(or shadow effect), the occurrence of characteristic intensity minima, or shadows, in the angular distribution of particles emanating from the lattice sites of a single crystal. The blocking effect is observed for positively charged heavy particles (protons, deuterons, and heavier ions). The shadows form in the directions of the crystallographic axes and planes.

Figure 1. Origin of the blocking effect

The appearance of a shadow in the direction of a crystallographic axis (an axial shadow) is caused by the deflection of particles originally traveling in the direction of the axis by the intra-atomic electric field of the atoms that are closest to the emitting site and are located in the same row (Figure 1). The distribution of the relative particle intensity γ in the shadow region is illustrated in Figure 2. The angular dimensions of the shadow are determined by the relation , where 2x₀ is the halfwidth of the shadow, eZ₁, is the charge of the moving particle, E is the energy of the moving particle, eZ₂ is the nuclear charge of the crystal atom, and l is the distance between neighboring atoms in the row. The intensity γ of the particle flux in the center of the

Figure 2. Angular distribution of the intensity of the flux of particles emanating from a crystal in the blocking effect

shadow for a perfect crystal, that is, a crystal without imperfections, is approximately one one-hundredth of that at the periphery.

The blocking effect was discovered in 1964 independently by A. F. Tulinov of the USSR and by B. Domeij and K. Björkqvist of Sweden. The particle beams in which the shadows were observed were of different origins. In Tulinov’s experiments the particles were products of nuclear reactions in the nuclei of the crystalline target under the action of accelerated particles. Domeij and Björkqvist introduced alpha-emitting nuclei into the crystal lattice sites by the ion implantation method and observed shadows in the angular distribution of the alpha particles emitted from the crystal. The first method was found to be more general, and it was used for virtually all subsequent experiments. In particular, this method made possible the observation of plane shadows—that is, regions of decreased particle intensity having the form of straight lines and lying in the directions of crystallographic planes. In recording plane shadows, nuclear emulsions are often used as the detector, since they permit the recording of a shadow pattern within a large solid angle. A complicated shadow pattern is formed on the emulsion.

The location of the spots and lines on a shadow pattern depends on the structure of the crystal and geometric conditions of the experiment. The intensity distribution within an individual axial or plane shadow is determined by many factors, including the composition and structure of the crystal, the type and energy of the moving particles, the temperature of the crystal, and the number of crystal defects. The spots and lines on the shadow pattern are of a fundamentally different nature from the spots and lines obtained when a crystal is studied by diffraction methods. Because of the small de Broglie wavelength of heavy particles, diffraction phenomena have virtually no effect on shadow formation.

The blocking effect is made use of in nuclear and solid-state physics. A method for measuring the duration τ of a nuclear reaction in the range 10^–16–10^–18 sec has been developed on the basis of the blocking effect. Information on the value of τ is extracted from the shape of the shadows in the angular distributions of charged nuclear-reaction products, since the shape is determined by the displacement of the compound nucleus from the lattice site during the lifetime of the nucleus. In solid-state physics, the shadow effect is made use of in studying the structure of crystals and the distribution of impurity atoms and defects. Methods based on the shadow effect are especially effective in studying thin single-crystal layers of a substance (10–1,000 angstroms).

The shadow effect belongs to the group of orientation phenomena arising in the interaction of particles with crystals. Another orientation phenomenon is the channeling of charged particles.