On the energy losses of fast charged particles

Matveev, V. I.; Макаров, Д. Н.; Gusarevich, E. S.

doi:10.1134/s0021364010170030

Cited by 17 publications

(34 citation statements)

References 12 publications

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“…(11), (19), and (24) (according to Eqs. (10) and (16)) gives the nonperturbative formula for straggling,…”

Section: Makarov Matveevmentioning

confidence: 99%

“…In addition, it was taken into account that dω = d 2 q/v 2 for small scat tering angles and k 0 ≈ k n ≈ k. Straggling is given by the formula (9) Similar to [10], where energy losses were considered in the eikonal approximation, following [13], we sepa rate the integration region q min ≤ q ≤ q 1 into two parts, q min ≤ q ≤ q 0 and q 0 ≤ q ≤ q 1 (where q 0 is independent of n and v a /v Ӷ q 0 Ӷ 1), corresponding to low and high momentum transfers, respectively, and represent Ω 2 in the form…”

Section: General Considerationmentioning

confidence: 99%

“…Energy losses of fast charged particles colliding with atoms were considered in [10][11][12] in the eikonal approxima tion, which makes it possible, unlike the Bloch approach, to nonperturbatively take into account the contribution from intermediate impact parameters (comparable with the characteristic atomic size). Such an inclusion of nonperturbative effects can provide significant (up to 50%) corrections to the BetheBloch formula.…”

Section: N Makarov and V I Matveevmentioning

confidence: 99%

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Energy loss straggling of fast charged particles

Макаров

Matveev

2012

Jetp Lett.

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Energy loss straggling of fast charged particles colliding with atoms have been considered in the eikonal approximation. The result is represented in the form of the Fano formula with a nonperturbative correction. The known nonperturbative Titeica formula (which is transformed to the Fano formula when perturbation theory is applicable) is obtained only under certain approximations in eikonal calculations. It has been shown that straggling calculated with allowance for nonperturbative effects at large charges of the projectile can be significantly different (by an order of magnitude) from the results obtained by Titeica, Fano, and Bohr. Energy loss straggling of fast highly charged ions on hydrogen and copper atoms have been calculated. The latter results are compared to experimental data.

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“…(11), (19), and (24) (according to Eqs. (10) and (16)) gives the nonperturbative formula for straggling,…”

Section: Makarov Matveevmentioning

confidence: 99%

Section: General Considerationmentioning

confidence: 99%

Section: N Makarov and V I Matveevmentioning

confidence: 99%

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Energy loss straggling of fast charged particles

Макаров

Matveev

2012

Jetp Lett.

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“…These two levels act as an effective, local spin-1/2 degree of freedom. The mapping of charge occupation on a quantum dot to an effective spin degree of freedom is not new [95][96][97][98][99][100][101] and a number of related studies of quantum dots coupled to interacting onedimensional systems have been carried out. [102][103][104][105][106][107] However, the physics resulting from coupling such a quantum dot to a RR or RR state has only recently been touched upon in earlier work by the present authors.…”

Section: Exotic Resonant Level Modelsmentioning

confidence: 99%

Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots

2010

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In this paper, we study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state. We assume the dot is small enough that its level spacing is large compared to both the temperature and the coupling to the spatially proximate bulk non-Abelian fractional quantum Hall state. We focus on the physics of level degeneracy with electron number on the dot. The physics of such a resonant level is governed by a k-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction =2+k / ͑k +2͒ or its particle-hole conjugate at =2+2/ ͑k +2͒. The k-channel Kondo model is channel symmetric even without fine tuning any couplings in the former state; in the latter, it is generically channel asymmetric. The two limits exhibit non-Fermi-liquid and Fermi-liquid properties, respectively, and therefore may be distinguished. By exploiting the mapping between the resonant level model and the multichannel Kondo model, we discuss the thermodynamic and transport properties of the system. In the special case of k = 2, our results provide a distinct venue to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction =5/ 2. We present numerical estimates for realizing this scenario in experiment.

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“…At present, ionization energy losses during colli sions of fast charged particles with atoms of a target substance are usually calculated using the Bethe-Bloch formula with standard corrections [1][2][3][4], including the Barkas factor. The need to introduce the latter correction into the Bethe-Bloch theory of energy losses was recognized upon experimental observation [5] of a several percent difference between the ranges of π + and πmesons with identical energies in a photoemulsion.…”

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An analytical formula for the Barkas correction to the theory of ion stopping

2015

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At present, ionization energy losses during colli sions of fast charged particles with atoms of a target substance are usually calculated using the Bethe-Bloch formula with standard corrections [1][2][3][4], including the Barkas factor. The need to introduce the latter correction into the Bethe-Bloch theory of energy losses was recognized upon experimental observation [5] of a several percent difference between the ranges of π + and πmesons with identical energies in a photoemulsion. Until the Barkas correction is small, it is possible to calculate this quantity in the sec ond order of perturbation theory [6] in the region of its applicability-i.e., at Z/v Ӷ 1, where Z is the projec tile charge and v is its velocity (here and below, atomic units are employed). However, if the energy losses have to be determined for heavy ions rather than light ones, the Barkas correction can become large (about 100% of the value given by the Bethe-Bloch theory) [1, 7-10], so that a nonperturbative consideration becomes necessary. Unfortunately, exact nonperturbative quan tum mechanical solution of the problem is yet not available. For this reason, the Barkas correction, whenever significant, is calculated using various fitting parameters or rough approximations based on classi cal notions [5,7].Quantum mechanical calculation of the Barkas correction is only possible in simple cases of numerical solution of the Schrödinger equation [11]. This cor rection introduces additional terms into the Bethe-Bloch formula, which depend only on the odd powers of the charge of a retarded particle. For this reason, it is a common practice to use model ion-atom interac tion potentials. For a short range model potential, the exactly calculated effective stopping involves both even and odd powers of the ion charge. Therefore, only terms dependent on the odd powers of this charge represent the Barkas correction, although the Schrödinger equation has still to be numerically solved [12]. In selecting a model potential, its effective radius α has to be introduced. Usually (see, e.g., [10,12]), a Yukawa type potential is selected and it is assumed that α = v/ω, where v is the ion velocity and ω is the char acteristic atomic frequency. This choice of α is based upon the coincidence of energy losses on a short range potential with parameter α and the classical Bohr for mula for energy losses at Z/v 2 Ӷ 1 and ω/v Ӷ 1 [13]. It should be noted that the Yukawa potential is not the only possible short range type. Some other potentials qualitatively reproducing the behavior of the Yukawa potential can also be used to determine the Barkas cor rection without any loss of accuracy. Thus, of all the standard corrections to the Bethe-Bloch formula, despite its wide use, the Barkas correction is still the least studied one and has no commonly accepted rep resentation.In the present work, a model potential has been selected that allows the Barkas correction to be analyt ically determined by quantum mechanical methods and simply calculated without any loss of accuracy ...

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On the energy losses of fast charged particles

Cited by 17 publications

References 12 publications

Energy loss straggling of fast charged particles

Energy loss straggling of fast charged particles

Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots

An analytical formula for the Barkas correction to the theory of ion stopping

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