Spectral reconstruction of high-flux GeV gamma rays from pair spectra using hybrid Tikhonov–D’Agostini unfolding

Abstract

High-energy gamma rays are essential probes in nuclear physics and strong-field quantum electrodynamics, yet their spectral characterization remains challenging in the high-flux regime. Although these gamma rays can be detected indirectly via electron-positron pair production, spectral reconstruction requires solving an ill-conditioned inverse problem formulated by the pair spectrum and the response matrix. Here, we present a practical method for spectral reconstruction of high-flux, GeV-scale gamma rays based on positron measurements with a high-Z converter and a magnetic pair spectrometer. The response matrix was constructed from Monte Carlo simulations incorporating the measurement configuration and the procedure used to convert detector signals into positron energy spectra. The resulting inverse problem was solved by combining non-negative Tikhonov regularization with iterative D'Agostini unfolding. Validation using synthetic gamma-ray spectra demonstrated that the reconstruction recovers gamma-ray spectra within uncertainty bands that broaden appropriately as ill-conditioning increases. The framework was further applied to a measured positron spectrum from a Bethe-Heitler pair-production experiment using GeV-scale bremsstrahlung gamma rays from laser-wakefield-accelerated electrons. The reconstructed spectrum showed good agreement with the GEANT4 simulation, with a normalized root-mean-square error of 29% and an absolute photon yield within 14% of the simulated value, consistent with the shot-to-shot charge fluctuation range of the electron beam. The proposed reconstruction framework is applicable to a wide range of high-flux gamma-ray diagnostics and can also be extended to other ill-conditioned reconstruction problems involving strongly overlapping response functions. © 2026 Elsevier Ltd.