Machine learning based parametrization of the resolution function for the first experimental area (EAR1) of the n_TOF facility at CERN

TL;DR

The paper tackles the challenge of parametrizing the neutron-beam resolution function, which spans more than 10 orders of magnitude in energy, by employing a neural-network parametrization in the $\lambda$-representation $\mathcal{R}_\lambda(E,\lambda')$. It trains a feedforward network on a dense $E$–$\lambda'$ grid to obtain a smooth, compact model that can be transformed into the time-of-flight ($R_T$) and reconstructed-energy ($R_{\mathcal{E}}$) representations, including smearing due to the proton beam width. A dedicated C++ interface, rf_guide, wraps the trained network, performing normalization, fast smearing via FFT, and efficient transformations to alternate forms; the method is demonstrated on EAR1 Phase-3 data and applied to $^{53}$Cr$(n,\gamma)$ resonances with good agreement. The approach enables rapid reparameterization after changes to the neutron production chain and can be extended to EAR2 by incorporating sample-position as an additional input, offering a practical tool for n_TOF data analyses with preserved normalization and consistent cross-form representations.

Abstract

This study addresses a challenge of parametrizing a resolution function of the neutron beam from the neutron time of flight facility n_TOF at CERN. A difficulty stems from a fact that a resolution function exhibits rather strong variations in shape, over approximately 10 orders of magnitude in neutron energy. In order to avoid a need for a manual identification of the appropriate analytical forms - hindering past attempts at its parametrization - we take advantage of the versatile machine learning techniques. In particular, we parametrize it by training a multilayer feedforward neural network, relying on a key idea that such networks act as the universal approximators. The proof of concept is presented for a resolution function for the first experimental area of the n_TOF facility, from the third phase of its operation. We propose an optimal network structure for a resolution function in question, which is also expected to be optimal or near-optimal for other experimental areas and for different phases of n_TOF operation. In order to reconstruct several resolution function forms in common use from a single parametrized form, we provide a practical tool in the form of a specialized C++ class encapsulating the computationally efficient procedures suited to the task. Specifically, the class allows an application of a user-specified temporal spread of a primary proton beam (from a neutron production process at n_TOF) to a desired resolution function form.

Figures (8)

• Figure 1: Resolution function for the first experimental area (EAR1) of the n_TOF facility from the third phase (Phase-3) of its operation. Top (a): a form $R_T(E,T')$ dependent on the neutron time of flight $T$. Bottom (b): a form $R_{\mathcal{E}}(E,\mathcal{E}')$ dependent on the reconstructed neutron energy $\mathcal{E}$.
• Figure 2: A resolution function $R_\lambda(E,\lambda')$ dependent on the effective neutron moderation length $\lambda$. The top form (a) corresponds to those from Fig. \ref{['RF_tof_etof']}, coming directly from the FLUKA+MNCP simulations of the neutron production and transport. In the later text -- starting with Eq. (\ref{['trans2']}) -- it is denoted as $\mathcal{R}_\lambda$. The bottom form (b), smeared by the proton beam width $\sigma_T=7$ ns, corresponds to the real experimental situation and is later denoted as~$R_\lambda$.
• Figure 3: Neural network structure used for modeling a resolution function of EAR1 from Phase-3 of n_TOF operation. Each fully connected hidden layer consists of 15 neurons. Inputs correspond to $x=\lambda'/\text{(1 cm)}$ and $y=\log_{10}[E/\text{(1 eV)}]$. A single output is $z=\log_{10}[\mathcal{R}_\lambda/(\text{1 cm}^{-1})]$.
• Figure 4: Raw resolution function fitted by a single neural network, at neutron energies of (a) 40 meV, (b) 10 keV and (c) 2 MeV. A raw and fitted function correspond to an instantaneous proton beam irradiating a spallation target. A beam width of $7$ ns does not have a notable effect below 10 keV.
• Figure 5: Selected resonances from the n_TOF measurement of the $^{53}$Cr($n,\gamma$) reaction, compared to the reaction yields based on ENDF/B-VIII.0 data, with of without the resolution function having been applied.