Nonlinear ion-stopping calculations for a classical free-electron gas at high projectile energies

In this work, we solved the classical equations of motion and Poisson equation self-consistently, equivalent to the nonlinear Vlasov-Poisson equation, for a projectile moving in a static free-electron gas to calculate the full noncentral self-consistent electron-ion potential, and thus the ion stopping power. We investigated the origin of the Barkas effect, namely, the first nonlinear effect for projectiles at high velocities responsible for the difference between the energy-loss results for positively and negatively charged ions traversing the same target. This effect is strongly enhanced by the multipolar part of the electron-ion potential as first suggested by Lindhard [J. Lindhard, Nucl. Instr. and Meth. 132, 1438 (1976)]. Moreover, this effect is partially related to the nonconservation of the angular momentum in electron-ion collisions. These nonlinear calculations are applied to understanding the stopping of protons and antiprotons in Al at high projectile energie

Ground- and excited-state scattering potentials for the stopping of protons in an electron gas

The self-consistent electron–ion potential V(r) is calculated for H+ ions in an electron gas system as a function of the projectile energy to model the electronic stopping power for conduction-band electrons. The results show different self-consistent potentials at low projectile-energies, related to different degrees of excitation of the electron cloud surrounding the intruder ion. This behavior can explain the abrupt change of velocity dependent screening-length of the potential found by the use of the extended Friedel sum rule and the possible breakdown of the standard free electron gas model for the electronic stopping at low projectile energies. A dynamical interpolation of V(r) is proposed and used to calculate the stopping power for H+ interacting with the valence electrons of Al. The results are in good agreement with the TDDFT benchmark calculations as well as with experimental dat

Perda de energia e fragmentação de íons moleculares em cristais

Os fenômenos decorrentes da interação entre íons monoatômicos e a matéria têm sido amplamente estudados há décadas. No entanto, um esforço comparativamente menor tem sido despendido no estudo dos fenômenos decorrentes da interação entre feixes moleculares e a matéria, especialmente quando o alvo do feixe é um sólido cristalino. Tais fenômenos, como a transferência de energia entre o feixe e a matéria, a emissão de raios X induzidos pelos feixes e a geração de produtos de reação nuclear sofrem importantes modificações no caso de feixes moleculares. Essas alterações estão longe de ser explicadas por uma simples soma dos efeitos causados pelos componentes individuais do aglomerado iônico. Em particular, no caso de interação com sólidos cristalinos, a fragmentação dos aglomerados causada pela explosão coulombiana causa importantes efeitos sobre o fluxo de íons ao longo do sólido. Finalmente, efeitos de vizinhança entre os componentes do aglomerado alteram sensivelmente o valor da energia transferida entre este e o sólido. Na descrição desses fenômenos, empregou-se, neste trabalho, de um lado, a construção de um modelo teórico para a perda de energia de aglomerados e, de outro, técnicas experimentais envolvendo contagens de retroespalhamento, indução de raios X pelo feixe de íons e geração de produtos de reação nuclear por feixes de H+, H2 + e H3 + em Si e SIMOX. Como elo entre teoria e experimento, empregaram-se simulações que descrevem a interação entre os íons moleculares e o alvo. Pela primeira vez, alterações de fluxo de íons causadas pela explosão coulombiana foram quantificadas, valores de perda de energia foram obtidos e, finalmente, uma nova expressão simplificada para a transferência de energia foi obtida.Ion induced phenomena in matter have been studied for many decades. However, a comparatively minor effort was done in the subject of the interaction of molecular ions with the matter, especially for crystalline solid targets. Such phenomena, for instance, the energy transfer between ions and matter, the ion beam induced X ray emission and the nuclear reaction yield undergo important modifications under molecular ion bombardment. These modifications cannot be explained by the sum of effects induced by each ion component of the ionic cluster. Moreover, for the interaction between the cluster beam and crystalline solids, the cluster breakup induced by the Coulomb explosion leads to important effects in the ion flux distribution along the solid. Finally, vicinage effects among the cluster components change the energy transfer between this cluster and the solid. In order to describe those phenomena in this work, we have used, firstly, coupledchannel calculations to describe the cluster energy transfer, and developed a simple energy loss model. Secondly, backscattering, particle induced X ray emission and nuclear reaction analysis experiments have been measured for H+, H2 + and H3 + beams in Si and SIMOX targets. As a link between theory and experiments, we have performed computer simulations to describe the full interaction between the molecular ions and the target atoms. For the first time, cluster ion flux changes induced by the Coulomb explosion were quantified and, finally, a new simple expression for the cluster energy transfer was developed

Perda de energia e fragmentação de íons moleculares em cristais

Os fenômenos decorrentes da interação entre íons monoatômicos e a matéria têm sido amplamente estudados há décadas. No entanto, um esforço comparativamente menor tem sido despendido no estudo dos fenômenos decorrentes da interação entre feixes moleculares e a matéria, especialmente quando o alvo do feixe é um sólido cristalino. Tais fenômenos, como a transferência de energia entre o feixe e a matéria, a emissão de raios X induzidos pelos feixes e a geração de produtos de reação nuclear sofrem importantes modificações no caso de feixes moleculares. Essas alterações estão longe de ser explicadas por uma simples soma dos efeitos causados pelos componentes individuais do aglomerado iônico. Em particular, no caso de interação com sólidos cristalinos, a fragmentação dos aglomerados causada pela explosão coulombiana causa importantes efeitos sobre o fluxo de íons ao longo do sólido. Finalmente, efeitos de vizinhança entre os componentes do aglomerado alteram sensivelmente o valor da energia transferida entre este e o sólido. Na descrição desses fenômenos, empregou-se, neste trabalho, de um lado, a construção de um modelo teórico para a perda de energia de aglomerados e, de outro, técnicas experimentais envolvendo contagens de retroespalhamento, indução de raios X pelo feixe de íons e geração de produtos de reação nuclear por feixes de H+, H2 + e H3 + em Si e SIMOX. Como elo entre teoria e experimento, empregaram-se simulações que descrevem a interação entre os íons moleculares e o alvo. Pela primeira vez, alterações de fluxo de íons causadas pela explosão coulombiana foram quantificadas, valores de perda de energia foram obtidos e, finalmente, uma nova expressão simplificada para a transferência de energia foi obtida.Ion induced phenomena in matter have been studied for many decades. However, a comparatively minor effort was done in the subject of the interaction of molecular ions with the matter, especially for crystalline solid targets. Such phenomena, for instance, the energy transfer between ions and matter, the ion beam induced X ray emission and the nuclear reaction yield undergo important modifications under molecular ion bombardment. These modifications cannot be explained by the sum of effects induced by each ion component of the ionic cluster. Moreover, for the interaction between the cluster beam and crystalline solids, the cluster breakup induced by the Coulomb explosion leads to important effects in the ion flux distribution along the solid. Finally, vicinage effects among the cluster components change the energy transfer between this cluster and the solid. In order to describe those phenomena in this work, we have used, firstly, coupledchannel calculations to describe the cluster energy transfer, and developed a simple energy loss model. Secondly, backscattering, particle induced X ray emission and nuclear reaction analysis experiments have been measured for H+, H2 + and H3 + beams in Si and SIMOX targets. As a link between theory and experiments, we have performed computer simulations to describe the full interaction between the molecular ions and the target atoms. For the first time, cluster ion flux changes induced by the Coulomb explosion were quantified and, finally, a new simple expression for the cluster energy transfer was developed

Derivadas discretas : analogias com as derivadas de funções

15

Derivadas discretas : analogias com as derivadas de funções

15

Estudo de dinâmica caótica : conjunto de Mandelbrot e seqüência de Fibonacci

07

Coulomb heating of channeled C+ and C2+ molecules in Si

Si x-ray and backscattering yields have been measured as a function of the C⁺ and C₂⁺ entrance angle along the Si ‹100› channel in an energy interval between 900 and 2200 keV/atom. A significant enhancement of the x-ray production has been observed for the well-aligned C₂⁺ beam in comparison with the monoatomic case. It is shown that this effect results from the Coulomb explosion of the molecule during the channeling motion. By combining the Rutherford backscattering channeling (RBS-C) and the x-ray results we were able to determine the value of the transverse energy transfer as a function of the beam energy due to the break up process (Coulomb heating). This energy increases monotonically from 14 eV for 900 keV/atom up to 30 eV for 2200 keV/atom. In addition, we were able to predict the theoretical Coulomb heating values by combining calculations and simulations, the theoretical-experimental agreement, within the experimental errors, being quite reasonable

Coulomb heating of channeled C+ and C2+ molecules in Si

Si x-ray and backscattering yields have been measured as a function of the C⁺ and C₂⁺ entrance angle along the Si ‹100› channel in an energy interval between 900 and 2200 keV/atom. A significant enhancement of the x-ray production has been observed for the well-aligned C₂⁺ beam in comparison with the monoatomic case. It is shown that this effect results from the Coulomb explosion of the molecule during the channeling motion. By combining the Rutherford backscattering channeling (RBS-C) and the x-ray results we were able to determine the value of the transverse energy transfer as a function of the beam energy due to the break up process (Coulomb heating). This energy increases monotonically from 14 eV for 900 keV/atom up to 30 eV for 2200 keV/atom. In addition, we were able to predict the theoretical Coulomb heating values by combining calculations and simulations, the theoretical-experimental agreement, within the experimental errors, being quite reasonable