Quantum Coherence and Giant Enhancement of Positron Channeling Radiation

TL;DR

This paper presents a quantum-mechanical model of positron channeling radiation in diamond, revealing a giant coherence enhancement factor of 12-31 times over incoherent predictions, with implications for high-intensity gamma-ray sources.

Contribution

The work introduces a quantum coherence model explaining giant enhancement in positron channeling radiation, validated by numerical results and proposing experimental tests.

Findings

Coherent radiation intensity exceeds incoherent results by a factor of 12-31.

All occupied energy levels contribute constructively due to phase synchronization.

The model predicts a nonlinear angular dependence of peak intensity, enabling experimental verification.

Abstract

We present a quantum-mechanical calculation of positron channeling radiation in a planar harmonic potential, explicitly accounting for the interference between transition amplitudes from different transverse energy levels. Because the planar channel potential for positrons in diamond~(110) is well approximated by a parabola, the transverse spectrum is equidistant, $\varepsilon_n = \Omega(n+\tfrac{1}{2})$, and all $n \to n{-}j$ transitions radiate at the same Doppler-shifted frequency. The entry of the positron into the crystal under the sudden approximation creates a Glauber coherent state with population amplitudes $c_n$. Phase synchronization between the $c_n$ and the dipole matrix elements ensures that all occupied levels contribute constructively to the radiation amplitude, giving an intensity $I_{\rm coh} \propto |A_j|^2$ that exceeds the incoherent (Zhevago--Kumakhov) result by a factor $\mathcal{G} = 12\text{--}31$ for positron energies of $4\text{--}14$~GeV in diamond~(110). Numerical results agree with the experimental peak positions of Avakyan \emph{et al.}~\cite{Avakyan1982}. The enhancement is unique to positrons because their nearly harmonic channel potential is not replicated for electrons. We propose a decisive experimental test of the coherent model based on the predicted nonlinear angular dependence of the peak intensity. The transition from $N$- to $N^2$-scaling of the radiated intensity, driven by quantum coherence, opens a route toward high-intensity monochromatic gamma-ray sources for nuclear physics and materials science.