Calculation of mean excitation energies

Sauer, Stephan P. A.; Sabin, John R.; Oddershede, Jens

doi:10.1016/bs.aiq.2019.06.003

Cited by 12 publications

(14 citation statements)

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“…for the mean excitation energy I(Z) (see [26] and refs. therein), and density correction δ(Z, γ) in ( 16) accounts for dispersive dielectric susceptibility of the medium [8].…”

Section: Solution Of the Transport Equationmentioning

confidence: 99%

“…Before proceeding, let us analyze the structure of the obtained integral (26). Even though one of its entries, Ω in , looks somewhat cumbersome, involving a special function Ein, its second u-derivative is very simple:…”

Section: Solution Of the Transport Equationmentioning

confidence: 99%

“…To gain a deeper insight into the structure of the solution, we need to directly scrutinize the behavior of the double integral (26) in different regimes, corresponding to two main probability concentration regions manifest in Figs. 3a, 4a.…”

Section: Moderate Energy Transfers Large-thickness and Large-z Approx...mentioning

confidence: 99%

“…To be self-consistent, again, we should issue from double integral (26), which has to be formally evaluated in the corresponding limit. Actually, there are two possible ways of going to infinity in the Θ-λ plane, increasing one of the coordinates while holding the other of them fixed.…”

Section: Hard Scattering Region Large λmentioning

confidence: 99%

“…In fact, this asymptotics can be rigorously proven to hold for any fixed λ. The proof begins with noting that limit Θ → ∞ at fixed λ in integral (26) implies y ∼ Θ −2 → 0 at fixed u. The exponential e Ω el +Ωin may then be linearized in Ω el = − y 4 ln y0 y and Ω in (y/4Z, u) − Ω in (0, u) ≃ y/4Zu≪1 y 4Z (2 + ln u) [cf.…”

Section: Hard Scattering Region Large λmentioning

confidence: 99%

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Correlation between multiple scattering angle and ionization energy loss for fast electrons

Bondarenco

2020

Preprint

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A correlation between the angle of multiple scattering and the ionization energy loss for relativistic electrons in an amorphous medium is evaluated based on a solution of the transport equation. The correlation is found to be the strongest in the large deflection angle region, but also sizable at typical deflection angles, where it leads to a broadening of the angular distribution with the increase of the energy loss. The mean energy loss as a function of the deflection angle grows quadratically with the increase of the latter, but the proportionality coefficient changes when passing from the small-to the large-deflection angle region.

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“…for the mean excitation energy I(Z) (see [26] and refs. therein), and density correction δ(Z, γ) in ( 16) accounts for dispersive dielectric susceptibility of the medium [8].…”

Section: Solution Of the Transport Equationmentioning

confidence: 99%

Section: Solution Of the Transport Equationmentioning

confidence: 99%

Section: Moderate Energy Transfers Large-thickness and Large-z Approx...mentioning

confidence: 99%

Section: Hard Scattering Region Large λmentioning

confidence: 99%

Section: Hard Scattering Region Large λmentioning

confidence: 99%

See 3 more Smart Citations