Study of the higher-order corrections to the impact-parameter dependence of energy loss

Khodyrev, V.A.; Arnoldbik, W.M.; Iferov, G.A.; Boerma, D.O.

doi:10.1016/s0168-583x(99)01162-3

Cited by 4 publications

(9 citation statements)

References 19 publications

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“…Then, using the idea of the Lindhard-Scharff model [11], the impact-parameter dependence of energy loss in an ionatom collision, E(b), can be described in the local plasma frequency approach (the local current j(r, t) is calculated according to the electron density at a given point r of the atomic electron shell). This general model is presented in [13]. Here, for illustration, an example of the calculation is presented ( figure 2).…”

Section: Discussionmentioning

confidence: 99%

“…Using the introduced representation of energy loss, the Lindhard-Scharff model [11] for the stopping cross section (the local plasma frequency, LPF, approach) can be generalized [12] to describe E(b) in the linear response approach. The combination of this model with the exact description of energy loss to free electrons results in a general model [13] where both the Barkas and Bloch corrections to E(b) are described in a general scheme.…”

Section: A Khodyrevmentioning

confidence: 99%

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Enhanced Light Extraction in GaN-Based Light-Emitting Diodes with Holographically Fabricated Concave Hemisphere-Shaped Patterning on Indium–Tin-Oxide Layer

Seo

Lee

et al. 2010

Jpn. J. Appl. Phys.

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The energy loss in the collision of a moving charged projectile with a free electron is described in a rigorous approach. The collision is treated as stationary scattering of an electron in the projectile Coulomb field. In the laboratory frame, the picture can be represented as a spatial distribution of energy losses to the electron. It has been shown that the local rate of the energy gain can be presented as a product of the induced electron current and the projectile electric field. The analytical results and numerical calculations reveal a principal disagreement with the generally recognized condition for the classical description, η = Z 1 e 2 /hv 1 (Z 1 e and v are, respectively, the charge and velocity of the projectile): for any value of η, the quantum effects appear to be significant in the close vicinity of the projectile trajectory (small impact parameters) restricted by the distance ∼λ =h/mv. Essentially, the problem has been cleared in the qualitative analysis of collisions with electron wavepackets. The main results of the Bloch theory are reproduced in a simpler way. The clearer basis permits us to eliminate the ambiguity in the interpretation of the origin of the Bloch correction, which reflects in fact the evolution of the classical features in the quantum mechanical picture.where ψ is the logarithmic derivative of the -function. The correction is even over the projectile charge, L ≈ −1.202η 2 at small η.

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Section: Discussionmentioning

confidence: 99%

Section: A Khodyrevmentioning

confidence: 99%

Enhanced Light Extraction in GaN-Based Light-Emitting Diodes with Holographically Fabricated Concave Hemisphere-Shaped Patterning on Indium–Tin-Oxide Layer

Seo

Lee

et al. 2010

Jpn. J. Appl. Phys.

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“…Here o p 4pr p is the plasma frequency of the electron gas. For a degenerate electron gas, the summation over the initial electron momenta k 0 in (7) is restricted by the Fermi sphere, k 0 < k F 3p 2 r 1=3 , the weight factor gk 0 has a constant value normalized to unity. A positive imaginary increment id has been added to ensure that only the initial states jk 0 i are occupied at t ÀI.…”

Section: The Dielectric Approachmentioning

confidence: 99%

“…The local response acquires a de¢ned meaning if the energy loss is represented in the special form [7]:…”

Section: Introductionmentioning

confidence: 99%

“…The same RPA description, the dielectric approach [2], is used to treat the linear response of an electron gas on the ion Coulomb ¢eld. These results have already been used [7] in formulation of a calculation scheme where, additionally, the higher-order corrections over the projectile charge are taken into account. For this purpose, the results obtained in the linear response approach are combined with the exact description of energy loss to free electrons [8].…”

Section: Introductionmentioning

confidence: 99%

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The Local Plasma Frequency Approach in Description of the Impact-Parameter Dependence of Energy Loss

Khodyrev

2001

Phys. Scr.

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The LPF approach of Lindhard and Scharff is generalized to describe on the same basis the impact parameter dependence of energy loss in ion–atom collision. To make this feasible the energy loss is represented as an integral of the local energy deposition over the atomic shell volume. The local energy loss is determined by the induced electron current and the intensity of the projectile field at a given point. The LPF approach consists in an approximate description of the induced current using the corresponding expression for a uniform electron gas. With an appropriate description of the electron gas response, the atomic shell polarization and the state of electron motion are considered. The developed approach provides a possibility to test the accuracy of the customary approximation where the energy loss is expressed through the electron density on the ion trajectory, the local density approximation. A comparison with the available experimental results displays the adequateness of the developed approach if, additionally, the higher-order corrections over the projectile charge are taken into account.

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The Treatment of Energy Loss in Terms of Induced Current Density

Khodyrev

2004

Advances in Quantum Chemistry

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Study of the higher-order corrections to the impact-parameter dependence of energy loss

Cited by 4 publications

References 19 publications

Enhanced Light Extraction in GaN-Based Light-Emitting Diodes with Holographically Fabricated Concave Hemisphere-Shaped Patterning on Indium–Tin-Oxide Layer

Enhanced Light Extraction in GaN-Based Light-Emitting Diodes with Holographically Fabricated Concave Hemisphere-Shaped Patterning on Indium–Tin-Oxide Layer

The Local Plasma Frequency Approach in Description of the Impact-Parameter Dependence of Energy Loss

The Treatment of Energy Loss in Terms of Induced Current Density

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