Validation of spallation models for p+Al reactions at 180 MeV incident proton beam energy

Various observables measured at low beam energy of 180 MeV for proton induced reactions on 27Al targets have been compared with theoretical predictions of different spallation models. These models assume that the reactions proceed in two stages: the intranuclear cascade of nucleon–nucleon collisions followed by the de-excitation of equilibrated, excited remnants of the cascade. The calculations of the intranuclear cascade were performed by means of the INCL4.6 code, whereas the second stage of the reactions was realized using four different models: ABLA07, GEMINI++, GEM2, and SMM. It was found that the main properties of the experimental isobaric total production cross sections are reasonably well reproduced by all these spallation models. The shape of the energy averaged angular distributions of ejectiles with A = 7, 12, 16, 22, 24, and 25 was also well described by the models listed above, however the absolute magnitude of A = 7 and A = 25 data is strongly underestimated and overestimated, respectively. The theoretical energy spectra for A = 7, A = 16, and A = 22 are very similar for all the models and reproduce well the data for heavier ejectiles, whereas the A = 7 data deviate from the model cross sections for energies smaller than ≈ 10 MeV what may indicate the presence of a reaction mechanism not included in the spallation models. The following ranking of the four used models — all of them being coupled to the very same INCL4.6 INC model — was determined using the statistical H-test in a quantitative analysis: (1) GEMINI++, (2) SMM, (3) ABLA07, and (4) GEM2

Ranking and validation of spallation models for isotopic production cross sections of heavy residua

The production cross sections of isotopically identified residual nuclei of spallation reactions induced by ^{136}Xe projectiles at 500AMeV on hydrogen target were analyzed in a two-step model. The first stage of the reaction was described by the INCL4.6 model of an intranuclear cascade of nucleon-nucleon and pion-nucleon collisions whereas the second stage was analyzed by means of four different models; ABLA07, GEM2, GEMINI++ and SMM. The quality of the data description was judged quantitatively using two statistical deviation factors; the H-factor and the M-factor. It was found that the present analysis leads to a different ranking of models as compared to that obtained from the qualitative inspection of the data reproduction. The disagreement was caused by sensitivity of the deviation factors to large statistical errors present in some of the data. A new deviation factor, the A factor, was proposed, that is not sensitive to the statistical errors of the cross sections. The quantitative ranking of models performed using the A-factor agreed well with the qualitative analysis of the data. It was concluded that using the deviation factors weighted by statistical errors may lead to erroneous conclusions in the case when the data cover a large range of values. The quality of data reproduction by the theoretical models is discussed. Some systematic deviations of the theoretical predictions from the experimental results are observed

The predictive power of spallation models for isotopic cross sections

The experimental cross sections of isotopically identified products of spallation reactions induced by 136Xe projectiles at 1GeV/nucleon on hydrogen target were compared with predictions of a two-step model. The first stage of the reaction was described by the INCL++ model (version 5.3) of an intranuclear cascade of nucleon-nucleon and pion-nucleon collisions whereas the second stage was analyzed by means of four different models; ABLA07, GEM2, GEMINI ++ and SMM. Due to the fact that the experimental data cover a very broad range of elements; from Li$(Z=3)$ to Ba$(Z=56)$ , the analysis could impose severe constraints on the applied reaction models. The quality of data reproduction by the theoretical models is discussed. Some systematic deviations of the theoretical predictions from the experimental results are observed

Ranking and validation of the spallation models for description of intermediate mass fragment emission from p + Ag collisions at 480 MeV incident proton beam energy

Double-differential cross-sections $d^{2}\sigma/d\Omega dE$ for isotopically identified intermediate mass fragments ( 6Li up to 27Mg from nuclear reactions induced by 480 MeV protons impinging on a silver target were analyzed in the frame of a two-step model. The first step of the reaction was described by the intranuclear cascade model INCL4.6 and the second one by four different models (ABLA07,GEM2, GEMINI++, and SMM). The experimental spectra reveal the presence of low-energy, isotropic as well as high-energy, forward-peaked contributions. The INCL4.6 model offers a possibility to describe the latter contribution for light intermediate mass fragments by coalescence of the emitted nucleons. The qualitative agreement of the model predictions with the data was observed but the high-energy tails of the spectra were significantly overestimated. The shape of the isotropic part of the spectra was reproduced by all four models. The GEM2 model strongly underestimated the value of the cross-sections for heavier IMF whereas the SMM and ABLA07 models generally overestimated the data. The best quantitative description of the data was offered by GEMINI++, however, a discrepancy between the data and the model cross-sections still remained for almost all reaction products, especially at forward angles. It indicates that non-equilibrium processes are present which cannot be reproduced by the applied models. The goodness of the data description was judged quantitatively using two statistical deviation factors, the H-factor and the M-factor, as a tool for ranking and validation of the theoretical models

Ein Beitrag zur Interpretation von reaktorphysikalischen Experimenten mit Hilfe von Spline-Funktionen

Different procedures for approximation and Interpolation by using natural splines are studied and their applicability in analysis and curve fitting in experiments an reactor physics are shown. Using the definition of the natural spline function and its representation by B-splines in the firnt part of this report solutions of data fitting by a Lagrange variational problem and by least squares approximation are derived. The numerical problems arising from the solution of the linear systems of equations by fitting experimental data are well conditioned. In the second part the applications of fitting procedures are demonstrated. The analysis of dynamic transit reactivity measurements of simulated THTR pebbies in a critical facility are shown. The fissile content of the pebbles can be determined with minimum reproducibility. Calculations of photopeak pararneters of $\gamma$-spectra and the evaluation of physical reactor parameters from noise measurements, e. g. of the prompt decay constant, give good results using the spline fitting methods

The PISA Experiment : Spallation Products Identified by Bragg Curve Spectroscopy

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