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Register a new userEvolutions in photoelectric cross section calculations and their validation
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This paper updates and complements a previously published evaluation of computational methods for total and partial cross sections, relevant to modeling the photoelectric effect in Monte Carlo particle transport. It examines calculation methods that have become available since the publication of the previous paper, some of which claim improvements over previous calculations; it tests them with statistical methods against the same sample of experimental data collected for the previous evaluation. No statistically significant improvements are observed with respect to the calculation method identified in the previous paper as the state of the art for the intended purpose, encoded in the EPDL97 data library. Some of the more recent computational methods exhibit significantly lower capability to reproduce experimental measurements than the existing alternatives.
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Several total and partial photoionization cross section calculations, based on both theoretical and empirical approaches, are quantitatively evaluated with statistical analyses using a large collection of experimental data retrieved from the literature to identify the state of the art for modeling the photoelectric effect in Monte Carlo particle transport. Some of the examined cross section models are available in general purpose Monte Carlo systems, while others have been implemented and subjected to validation tests for the first time to estimate whether they could improve the accuracy of particle transport codes. The validation process identifies Scofields 1973 non-relativistic calculations, tabulated in the Evaluated Photon Data Library(EPDL), as the one best reproducing experimental measurements of total cross sections. Specialized total cross section models, some of which derive from more recent calculations, do not provide significant improvements. Scofields non-relativistic calculations are not surpassed regarding the compatibility with experiment of K and L shell photoionization cross sections either, although in a few test cases Ebels parameterization produces more accurate results close to absorption edges. Modifications to Biggs and Lighthills parameterization implemented in Geant4 significantly reduce the accuracy of total cross sections at low energies with respect to its original formulation. The scarcity of suitable experimental data hinders a similar extensive analysis for the simulation of the photoelectron angular distribution, which is limited to a qualitative appraisal.
In Monte Carlo particle transport codes, it is often important to adjust reaction cross sections to reduce the variance of calculations of relatively rare events, in a technique known as non-analogous Monte Carlo. We present the theory and sample code for a Geant4 process which allows the cross section of a G4VDiscreteProcess to be scaled, while adjusting track weights so as to mitigate the effects of altered primary beam depletion induced by the cross section change. This makes it possible to increase the cross section of nuclear reactions by factors exceeding 10^4 (in appropriate cases), without distorting the results of energy deposition calculations or coincidence rates. The procedure is also valid for bias factors less than unity, which is useful, for example, in problems that involve computation of particle penetration deep into a target, such as occurs in atmospheric showers or in shielding.
The assessment of the reliability of Monte Carlo simulations is discussed, with emphasis on uncertainty quantification and the related impact on experimental results. Methods and techniques to account for epistemic uncertainties, i.e. for intrinsic knowledge gaps in physics modeling, are discussed with the support of applications to concrete experimental scenarios. Ongoing projects regarding the investigation of epistemic uncertainties in the Geant4 simulation toolkit are reported.
Calculated fusion-evaporation cross sections from five different codes are compared to experimental data. The present comparison extents over a large range of nuclei and isotopic chains to investigate the evolution of experimental and calculated cross sections. All models more or less overestimate the experimental cross sections. We found reasonable agreement by using the geometrical average of the five model calculations and dividing the average by a factor of 11.2. More refined analyses are made for example for the 100Sn region.
Presently, models for the parameterization of cross sections for nodal diffusion nuclear reactor calculations at different conditions using histories and branches are developed from reactor physics expertise and by trial and error. In this paper we describe the development and application of a novel graph theoretic approach (GTA) to develop the expressions for evaluating the cross sections in a nodal diffusion code. The GTA generalizes existing nodal cross section models into a ``non-orthogonal and extensible dimensional parameter space. Furthermore, it utilizes a rigorous calculus on graphs to formulate partial derivatives. The GTA cross section models can be generated in a number of ways. In our current work we explore a step-wise regression and a complete Taylor series expansion of the parameterized cross sections to develop expressions to evaluate them. To establish proof-of-principle of the GTA, we compare numerical results of GTA generated cross section evaluations with traditional models for canonical PWR case matrices and the AP1000 lattice designs.
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