

Liam Schmidt

TL;DR

The paper addresses the measurability limits of correcting true coincidence summing in gamma-ray spectroscopy by generalizing the Semkow Gamma Formalism (SGF) and introducing a multiplicity expansion, along with a Partitioned Gamma Formalism (PGF) for gated probabilities. It derives 180-degree coincidence corrections for singles and gated cases, and quantifies the deviation between these approximations and the full correction via a multiplicity-dependent metric, showing inseparability between summed and 180-degree events that grows with ontic multiplicity. The work provides explicit expressions for summing-out and summing-in corrections, analyzes their limitations, and demonstrates that 180-degree corrections are statistically bounded rather than complete, especially as detector multiplicity increases. Together, these results establish a rigorous framework for evaluating coincidence-summing corrections in both standard and gated gamma-ray analyses, informing uncertainty budgets and guiding future experimental validation across decay schemes.

Abstract

We generalize the summing correction formalism of Semkow et.al 1990 into the Semkow Gamma Formalism and extend it into a multiplicity expansion. We use this formalism to calculate the matrix probabilities for 180 degree coincidence events as a method for correcting coincidence summing, and show the deviation between the full correction and this correction as a function of multiplicity. We further extend this to the Partitioned Gamma Formalism, to calculate probabilities for gated gamma rays; where two gammas of interest are taken in multi-detector coincidence. We look at the summing correction that is involved in the gated gammas and calculate deviations in a manner similar to that done to the singles. We define terms such as measurability and ontic and epistemic events and show that within our definitions, coincidence summing is not sufficiently measurable, or rather, its sufficient measurability is statistically bounded by the deviations we derive.

On the Measurability of True Coincidence Summing in Gamma-Ray Spectroscopy

TL;DR

The paper addresses the measurability limits of correcting true coincidence summing in gamma-ray spectroscopy by generalizing the Semkow Gamma Formalism (SGF) and introducing a multiplicity expansion, along with a Partitioned Gamma Formalism (PGF) for gated probabilities. It derives 180-degree coincidence corrections for singles and gated cases, and quantifies the deviation between these approximations and the full correction via a multiplicity-dependent metric, showing inseparability between summed and 180-degree events that grows with ontic multiplicity. The work provides explicit expressions for summing-out and summing-in corrections, analyzes their limitations, and demonstrates that 180-degree corrections are statistically bounded rather than complete, especially as detector multiplicity increases. Together, these results establish a rigorous framework for evaluating coincidence-summing corrections in both standard and gated gamma-ray analyses, informing uncertainty budgets and guiding future experimental validation across decay schemes.

Abstract

We generalize the summing correction formalism of Semkow et.al 1990 into the Semkow Gamma Formalism and extend it into a multiplicity expansion. We use this formalism to calculate the matrix probabilities for 180 degree coincidence events as a method for correcting coincidence summing, and show the deviation between the full correction and this correction as a function of multiplicity. We further extend this to the Partitioned Gamma Formalism, to calculate probabilities for gated gamma rays; where two gammas of interest are taken in multi-detector coincidence. We look at the summing correction that is involved in the gated gammas and calculate deviations in a manner similar to that done to the singles. We define terms such as measurability and ontic and epistemic events and show that within our definitions, coincidence summing is not sufficiently measurable, or rather, its sufficient measurability is statistically bounded by the deviations we derive.

Paper Structure

This paper contains 15 sections, 66 equations, 3 figures.

Table of Contents

  1. Introduction
  2. History of Summing Corrections
  3. The Ontic-Epistemic Division of Events
  4. Coincidence Summing
  5. Multiplicity Events
  6. Summing Corrections
  7. Summing Out
  8. Summing In
  9. Multiplicity Expansion and Summing Inseparability
  10. Gated Probabilities
  11. Summing Corrections
  12. Summing Out
  13. Summing In
  14. Summing Inseparability
  15. Conclusion

Figures (3)

  • Figure 1: Basic decay scheme for coincidence summing.
  • Figure 2: General decay scheme diagram.SEMKOW1990437
  • Figure 3: Set diagram showing the inseparability of the summing and coincidence events