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James A Lock - One of the best experts on this subject based on the ideXlab platform.
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high order Rainbows of a spherical particle produced by near grazing incident light
Applied Optics, 2017Co-Authors: James A LockAbstract:This study is concerned with the formation of high-order Rainbows by near-grazing light incident on a spherical particle. As the number of internal reflections involved increases, the incident Descartes ray strikes the sphere surface increasingly closer to its edge, where the predictions of ray theory and Airy theory become invalid. The deflection angle of the confluence of the stationary points of the phase of the partial wave scattering amplitudes is studied as a function of rainbow order and sphere radius. It is found that as the rainbow order increases, the angular interval over which the upper supernumerary ray stationary point occurs shrinks to zero. In addition, for deflection angles beyond the confluence of the upper supernumerary ray with the tunneling ray, intensity oscillations are due to interference of the field of the lower supernumerary ray with that of the edge region Fock transition, rather than interference between the upper and lower supernumerary rays.
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Rainbows by elliptically deformed drops. II. The appearance of supernumeraries of high-order Rainbows in rain showers
Applied optics, 2017Co-Authors: Gunther P. Können, James A LockAbstract:The appearance of supernumeraries of high-order Rainbows in heavy rain showers is explored for Rainbows up to order five (p=6). This is done by using a combination of the ray-theory-based first-order Mobius approximation for high-order Rainbows with the Airy approximation of the rainbow radiance distribution. We conclude that supernumerary formation of Rainbows of order three, four, and five is possible in natural rain showers. Supernumeraries of the third-order and fourth-order Rainbows are preferentially formed near the bottom of these Rainbows. A strategy for observing supernumeraries of high-order Rainbows is proposed.
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Rainbows by elliptically deformed drops. I. Möbius shift for high-order Rainbows
Applied optics, 2017Co-Authors: James A Lock, Gunther P. KönnenAbstract:Using ray theory, the Mobius shift of the (p−1)-order rainbow angle for a particle having an elliptical cross section is obtained to first order in the ellipticity as a function of the tilt of the ellipse with respect to the propagation direction of the incoming rays. The result is then adapted to the geometry of scattering of light rays from the sun by a falling water drop as a function of sun height angle. The variation in the angular spacing between the supernumeraries is determined as a function of location along the rainbow arc, the conditions under which the rainbow angle is insensitive to drop flattening were determined, and the dependence of the Mobius shift on the drop refractive index is shown for Rainbows up to fourth order (p=5).
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Rainbows in the grass i external reflection Rainbows from pendant droplets
Applied Optics, 2008Co-Authors: James A Lock, Charles L. Adler, Richard W FleetAbstract:In the mid-morning on a sunny day one can sometimes see glare spots associated with uncolored “rainbow” (i.e., fold) caustics due to the sunlight reflected from the surface of dew or guttation drops. We show that these dewdrop reflection Rainbows are due to places on the droplet (i.e., from an “inflection circle”) where its Gaussian curvature becomes zero. We work out the theory of such caustics with horizontally incident light and present a comparison of the theory to measurements made in the laboratory.
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Experimental observation of total-internal-reflection Rainbows
Applied optics, 2003Co-Authors: Charles L. Adler, James A Lock, Jonathon Mulholland, Brian Keating, Diana EkelmanAbstract:A new class of Rainbows is created when a droplet is illuminated from the inside by a point light source. The position of the rainbow depends on both the index of refraction of the droplet and the position of the light source, and the rainbow vanishes when the point source is too close to the center of the droplet. Here we experimentally measure the position of the transmission and one-internal-reflection total-internal-reflection Rainbows, and the standard (primary) rainbow, as a function of light-source position.
N Neskovic - One of the best experts on this subject based on the ideXlab platform.
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quantum primary Rainbows in transmission of positrons through very short carbon nanotubes
Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms, 2016Co-Authors: Marko Cosic, S. Petrovic, N NeskovicAbstract:Abstract This paper is devoted to a quantum mechanical consideration of the transmission of positrons of a kinetic energy of 1 MeV through very short (11, 9) single-wall chiral carbon nanotubes. The nanotube lengths are between 50 and 320 nm. The transmission process is determined by the rainbow effects. The interaction potential of a positron and the nanotube is deduced from the Molire’s interaction potential of the positron and a nanotube atom using the continuum approximation. We solve numerically the time-dependent Schrodinger equation, and calculate the spatial and angular distributions of transmitted positrons. The initial positron beam is assumed to be an ensemble of non-interacting Gaussian wave packets. We generate the spatial and angular distributions using the computer simulation method. The examination is focused on the spatial and angular primary Rainbows. It begins with an analysis of the corresponding classical Rainbows, and continues with a detailed investigation of the amplitudes and phases of the wave functions of transmitted positrons. These analyses enable one to identify the principal and supernumerary primary Rainbows appearing in the spatial and angular distributions. They also result in a detailed explanation of the way of their generation, which includes the effects of wrinkling of each wave packet during its deflection from the nanotube wall, and of its concentration just before a virtual barrier lying close to the corresponding classical rainbow. The wrinkling of the wave packets occurs due to their internal focusing. In addition, the wave packets wrinkle in a mutually coordinated way. This explanation may induce new theoretical and experimental investigations of quantum Rainbows occurring in various atomic collision processes.
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proton silicon interaction potential extracted from high resolution measurements of crystal Rainbows
Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms, 2015Co-Authors: S. Petrovic, N Neskovic, Marko Cosic, M Motapothula, M B H BreeseAbstract:Abstract This study provides a way to produce very accurate ion–atom interaction potentials. We present the high-resolution measurements of angular distributions of protons of energies between 2.0 and 0.7 MeV channeled in a 55 nm thick (0 0 1) silicon membrane. Analysis is performed using the theory of crystal Rainbows in which the Moliere’s interaction potential is modified to make it accurate both close to the channel axis and close to the atomic strings defining the channel. This modification is based on adjusting the shapes of the rainbow lines appearing in the transmission angle plane, with the resulting theoretical angular distributions of transmitted protons being in excellent agreement with the corresponding experimental distributions.
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superfocusing of channeled protons and crystal Rainbows
Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms, 2009Co-Authors: N Neskovic, S. Petrovic, D. BorkaAbstract:Abstract This study is devoted to the effect of superfocusing of protons having the energy of 2 MeV in a 〈1 0 0〉 channel of a Si crystal. The analysis is performed by the theory of crystal Rainbows. We analyze the superfocusing effect in the first rainbow cycle. The evolution of the spatial distribution of channeled protons is examined by the numerical solution of the proton equations of motion in the transverse position plane. We demonstrate that the superfocusing effect is a reduced crystal rainbow effect, in which the rainbow line comes to a point.
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Rainbows in transmission of high energy protons through carbon nanotubes
European Physical Journal B, 2005Co-Authors: S. Petrovic, D. Borka, N NeskovicAbstract:We investigate theoretically the angular distribution and the Rainbows in the case of 1 GeV protons transmitted through the 1 μm long rope of (10, 10) single-wall carbon nanotubes. The angular distribution of transmitted protons is generated by the computer simulation method using the numerical solution of the proton equations of motion. Then, the rainbow lines corresponding to the angular distribution are determined. The analysis shows that the rainbow pattern defines the angular distribution – all its pronounced maxima except the maximum lying at the origin are the rainbow maxima. A possible application of the rainbow effect for characterization of nanotubes is suggested.
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Rainbows with a si thin crystal
European Physical Journal B, 2000Co-Authors: N Neskovic, S. Petrovic, L ZivkovicAbstract:This study is devoted to the transmission of Ne10+ ions through a \(\) Si thin crystal. The ion energy is 60 MeV and the crystal thickness is varied from 159 to 478 atomic layers, i.e. within the first rainbow cycle. The analysis is performed by the theory of crystal Rainbows. The angular distribution of the transmitted ions is generated by the computer simulation method. Then, the rainbow lines in the scattering angle plane are determined. These lines ensure the full explanation of the angular distribution.
Petrović, Srđan M. - One of the best experts on this subject based on the ideXlab platform.
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Quantum Rainbows in Positron Transmission through Carbon Nanotubes
'MDPI AG', 2019Co-Authors: Ćosić Marko, Petrović, Srđan M., Nešković, Nebojša B.Abstract:Here we report the results of the theoretical investigation of the transmission of channeled positrons through various short chiral single walled carbon nanotubes (SWCNT). The main question answered by this study is “What are the manifestations of the rainbow effect in the channeling of quantum particles that happens during the channeling of classical particles?” To answer this question, the corresponding classical and quantum problems were solved in parallel, critically examined, and compared with each other. Positron energies were taken to be 1 MeV when the quantum approach was necessary. The continuum positron-nanotube potential was constructed from the thermally averaged Molière’s positron-carbon potential. In the classical approach, a positron beam is considered as an ensemble of noninteracting particles. In the quantum approach, it is considered as an ensemble of noninteracting wave packages. Distributions of transmitted positrons were constructed from the numerical solutions of Newton’s equation and the time-dependent Schrödinger equation. For the transmission of 1-MeV positrons through 200-nm long SWCNT (14; 4), in addition to the central maximum, the quantum angular distribution has a prominent peak pair (close to the classical Rainbows) and two smaller peaks pairs. We have shown that even though the semiclassical approximation is not strictly applicable it is useful for explanation of the observed behavior. In vicinity of the most prominent peak, i.e., the primary rainbow peak, rays interfere constructively. On one of its sides, rays become complex, which explains the exponential decay of the probability density in that region. On the other side, the ray interference alternates between constructive and destructive, thus generating two observed supernumerary rainbow peaks. The developed model was then applied for the explanation of the angular distributions of 1-MeV positrons transmitting through 200 nm long (7, 3), (8, 5), (9, 7), (14, 4), (16, 5) and (17, 7) SWCNTs. It has been shown that this explains most but not all rainbow patterns. Therefore, a new method for the identification and classification of quantum Rainbows was developed relying only on the morphological properties of the positron wave function amplitude and the phase function families. This led to a detailed explanation of the way the quantum Rainbows are generated. All wave packets wrinkle due to their internal focusing in a mutually coordinated way and are concentrated near the position of the corresponding classical rainbow. This explanation is general and applicable to the investigations of quantum effects occurring in various other atomic collision processes
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Investigation of the graphene thermal motion by rainbow scattering
'Elsevier BV', 2019Co-Authors: Ćosić Marko, Petrović, Srđan M., Hadžijojić Milivoje, Rymzhanov Ruslan, Bellucci StefanoAbstract:The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called Rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on Rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, Rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.This is the peer-reviewed version of the article: Ćosić, M., M. Hadžijojić, R. Rymzhanov, S. Petrović, and S. Bellucci. "Investigation of the graphene thermal motion by rainbow scattering." Carbon 145 (2019): 161-174. [10.1016/j.carbon.2019.01.020]Published version: [https://vinar.vin.bg.ac.rs/handle/123456789/8022
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Investigation of the graphene thermal motion by rainbow scattering
2019Co-Authors: Ćosić Marko, Petrović, Srđan M., Hadžijojić Milivoje, Rymzhanov Ruslan, Bellucci StefanoAbstract:The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called Rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on Rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, Rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.This is the peer-reviewed version of the article: Ćosić, M., M. Hadžijojić, R. Rymzhanov, S. Petrović, and S. Bellucci. "Investigation of the graphene thermal motion by rainbow scattering." Carbon 145 (2019): 161-174. [10.1016/j.carbon.2019.01.020
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Universal axial (0 0 1) rainbow channeling interaction potential
2019Co-Authors: Petrović, Srđan M., Starčević Nikola, Ćosić MarkoAbstract:This work is devoted to the construction of the universal axial (0 0 1) rainbow channeling proton-crystal interaction potential. It has been done by modifying the Moliere's interaction potential. We show that for very thin crystals with the cubic crystallographic structure, in the (0 0 1) orientation with respect to 2 MeV proton beams, it is possible to obtain a universal proton-crystal interaction potential from the morphological analysis of the Rainbows in the proton transmission angular plane. © 201
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Investigation of the graphene thermal motion by rainbow scattering
2019Co-Authors: Ćosić Marko, Petrović, Srđan M., Hadžijojić Milivoje, Rymzhanov Ruslan, Bellucci StefanoAbstract:The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called Rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on Rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, Rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion. © 2019 Elsevier Lt
Ćosić Marko - One of the best experts on this subject based on the ideXlab platform.
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Quantum Rainbows in Positron Transmission through Carbon Nanotubes
'MDPI AG', 2019Co-Authors: Ćosić Marko, Petrović, Srđan M., Nešković, Nebojša B.Abstract:Here we report the results of the theoretical investigation of the transmission of channeled positrons through various short chiral single walled carbon nanotubes (SWCNT). The main question answered by this study is “What are the manifestations of the rainbow effect in the channeling of quantum particles that happens during the channeling of classical particles?” To answer this question, the corresponding classical and quantum problems were solved in parallel, critically examined, and compared with each other. Positron energies were taken to be 1 MeV when the quantum approach was necessary. The continuum positron-nanotube potential was constructed from the thermally averaged Molière’s positron-carbon potential. In the classical approach, a positron beam is considered as an ensemble of noninteracting particles. In the quantum approach, it is considered as an ensemble of noninteracting wave packages. Distributions of transmitted positrons were constructed from the numerical solutions of Newton’s equation and the time-dependent Schrödinger equation. For the transmission of 1-MeV positrons through 200-nm long SWCNT (14; 4), in addition to the central maximum, the quantum angular distribution has a prominent peak pair (close to the classical Rainbows) and two smaller peaks pairs. We have shown that even though the semiclassical approximation is not strictly applicable it is useful for explanation of the observed behavior. In vicinity of the most prominent peak, i.e., the primary rainbow peak, rays interfere constructively. On one of its sides, rays become complex, which explains the exponential decay of the probability density in that region. On the other side, the ray interference alternates between constructive and destructive, thus generating two observed supernumerary rainbow peaks. The developed model was then applied for the explanation of the angular distributions of 1-MeV positrons transmitting through 200 nm long (7, 3), (8, 5), (9, 7), (14, 4), (16, 5) and (17, 7) SWCNTs. It has been shown that this explains most but not all rainbow patterns. Therefore, a new method for the identification and classification of quantum Rainbows was developed relying only on the morphological properties of the positron wave function amplitude and the phase function families. This led to a detailed explanation of the way the quantum Rainbows are generated. All wave packets wrinkle due to their internal focusing in a mutually coordinated way and are concentrated near the position of the corresponding classical rainbow. This explanation is general and applicable to the investigations of quantum effects occurring in various other atomic collision processes
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Investigation of the graphene thermal motion by rainbow scattering
'Elsevier BV', 2019Co-Authors: Ćosić Marko, Petrović, Srđan M., Hadžijojić Milivoje, Rymzhanov Ruslan, Bellucci StefanoAbstract:The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called Rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on Rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, Rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.This is the peer-reviewed version of the article: Ćosić, M., M. Hadžijojić, R. Rymzhanov, S. Petrović, and S. Bellucci. "Investigation of the graphene thermal motion by rainbow scattering." Carbon 145 (2019): 161-174. [10.1016/j.carbon.2019.01.020]Published version: [https://vinar.vin.bg.ac.rs/handle/123456789/8022
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Investigation of the graphene thermal motion by rainbow scattering
2019Co-Authors: Ćosić Marko, Petrović, Srđan M., Hadžijojić Milivoje, Rymzhanov Ruslan, Bellucci StefanoAbstract:The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called Rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on Rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, Rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.This is the peer-reviewed version of the article: Ćosić, M., M. Hadžijojić, R. Rymzhanov, S. Petrović, and S. Bellucci. "Investigation of the graphene thermal motion by rainbow scattering." Carbon 145 (2019): 161-174. [10.1016/j.carbon.2019.01.020
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Universal axial (0 0 1) rainbow channeling interaction potential
2019Co-Authors: Petrović, Srđan M., Starčević Nikola, Ćosić MarkoAbstract:This work is devoted to the construction of the universal axial (0 0 1) rainbow channeling proton-crystal interaction potential. It has been done by modifying the Moliere's interaction potential. We show that for very thin crystals with the cubic crystallographic structure, in the (0 0 1) orientation with respect to 2 MeV proton beams, it is possible to obtain a universal proton-crystal interaction potential from the morphological analysis of the Rainbows in the proton transmission angular plane. © 201
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Investigation of the graphene thermal motion by rainbow scattering
2019Co-Authors: Ćosić Marko, Petrović, Srđan M., Hadžijojić Milivoje, Rymzhanov Ruslan, Bellucci StefanoAbstract:The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called Rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on Rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, Rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion. © 2019 Elsevier Lt
S. Petrovic - One of the best experts on this subject based on the ideXlab platform.
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quantum primary Rainbows in transmission of positrons through very short carbon nanotubes
Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms, 2016Co-Authors: Marko Cosic, S. Petrovic, N NeskovicAbstract:Abstract This paper is devoted to a quantum mechanical consideration of the transmission of positrons of a kinetic energy of 1 MeV through very short (11, 9) single-wall chiral carbon nanotubes. The nanotube lengths are between 50 and 320 nm. The transmission process is determined by the rainbow effects. The interaction potential of a positron and the nanotube is deduced from the Molire’s interaction potential of the positron and a nanotube atom using the continuum approximation. We solve numerically the time-dependent Schrodinger equation, and calculate the spatial and angular distributions of transmitted positrons. The initial positron beam is assumed to be an ensemble of non-interacting Gaussian wave packets. We generate the spatial and angular distributions using the computer simulation method. The examination is focused on the spatial and angular primary Rainbows. It begins with an analysis of the corresponding classical Rainbows, and continues with a detailed investigation of the amplitudes and phases of the wave functions of transmitted positrons. These analyses enable one to identify the principal and supernumerary primary Rainbows appearing in the spatial and angular distributions. They also result in a detailed explanation of the way of their generation, which includes the effects of wrinkling of each wave packet during its deflection from the nanotube wall, and of its concentration just before a virtual barrier lying close to the corresponding classical rainbow. The wrinkling of the wave packets occurs due to their internal focusing. In addition, the wave packets wrinkle in a mutually coordinated way. This explanation may induce new theoretical and experimental investigations of quantum Rainbows occurring in various atomic collision processes.
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proton silicon interaction potential extracted from high resolution measurements of crystal Rainbows
Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms, 2015Co-Authors: S. Petrovic, N Neskovic, Marko Cosic, M Motapothula, M B H BreeseAbstract:Abstract This study provides a way to produce very accurate ion–atom interaction potentials. We present the high-resolution measurements of angular distributions of protons of energies between 2.0 and 0.7 MeV channeled in a 55 nm thick (0 0 1) silicon membrane. Analysis is performed using the theory of crystal Rainbows in which the Moliere’s interaction potential is modified to make it accurate both close to the channel axis and close to the atomic strings defining the channel. This modification is based on adjusting the shapes of the rainbow lines appearing in the transmission angle plane, with the resulting theoretical angular distributions of transmitted protons being in excellent agreement with the corresponding experimental distributions.
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superfocusing of channeled protons and crystal Rainbows
Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms, 2009Co-Authors: N Neskovic, S. Petrovic, D. BorkaAbstract:Abstract This study is devoted to the effect of superfocusing of protons having the energy of 2 MeV in a 〈1 0 0〉 channel of a Si crystal. The analysis is performed by the theory of crystal Rainbows. We analyze the superfocusing effect in the first rainbow cycle. The evolution of the spatial distribution of channeled protons is examined by the numerical solution of the proton equations of motion in the transverse position plane. We demonstrate that the superfocusing effect is a reduced crystal rainbow effect, in which the rainbow line comes to a point.
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Rainbows with Carbon Nanotubes
2008Co-Authors: S. Petrovic, D. BorkaAbstract:This review is devoted to the rainbow effect that occurs in ion channeling through carbon nanotubes. We shall present the Rainbows in channeling of 1 GeV protons through the straight and bent bundles of (10, 10) single-wall carbon nanotubes (SWCNs), and in channeling of 0.233 MeV protons through the straight (11, 9) SWCNs. The Rainbows are obtained using the theory of crystal Rainbows, which has been demonstrated to be the proper theory of ion channeling in thin crystals. The applicability of the rainbow effect for characterization of nanotubes, and for clarifying the problem of guiding high energy ion beams with them is discussed.
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Rainbows in transmission of high energy protons through carbon nanotubes
European Physical Journal B, 2005Co-Authors: S. Petrovic, D. Borka, N NeskovicAbstract:We investigate theoretically the angular distribution and the Rainbows in the case of 1 GeV protons transmitted through the 1 μm long rope of (10, 10) single-wall carbon nanotubes. The angular distribution of transmitted protons is generated by the computer simulation method using the numerical solution of the proton equations of motion. Then, the rainbow lines corresponding to the angular distribution are determined. The analysis shows that the rainbow pattern defines the angular distribution – all its pronounced maxima except the maximum lying at the origin are the rainbow maxima. A possible application of the rainbow effect for characterization of nanotubes is suggested.
