[Paper Review] Channeling, Radiation and Reactions in Crystals at High Energy

V.G. Baryshevsky|arXiv (Cornell University)|Nov 3, 2024

Crystallography and Radiation Phenomena4 citations

TL;DR

This paper presents a comprehensive quantum and classical theory of channeling, radiation, and particle reactions in single crystals at relativistic energies. It models channeled particles as 2D/1D relativistic atoms, deriving spectral and angular distributions of emitted γ-quanta via dipole and quasi-classical approximations, and reveals anomalous Doppler effects, parametric radiation, and interference phenomena, with key results showing enhanced photon emission at specific angles and energy levels due to quantum interference and refractive effects in crystals.

ABSTRACT

Author-made translation of the book published in Russian in 1982. Chapter 1. Channeling of High-Energy Particles in Crystals. Chapter 2. A Channeled Fast Particle as a 2D (1D) Relativistic Atom. Chapter 3. The Foundations of the Theory of $γ$-quanta Emission in Crystals under Channeling Conditions. Chapter 4. The Influence of $γ$-quanta Refraction and Diffraction on Angular and Spectral Characteristics of Radiation Produced by Particles in Crystals. Chapter 5. Classical Theory of Radiation Formation by Particles in a Medium. Chapter 6. Scattering and Radiation in Crystals Exposed to Variable Fields. Chapter 7. Interference of Independently Generated Beams of $γ$-quanta. Chapter 8. Theory of Measurement of Nuclear Reaction Times Using Shadow Effect. Yield of Reactions Induced by High-energy Particles in Crystals. Chapter 9. Spin Rotation and Radiative Self-Polarization of Particles Moving in Bent Crystals. Chapter 10. The Influence of Radiative Transitions on Channeling of Charged Particles in Crystals.

Motivation & Objective

• To develop a unified quantum and classical framework for understanding high-energy particle channeling in single crystals.
• To analyze spontaneous and induced photon emission (γ-quanta) from channeled particles, including spectral, angular, and polarization characteristics.
• To investigate the role of refractive and diffractive effects in modifying radiation patterns and enhancing emission under specific conditions.
• To explore spin dynamics, radiative self-polarization, and particle lifetime effects due to radiation losses in channeling.
• To connect theoretical predictions with observable phenomena such as interference, super-radiation, and shadow effects in nuclear reaction time measurements.

Proposed method

• Formulates the effective periodic potential $ V(\vec{r}) $ using Fourier expansion with reciprocal lattice vectors $ \vec{\tau} $, incorporating Debye-Waller factors and atomic form factors.
• Applies quantum theory of channeling to derive energy-band spectra for electrons and positrons, modeling transverse motion in 1D or 2D potential wells.
• Derives spectral and angular distributions of emitted photons using dipole approximation and quasi-classical approximation, including parametric radiation in Bragg and Laue geometries.
• Introduces complex and anomalous Doppler effects in absorption media by analyzing phase-matching conditions in moving or refractive crystal frames.
• Models radiation from channeled particles in refractive media using modified wave amplitudes $ A_\tau $, with interference between multiple diffraction orders.
• Uses interference theory to analyze coherent emission from independent beams and induced scattering effects, including super-radiation in channeling conditions.

Experimental results

Research questions

• RQ1 How do quantum energy bands of transverse motion in crystals influence the emission spectrum of channeled relativistic particles?
• RQ2 What are the conditions under which anomalous and complex Doppler effects emerge in photon emission from channeled particles in absorbing media?
• RQ3 How does the refractive index of a crystal modify the angular and spectral distribution of parametric radiation from channeled particles?
• RQ4 In what way do interference effects between multiple diffraction orders enhance or suppress photon emission in channeling regimes?
• RQ5 Can the shadow effect in nuclear reactions be used to measure sub-femtosecond reaction times via channeled particle dynamics?

Key findings

• The amplitude of mirror-reflected waves $ A_0 $ in channeling transitions depends on the transverse momentum $ k_{0x} $ and the zone number $ n $, with $ A_0 \to B $ (standard mirror reflection) when $ \beta \gg \theta_L $, the Lindhard angle.
• At $ \beta = 0 $, $ A_0 $ is minimized due to dominance of low-lying transverse energy levels, while $ A_{\tau \neq 0} $ increases due to enhanced $ W_n $-function contributions, leading to observable intensity maxima in reflected particles.
• For glancing angles $ \alpha \sim \vartheta_{cr} $, total mirror reflection occurs at $ \beta > \theta_L $, with $ A_0 \to 1 $, while at $ \beta = 0 $, a minimum in reflected intensity is predicted due to destructive interference.
• Experimental data from Mashkova et al. (1970) on 30 keV Ar+ ions in Cu crystals show good agreement: maximum reflection at $ \alpha = 10-15^\circ, \beta = 0 $, and minimum at $ \alpha = 5^\circ, \beta = 0 $, confirming the theoretical model.
• Surface channeling of electrons and positrons leads to radiative transitions between transverse energy levels, producing detectable photon emission modulated by quantum interference.
• Induced transitions from polarized electromagnetic waves cause particle polarization and lead to quantum modulation of the reflected beam, demonstrating coherent control of channeled particle states.