Strong Enhancement of Electromagnetic Shower Development in Oriented Scintillating Crystals and Implications for Particle Detectors

Abstract

A particle traversing a crystal aligned with one of its crystallographic axes experiences a strong electromagnetic field that is constant along the direction of motion over macroscopic distances. For $e^\pm$ and $γ$-rays with energies above a few $\mathrm{GeV}$, this field is amplified by the Lorentz boost, to the point of exceeding the Schwinger critical field $\mathcal{E}_0 \sim 1.32 \times 10^{16}~\mathrm{V/cm}$. In this regime, nonlinear quantum-electrodynamical effects occur, such as the enhancement of intense electromagnetic radiation emission and pair production, so that the electromagnetic shower development is accelerated and the effective shower length is reduced compared to amorphous materials. We have investigated this phenomenon in lead tungstate (PbWO$_4$), a high-$Z$ scintillator widely used in particle detection. We have observed a substantial increase in scintillation light at small incidence angles with respect to the main lattice axes. Measurements with $120$-$\mathrm{GeV}$ electrons and $γ$-rays between $5$ and $100~\mathrm{GeV}$ demonstrate up to a threefold increase in energy deposition in oriented samples. These findings challenge the current models of shower development in crystal scintillators and could guide the development of next-generation accelerator- and space-borne detectors.

Figures (6)

• Figure 1: Average continuous axial potential felt by $e^{+}$ (opposite sign for $e^{-}$) for two of the main PbWO$_4$ axes as a function of the distance in transverse direction from the atomic string. The corresponding crystal structure is shown in the insert.
• Figure 2: Scheme of the experimental setup in various configurations---optimized for thin crystal alignment (top), for enhanced hermeticity (center) and for measurements with tagged photons (bottom).
• Figure 3: Experimental measurement with $120~\mathrm{GeV}$ electrons in the $4.6~X_0$ PbWO$_4$ sample: (a) distribution of the deposited energy, $E_{\mathrm{dep}}$, in the crystal in randomly oriented and axial configurations, and corresponding simulated (dashed) curves; (b)$E_{\mathrm{dep}}$ as a function of the angle between the beam and the axial direction, $\theta_{\text{mis}}$; (c) corresponding energy deposited in the calorimeter positioned downstream of the crystal, $E_{\mathrm{CAL}}$, as a function of $\theta_{\text{mis}}$. The vivid part of the contour plot corresponds to the experimental data; the shaded part to a linear interpolation between Delaunay triangles calculated from the available data. The green squares indicate the mean values at different angles. The point on the $x$-axis corresponding to the randomly oriented configuration ($\sim 50~\mathrm{mrad}$) is not to scale.
• Figure 4: Measurements on the $1~X_0$ sample. Left: $E_{\mathrm{dep}}$ by $120~\mathrm{GeV}$ electrons as a function of $\theta_{\text{mis}}$. The vivid part of the contour plot corresponds to the experimental data; the shaded part to a linear interpolation between Delaunay triangles calculated from the available data. The green squares indicate the mean values at different angles. The angle corresponding to the randomly oriented configuration ($\sim$$50~\mathrm{mrad}$) is not to scale. Right: Mean $E_{\mathrm{dep}}$ by photons as a function of their energy, at different values of $\theta_{\text{mis}}$. Curves from the corresponding simulations (dashed lines) and extrapolations to $120~\mathrm{GeV}$ (squares) are also shown for the randomly oriented and axial cases. The extrapolations have been computed by fitting the experimental data to a logarithmic function.
• Figure 5: Measurements performed with the $120~\mathrm{GeV}$ electron beam as a function of the crystal thickness. (a) Mean $E_{\mathrm{dep}}$ in axial and random alignment. (b) Difference between $E_{\mathrm{dep}}^{\mathrm{rnd}}$ and $E_{\mathrm{dep}}^{\mathrm{ax}}$ normalized to the beam energy. (c) Ratio between $E_{\mathrm{dep}}^{\mathrm{rnd}}$ and $E_{\mathrm{dep}}^{\mathrm{ax}}$. The solid curves were obtained with simulations.