Corrections to the Bethe-Bloch formula for average ionization energy loss of relativistic heavy nuclei Close collisions

Morgan, S. H.; Eby, P. B.

doi:10.1016/0029-554x(73)90303-0

Cited by 20 publications

(12 citation statements)

References 5 publications

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“…Finally, the Matt and B1och corrections from Ahlen (1978a) Morgan and Eby (1973). They agree within 1% for total stopping power with those values obtained from the formulae of Ahlen (1978a) for the Matt corrections.…”

Section: In the CM Framesupporting

confidence: 78%

“…They agree within 1% for total stopping power with those values obtained from the formulae of Ahlen (1978a) for the Matt corrections. Morgan and Eby (1973) show that similar accuracy is obtained for jZ 1 !/S < 20 with the second Born -83-approximation to the Matt cross section and for jZ 1 j/S <55 with the third Born approximation.…”

Section: In the CM Framesupporting

confidence: 75%

“…Radiative corrections have been shown to be quite small in the previous sub-section and it is sufficient to evaluate the cross section for scattering in a static field with complete neglect of the electromagnetic field. Matt (1929,1932) (1972) and Morgan and Eby (1973) have performed such calculations for several values of Z 1 and B which agree with Jackson and McCarthy's results for Z 1 < 20. Ahlen (1978a) has taken advantage of the Z 1 7 expansion derived by Curr (1955) for the Mott cross section to obtain an analytical expression for the stopping power which is valid to within 1% for IZ 1 I/B < 100.…”

Section: Failure Of the First Born Approximationsupporting

confidence: 72%

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Theoretical and experimental aspects of the energy loss of relativistic heavily ionizing particles

1980

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Section: In the CM Framesupporting

confidence: 78%

Section: In the CM Framesupporting

confidence: 75%

Section: Failure Of the First Born Approximationsupporting

confidence: 72%

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Theoretical and experimental aspects of the energy loss of relativistic heavily ionizing particles

1980

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“…McCurthy [16] and independently by Morgan and Eby [15], based on the approximate McKinley− Feshbach results for the Mott-exact cross section (𝑑𝜎/𝑑𝐸) 𝑀𝑀𝐹 [17], reads 0 .…”

Section: Basic Formulaementioning

confidence: 98%

Comparison of the Lindhard–Sørensen and Mott–Bloch Corrections to the Bethe Stopping Formula at Moderately Relativistic Energies

Kats

Halenka

Voskresenskaya

2021

Phys. Part. Nuclei Lett.

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The results of numerical calculating the total Mott−Bloch correction to the Bethe stopping formula and the Lindhard−Sørensen correction in the point nucleus approximation, as well as the Mott correction and the difference between the Lindhard−Sørensen and Bloch corrections, which were obtained by some rigorous and approximate methods, are compared for the ranges of a gamma factor 1 ≲ 𝛾 ≲ 10 and the ion nuclear charge number 6 ≤ Z ≤ 114. It is shown that the accurate calculation of the Mott−Bloch correction based on the Mott exact cross section using a method previously proposed by one of the authors gives excellent agreement between its values and the values of the Lindhard−Sørensen correction in the 𝛾 and Z ranges under consideration. In addition, it is demonstrated that the results of stopping power calculations obtained by the two above-mentioned rigorous methods coincide with each other up to the seventh significant digit and provide the best agreement with experimental data in contrast with the results of some approximate methods, such as the methods of Ahlen, Jackson−McCarthy, etc.

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“…However, for the dE/dx measurement the truncated mean over 65% lowest-charge pad-row outputs is used to reduce the fluctuations originating from Landau tail developing towards the higher values in the distribution of the deposited charge [117]. The mean ionization energy loss dE/dx for a given particle type is often described by the Bethe-Bloch formula [120] as following:…”

Section: Tpcmentioning

confidence: 99%

Studies of collective effects in pp collisions at the LHC with the balance function for identified particles

Khabanova¹

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A new state of matter, where quarks and gluons are not confined inside hadrons, called quark-gluon plasma (QGP), was predicted to exist at sufficiently high temperatures and energy densities by the theory of strong interactions, quantum chromodynamics (QCD) around 50 years ago. At present, this state can be created in the collisions between heavy ions accelerated to ultra-relativistic speeds, which provides a unique possibility to explore the behaviour of strongly interacting matter under extreme conditions. Experimental measurements at RHIC and the LHC allowed to conclude that the medium formed in heavy-ion collisions is strongly coupled and is well described by relativistic viscous hydrodynamic equations for a perfect liquid. These properties lead to the collective expansion of all particles produced in the collision with a common velocity, i.e. collective flow. For some of these measurements, proton-nucleus and proton-proton collisions, referred to as small systems, where QGP was not expected to form, have been used as a reference. Recently, this expectation has been confronted by intriguing results reported by experiments at RHIC and the LHC that indicate the presence of collective flow also in small systems. The origin of this effect is not fully understood. In particular, it is not clear whether it is caused by the QGP formation or other alternative mechanisms that can lead to similar patterns as hydrodynamic flow without involving the QGP expansion, such as color reconnection. To investigate it better, the balance function which studies the charge-dependent part of two-particle correlations in the relative pseudorapidity (∆η) and azimuthal angle (∆ϕ) of the particle pair can be used. In heavy-ion collisions, this measurement has been used as an effective tool to investigate the properties of the QGP evolution such as the hadronization time, the freeze-out conditions and to characterise its collective motion. In this thesis, the analysis of the balance function for identified particles in proton-proton collisions at √ s = 5.02 TeV collected by the ALICE experiment is presented. The results are shown for pion, kaon and proton pairs in the low transverse momentum range. In addition, a comparison of the data in pp and p-Pb collisions at the same energy is presented. Furthermore, the data in v pp are compared with predictions from two different tunes of the PYTHIA8 Monte Carlo model: with and without color reconnection. This mechanism leads to correlations between particles at the microscopic level due to the string recombination. New findings presented in this work show that balance function results for identified hadrons are not in agreement with the expected effect of collective flow in small systems. Moreover, neither of PYTHIA8 tunes is able to reproduce experimental data.

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Corrections to the Bethe-Bloch formula for average ionization energy loss of relativistic heavy nuclei Close collisions

Cited by 20 publications

References 5 publications

Theoretical and experimental aspects of the energy loss of relativistic heavily ionizing particles

Theoretical and experimental aspects of the energy loss of relativistic heavily ionizing particles

Comparison of the Lindhard–Sørensen and Mott–Bloch Corrections to the Bethe Stopping Formula at Moderately Relativistic Energies

Studies of collective effects in pp collisions at the LHC with the balance function for identified particles

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