Quantum Coherence and Giant Enhancement of Positron Channeling Radiation

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, ${\epsilon }_n=\mathrm{\Omega }(n+\frac{1}{2})$, 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 $I_{\mathrm{c}\mathrm{o}\mathrm{h}}\propto \mathrm{\mid }{A}_j{\mathrm{\mid }}^2$ 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.