Quantum Coherence and Giant Enhancement of Positron Channeling Radiation

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, $\varepsilon_n = Ω(n+\tfrac{1}{2})$, 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.

Figures (3)

• Figure 1: Level population $P_n = |c_n|^2$ vs entrance angle $\theta_{\rm in}$ and quantum number $n$ for $E=10$ GeV in diamond (110) ($\theta_{\rm L}\approx 68\;\mu$rad). The Poisson distribution shifts toward higher $n$ as $\theta_{\rm in}$ increases, increasing the number of coherently contributing levels and hence the enhancement $\mathcal{G}$.
• Figure 2: First-harmonic spectral intensity for $E = 4, 6, 10$, and $14$ GeV in diamond (110), computed at $\theta_{\rm in}=31\;\mu$rad. Red solid: coherent model (Eq. \ref{['eq:Icoh']}). Blue dashed: incoherent model (Eq. \ref{['eq:incoh']}). The enhancement factors $\mathcal{G}$ are shown above each panel. Peak positions agree with the SLAC experimental values of Avakyan et al.Avakyan1982.
• Figure 3: Enhancement factor $\mathcal{G}(\theta_{\rm in}/\theta_{\rm L})$ for $E = 4, 6, 10$, and $14$ GeV in diamond (110), computed at each energy up to $0.85\,\theta_{\rm L}$. At small angles $\mathcal{G} \propto \theta_{\rm in}^2$ (grey dashed reference), confirming the analytic estimate $\mathcal{G} \approx n_0 = \tfrac{1}{2}(\theta_{\rm in}/\theta_{\rm L})^2 \cdot(V_0/\Omega)$. The incoherent model gives $\mathcal{G}\equiv 1$ (not shown). The quadratic growth with $\theta_{\rm in}$ is the key experimental signature of the coherent mechanism (see the Experimental Test section below).