CERN Accelerating science

Setup for the measurement of the $^{235}$U(n,f) cross section. Fission events were measured with a Parallel Plate Ionization Chamber and an array of Parallel Plate Avalanche Counters. Recoil protons were detected and identified by three different telescopes, placed at small angles out of the neutron beam.

Geometrical drawing of the multi-stage telescope: the two silicon detectors followed by the four plastic scintillators.

Sample signals produced by the two silicon detectors, shown in blue and red. The signal from the first plastic scintillator is shown in green.

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: : Monte Carlo simulation of a 56 MeV neutron energy beam impinging on a 2-mm thick polyethylene target. Figure~\ref{DEE_54MeV_sili} shows the energy deposited by protons, deuterons, tritons and $\alpha$ in the first silicon detector, $\Delta$E, as a function of the energy deposited in the second silicon detector, E. The $\Delta$E-E matrix~\ref{DEE_54MeV_Scint} shows the energy deposited by protons, deuterons in the first scintillator as a function of the energy deposited by protons and d in the second one.

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: : In the left panel the efficiency is studied through an isotropic proton source placed in the polyethylene sample position. The efficiency thus calculated incorporates the evaluation of the solid angle subtended by the telescope and the effect due to multiple scattering suffered by protons in the target and in the detector itself. In the right panel the fraction of protons detected by the telescope divided by total number of neutrons hitting an hydrogen sample with a thickness and an areal density of 0.384~mm and 0.91~g/cm$^2$ is shown.

: Hydrogen sample

: : $\Delta$E-E matrices are generated by Monte Carlo simulations with a 120-MeV neutron beam. Figure~\ref{fig:DEE_H_120} shows the output of an H sample placed on the neutron beam. The detected protons can only derive from the n-p scattering reaction, in fact all the events are positioned in a narrow region of the matrix. Figure~\ref{fig:DEE_C_120} displays the $\Delta$E-E matrix from the neutron beam hitting a carbon sample. In this case there are two groups of events related to the families of protons and deuterons; the events are distributed throughout the hyperbola without any peak.

Ratio between protons from n+C reactions, normalized to the number of carbon atoms contained in the polyethylene, and the total number of protons recorded when a C$_2$H$_4$ target is placed in the neutron beam. In the region (a), the events in coincidence between the two silicon detectors are shown. In regions (b), (c), and (d), the coincidences between the first two, three and four scintillators are shown, respectively. In each change of configuration, the number of events from the carbon shows a sharp drop, followed by gradual increase with energy.

: Data - C$_2$H$_4$ sample

: MC - C$_2$H$_4$ sample : Data - C sample

: MC - C sample : Data - H

: MC - H : Figures~\ref{fig:DEE_Poli_Dati} and~\ref{fig:DEE_C_Dati} display the $\Delta$E-E matrices produced by the experimental data, choosing the events of neutrons with energy of (74.8\,$\pm$\,2.2)~MeV hitting the 2~mm thick C$_2$H$_4$ and the 1~mm thick C sample, respectively. Figures~\ref{fig:DEE_Poli_MC} and~\ref{fig:DEE_C_MC} show the same $\Delta$E-E matrices but obtained through data from simulations. In each matrix, only the proton hyperbola was selected and the subtraction between the two samples was performed. The one-dimensional histograms in the bottom panels show the result of the subtraction between the two samples for the data, the figure~\ref{fig:H_Dati}, and for the simulations in~\ref{fig:H_MC}.

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The ratios between the different configurations, in the energy range where they overlap, are shown. Taking into account the coincidence between only the first two scintillators, in the energy range between 100 and 160~MeV, the telescope is working in the punch-through condition in fact the protons stop in the third scintillator. The same situation is for the energy range between 160 and 330~MeV requiring the coincidence 1-2-3 instead of coincidence among all the scintillators.

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: : Time difference between two consecutive events recorded by a silicon detector, in figure~\ref{fig:deadtime_sili}, and a plastic telescope scintillator, in figure~\ref{fig:deadtime_sci}.

: Silicon detectors

: Plastic scintillators : Dead time correction calculated with the formula~\ref{formula:deadtime} for the coincidence between the silicon detectors (in parasitic pulse mode), in figure~\ref{fig:deadtime_sili_corr}, and for the different configurations between the plastic scintillators (in dedicated pulse mode), in figure~\ref{fig:deadtime_sci_corr}.

The ratio between the counts recorded in dedicated and the parasitic mode of the PS pulse corrected for the dead time factor.

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: : (Left) Schematic view of the experimental setup with three PPACs and two uranium samples in between. All dimensions are expressed in mm. (Right) Fission detection concept using two PPACs surrounding the target. The fission fragments emitted from the target cross the two detectors.

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: : Characterization of the thickness of the deposited material of one of the samples of $^{235}$U used in the measurement. (Left) $\alpha$ radioactivity from $^{234}$U isotope. (Right) Results of the Coulomb scattering measurement using a 2~MeV proton beam.

: : Characterization of the thickness of the deposited material of one of the samples of $^{235}$U used in the measurement. (Left) $\alpha$ radioactivity from $^{234}$U isotope. (Right) Results of the Coulomb scattering measurement using a 2~MeV proton beam.

: Target 1

: Target 2 : Distribution of the counts relative to cos\,$\theta$, obtained by the four localisation signals, of the two uranium targets, for low neutron energy (E$_n\,<$10~keV). In this energy region, the emission is isotropic, therefore, a 100\% angular efficiency would lead to a constant number of counts as depicted by the horizontal dashed green line.

: Target 1 - 6.3~MeV $<$ $E_n$ $<$ 10~MeV

: Target 1 - 630~MeV $<$ $E_n$ $<$ 1~GeV : Example of angular distribution for $^{235}$U, in two different neutron energy ranges. The green solid line is a result of the fit using the formula~\ref{fit}, the red one is the fit reported in figure~\ref{fig:effi_1}.

Global efficiency calculated taking into account the geometric factor, the fission fragments absorption effect and the angular distribution of the products.