Abstract
The coherent process of particle deflection by aligned atomic strings and planes of oriented crystals is accompanied by incoherent scattering by atomic cores. While the coherent particle deflection, described by the axial or planar averaged potential, becomes more and more classical at high energies, the incoherent scattering of relativistic particles remains essentially quantum. Though the incoherent scattering of relativistic particles in crystals reminds the scattering by atoms of an amorphous medium at a large momentum transfer, at small ones the incoherent scattering process in crystals is modified by the influence of the inhomogeneity of the atom distribution in the plane normal to the crystal axis or plane. We present a theory of incoherent scattering of high energy particles in oriented crystals, which takes into consideration both its quantum nature and the impact of the atom distribution inhomogeneity. The axial case is considered as a more general example. The way to incorporate the revealed quantum features into classical trajectory simulations is also outlined.
Highlights
High energy particle interaction with oriented crystals makes it possible to both observe many remarkable phenomena and apply them to develop diverse sources of x and gamma radiation [1,2,3], to efficiently deflect high energy particle beams [4,5,6], to measure and even to modify elementary particle properties, such as magnetic momenta [1], and to reduce the thickness of particle detectors as well as to make the latter sensitive to both the direction and polarization [7,8,9,10]
All the pronounced effects, induced by the coherent particle interaction with an oriented crystal lattice, are described by the averaged potential of atomic strings or planes [11,12] introduced by Lindhard, who proved that the particle motion in the averaged potential can be treated classically at a high enough energy
We reveal that the strong enough inhomogeneity of the string atom nuclei distribution in the plane of transverse particle motion results in the impossibility to introduce a local scattering probability for the small angles and, to preserve the classical trajectory simulations, suggest to apply the newly introduced mean scattering angles
Summary
High energy particle interaction with oriented crystals makes it possible to both observe many remarkable phenomena and apply them to develop diverse sources of x and gamma radiation [1,2,3], to efficiently deflect high energy particle beams [4,5,6], to measure and even to modify elementary particle properties, such as magnetic momenta [1], and to reduce the thickness of particle detectors as well as to make the latter sensitive to both the direction and polarization [7,8,9,10]. This way, a fundamental problem of treating quantum effects in the incoherent scattering of high energy particles, moving along classical trajectories in the averaged crystal potential, arises. The uniform flux approximation, loses its applicability, making it necessary to describe incoherent particle scattering at each point individually, taking into consideration the behavior of the nuclear density at reaching R > u1 distances from the trajectory This problem is readily solved by the quantum treatment of transverse particle motion [25,26], being, both really necessary and practically feasible only at the electron and positron energies of a few dozen MeV and less. Considerable attention is paid to the interrelation of single and multiple scattering processes, quite differently treated for decades
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