Applying Gaussian Mixture Models to Track Reconstruction in Inelastic Scattering Experiments with Active Targets

TL;DR

Reconstructing low-energy recoil tracks in active-target detectors is challenging due to overlapping beam and ejectile trajectories. The authors combine DBSCAN clustering with a Gaussian Mixture Model (GMM) approach, selecting the number of components K via BIC and regularizing clusters using Mahalanobis-distance-based p-values and continuity metrics. The results show that GMM-based reconstruction improves accuracy, precision, and efficiency for short, small-angle tracks and remains competitive at larger angles compared to the RANSAC baseline, with enhanced handling of attenuation-zone voxels. This probabilistic framework enhances kinematic extraction in active-target experiments and paves the way for extension to higher-multiplicity events and real data analysis.

Abstract

Active targets such as ACTAR TPC are well suited for studying giant resonances in unstable nuclei via inelastic scattering in inverse kinematics. A key challenge in such measurements is the detection of low-energy ejectiles emitted at small angles relative to the beam direction. Accurate reconstruction of these tracks is essential for disentangling different resonance modes. Probabilistic models such as the Gaussian Mixture Model (GMM) are particularly effective in capturing the complex covariance structures characteristic of the beam-recoil interface in narrow-angle events. In this work, we present a track reconstruction approach based on the GMM, specifically designed for inelastic scattering experiments with active targets. Special emphasis is placed on the treatment of low-energy tracks. The proposed method is demonstrated on simulated data of the $^{58}\mathrm{Ni}(α,α')^{58}\mathrm{Ni}$ reaction at an incident energy of $E=49$~MeV/nucleon, generated under conditions representative of the experiment carried out at GANIL for the same reaction.

Figures (12)

• Figure 1: Example event recorded with ACTAR TPC for ^58Ni($\alpha$,$\alpha^\prime$)^58Ni. The beam enters the active volume -- a cubic chamber of dimensions $256 \times 256 \times 256$ mm$^3$ -- at $X = 0$ mm, $Y = 128$ mm, $Z = 128$ mm. The segmented pad plane is located in the $XY$ plane at $Z = 256$ mm. The $Z$ coordinate corresponds to the electron drift time to the segmented plane; values are in arbitrary units.
• Figure 2: An event from the experimental data of the ^58Ni($\alpha$,$\alpha^\prime$)^58Ni reaction, as recorded in ACTAR TPC. (a) Cluster identified using the DBSCAN algorithm is shown in blue, excluded voxels are shown in red (only one cluster is identified in this event); (b) Fifth Nearest neighbour distance $d_\mathrm{NN}$ in mm (sorted), measured for each voxel $i$ recorded in the event; (c) Evaluation of the normalized Bayesian Information Criterion (BIC) score $B(K)$ as a function of the number of components $K$; (d), (e), and (f): respectively $XY$, $YZ$, and $XZ$ projections of the $K=4$ clusters identified using the GMM; each color correspond to a single identified component $k$. We recognize the beam track, identified as two separate tracks (purple and yellow) by the GMM, and two scattered tracks.
• Figure 3: Assignment of posterior probabilities $\gamma_{ki}$ of voxels $i$ to one component $k$ --- the blue component in (c) and (f) --- in successive iterations. (a) projection of voxels $i$ on the $XY$ plane, color-coded by their probabilistic assignment $\gamma_{ki}$: red are excluded voxels ($\gamma_{ki}$ = 0), green are assigned voxels ($\gamma_{ki}$ = 1), pink are "soft-assigned" voxels ($0 < \gamma_{ki} < 1$). The black cross marks the assigned mean vector $\bm{\upmu_k}$ and the number is the prior $\pi_k$; (b) posterior probabilities ($\gamma_{ki}$) for each voxel $i$; (c) identified color-coded components; (d), (e), (f): same as (a), (b), (c) but for the successive iteration.
• Figure 4: Clusters from a ^58Ni($\alpha$,$\alpha^\prime$)^58Ni event recorded in ACTAR TPC, color-coded by their component $k$. (a) Assigned components by GMM; (b),(c) Re-assignment after a certain number of iterations; (d) Assigned components after regularization.
• Figure 5: Relative frequency of the pairwise metric $p_{kl}$ computed between all distinct pairs of predicted GMM tracks $K$ in an event, for the entire simulated data set. Three categories of the metric are shown: Beam-Beam Metric $p_{kl}^{(BB)}$, Ejectile-Ejectile Metric $p_{kl}^{(EE)}$, Beam-Ejectile Metric $p_{kl}^{(BE)}$.