Angular distribution of ions axially channeled in a very thin crystal: Experimental and theoretical results

Krause, H. F.; Barrett, J.H.; Datz, S.; Dittner, P.F.; Jones, N. L.; Campo, J. Gómez del; Vane, C. R.

doi:10.1103/physreva.49.283

Cited by 75 publications

(30 citation statements)

References 24 publications

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“…The parameters of the ZBL potential as well as of the M(a F ) potential were determined to make them accurate dominantly for small ion-atom distances. In analyzing their experimental results, Krause et al [20] concluded that they were better reproduced by the Molière's potential with the Thomas-Fermi screening radius, being a TF = 9p 2 =128 À Á 1=3 =Z 1=3 2 a 0 , than by the M(a F ) potential. We denote it as the M(a TF ) potential.…”

Section: Interaction Potentialsmentioning

confidence: 95%

See 1 more Smart Citation

Proton–silicon interaction potential extracted from high-resolution measurements of crystal rainbows

Petrović

Nešković

Ćosić

et al. 2015

Nuclear Instruments and Methods in Physics Research Section B:

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Section: Interaction Potentialsmentioning

confidence: 95%

“…The same group performed another measurement of crystal rainbows [20], using 2-9 MeV protons and 6-30 MeV C 4+ , C 5+ and C 6+ ions transmitted through 179 and 190 nm thick (0 0 1) silicon crystals. For protons, the corresponding values of K were from 0.29 to 0.66, and for carbon ions, they were from 0.29 to 0.85.…”

Section: Measurements Of Crystal Rainbowsmentioning

confidence: 99%

Proton–silicon interaction potential extracted from high-resolution measurements of crystal rainbows

Petrović

Nešković

Ćosić

et al. 2015

Nuclear Instruments and Methods in Physics Research Section B:

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“…The crystal rainbow effect was observed experimentally by Krause et al (1986Krause et al ( , 1994. In the former measurement, the projectiles were 7 MeV protons, and they were transmitted through the axial channels of either a 140-nm-thick <100> or a 198-nm-thick <110> silicon crystal.…”

Section: Crystal Rainbowsmentioning

confidence: 97%

Rainbow Lenses

Nešković

Beličev

Telečki

et al. 2014

Advances in Imaging and Electron Physics

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“…In principle, the stationary quasitemperature value 1/F 21 can be related to the stationary variance of the transverse CP energy. But we followed another approach based on balance equation (12), which allowed calculating the contributions of particle diffusion to the transverse-energy space (the "heating" of subsystem 2) and of the dissipative process (i.e., the cooling of subsystem 2) separately. If we had followed the approach with straightforward calculation of the diffusion, then it would have proved impossible to include the CP energy dissipation due to electron entrainment by an oscillating scattering center in the channel [4].…”

Section: Quasitemperature As the Modulus Of The Quasiequilibrium Distmentioning

confidence: 99%

Dependence of equilibrium properties of channeled particles on the transverse quasitemperature

Kashlev

2006

Theor Math Phys

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We use methods of nonequilibrium thermodynamics to investigate the quasiequilibrium and kinetic characteristics of channeled particles regarded as a separate thermodynamic subsystem. For the channeled particles, we derive the energy-momentum balance equation in the moving coordinate system and show that the solution of the balance equation provides an expression for the main thermodynamic parameter, the transverse quasitemperature of the channeled-particle subsystem. We study the quasiequilibrium angular distribution of particles after their passage through a thin single crystal, the quasiequilibrium distribution over the particle exit angles under backscattering conditions, and also the rate constant for the nonequilibrium (dechanneling) process at large deviations of the system as a whole from the thermodynamic equilibrium. We discuss a measurement method for the particle beam transverse temperature over the peak height of the angular particle distribution found in the framework of a "shoot-through" experiment. Thermodynamic parameters of the channeled-particle subsystemAccording to [1], for fast particles incident on a crystal at small angles not exceeding the critical value, the beam of particles moving along the crystallographic planes (axes) splits into two fractions, namely, channeled and chaotic ones. The formation of the two particle fractions occurs at a penetration depth L of the order of the coherence length L coh ∼ 10 4Å [2]. Therefore, as a rule, analytic calculations are based on the property that a quasiequilibrium distribution over the transverse energies is attained in the channeled-particle (CP) subsystem at a depth ∼ L coh . At this depth, the probability amplitudes in the CP density-matrix equation are damped, but the diagonal matrix entries characterizing the occupancy of the transverse-energy levels are preserved. Therefore, a quasiequilibrium statistical operator ρ l [3], [4] and a quasiequilibrium CP distribution can be introduced at a depth ∼ L coh .If the chaotic part of the beam is excluded from consideration for simplicity, then the remaining part of the system should be further divided into two parts, first, the thermostat (i = 1) including the crystal lattice and the electron gas and, second, the light atomic particles (i = 2) moving in the channel regime. It is convenient to take the Hamiltonians P 1i = H i of the two subsystems, the total momenta P 2i = P i , and the numbers of particles P 3i = N i as the coordinates P mi . As is known [1], CP-electron collisions occur most frequently, and we therefore confine ourself to taking only the particle-electron collisions into account. Then the CP Hamiltonian is written in the form P 21 = H 2 = H (2) 0 + H (2) int + H (2) int , where H (2) 0 includes the continuous atomic chain (or plane) potential U a describing the action of the regular lattice on the CP under conditions of correlated collisions [1]. The total Hamiltonian of the system is H = H 1 + H 2 .

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Angular distribution of ions axially channeled in a very thin crystal: Experimental and theoretical results

Cited by 75 publications

References 24 publications

Proton–silicon interaction potential extracted from high-resolution measurements of crystal rainbows

Proton–silicon interaction potential extracted from high-resolution measurements of crystal rainbows

Rainbow Lenses

Dependence of equilibrium properties of channeled particles on the transverse quasitemperature

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