High-Energy Interference Effect of Bremsstrahlung and Pair Production in Crystals

With the use of monocrystalline targets for bremsstrahlung and pair production experiments, interference phenomena are expected to occur which will markedly change the $\gamma$-ray spectrum as well as the pair energy distribution, for certain angles giving enhancement of radiation and pairs. The effect increases with energy; it sets in at $\delta \lesssim n_0\left(\frac{2\pi }{a}\right)$, where $\delta$ is the minimum momentum transfer to the target atoms, $a$ the lattice constant, and $n_0$ a number of the order 2 or 3. This corresponds to ∼200-Mev primary energy for bremsstrahlung, ∼1 Bev for pair production. The effect is confined to angles between the primary beam and a line of atoms, of order $\theta \lesssim \left(\frac{a_{\mathrm{screen}}}{{\lambda }_C}\right)\left(\frac{m{c}^2}{E}\right)$. The temperature motion of the lattice reduces the interference effect to some extent. The Born approximation was used for the quantitative analysis of the problem.