Energy-Loss Effect in K-Shell Ionization

Mukoyama, Takeshi

doi:10.1142/s0129083598000261

Cited by 5 publications

(10 citation statements)

References 13 publications

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“…Indeed, Mukoyama has already demonstrated this to be the case. 51 Moreover, in the 0.12 < < 0.6 range, his cross sections for Cu, Ag, Au and U calculated with the exact limits for the momentum transfer and the Dirac hydrogenic wavefunctions exceeded-in line what is seen in Fig. 4-the results of the PWBA calculation that included the energy loss and relativistic effects according to the prescription of the ECPSSR theory.…”

Section: The Eecpsshsr Theorysupporting

confidence: 68%

“…This indicates that the Brandt-Lapicki method for correction of the electronic relativistic effect should be used only with their energy-loss method' (the italic added for emphasis). 51 As seen in Fig. 5, the ECPSSR tables of Cohen and Harrigan 57 and the ECPSSR codes 26,58 that evaluate innershell cross sections with the exact momentum transfer limits overestimate the ECPSSR cross sections; at worse this miscalculation for K-shell ionization of uranium due to less the 1-MeV protons leads to almost a 30% overestimate.…”

Section: The Eecpsshsr Theorymentioning

confidence: 97%

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The status of theoretical K‐shell ionization cross sections by protons

Lapicki

2005

X-Ray Spectrometry

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The accuracy of PIXE analysis depends on inner-shell ionization cross sections that are often calculated in the ECPSSR theory which accounts with analytical functions for the energy (E) loss and Coulomb (C) deflection of the projectile plus for the perturbed-stationary state (PSS) and relativistic (R) nature of the target's inner shell. Although the ECPSSR is within 10% overall agreement with the K-shell data -as the proton energy falls below 0.1 to 1 MeV, respectively, in ionization of light-to heavy-target atoms -the ECPSSR increasingly overestimates the empirical database of Paul and Sacher (1989). Except for an enhancement of this overestimate at low energies, a modified ECPSSR based on the Chen-Crasemann (1985, 1989) plane wave Born approximation -evaluated with the exact limits for the momentum transfers and the Dirac-Hartree-Slater wavefunctions -yields cross sections that remain within 10% of the data and the ECPSSR theory. Codes that use only the exact limits instead of the energy-loss function are confirmed to be improper for evaluation of the ECPSSR. Further enhancement of the cross sections at the low energies is limited to light target atoms after the function derived in the separated atom approach to account for the PSS effect is joined with an expression obtained in the united atom limit. An empirical database, updated with cross sections from post-1989 publications, is normalized to the modified ECPSSR theory and various forms of the Coulomb deflection factor are revisited.

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Section: The Eecpsshsr Theorysupporting

confidence: 68%

Section: The Eecpsshsr Theorymentioning

confidence: 97%

The status of theoretical K‐shell ionization cross sections by protons

Lapicki

2005

X-Ray Spectrometry

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“…However, it should be noted that the cross section σ PWBA K (θ, η) is calculated with approximate limits of momentum transfer and the correction for the energy-loss effect is made through the parameter z K . We have shown [27] that when the relativistic correction is made through m R η in f (θ, η) with the exact limits of momentum transfer, called the CPSSR model, the electronic relativistic effect [14], and the squares the SLBA by Reading et al [15]. is overestimated at low energies and gives larger values for σ PWBA K (θ, η).…”

Section: Resultsmentioning

confidence: 99%

K-shell ionization cross sections of atoms by muons and pions

Mukoyama

Tőkési

2019

Eur. Phys. J. D

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The K-shell ionization cross sections of copper and silver atoms by muons and pions with negative and positive charge have been calculated with the classical trajectory Monte Carlo method and the planewave Born approximation with corrections for the Coulomb-deflection and binding-energy effects. Both results are in good agreement with each other. The obtained cross sections for muons on copper are also compared with the coupled-channels calculations. The dependence of the K-shell ionization cross sections on the sign of the projectile as well as on the projectile mass is discussed.

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“…Correct eCPSSR (equations (14) or (15)): the CPSSR cross sections using correct integration limits. Wrong eCPSSR (equation 13 Similar to Mukoyama [22], we shall rely on the criterion which type of calculation agrees better with the RPWBA values. In order to make the comparison possible, we calculated the cross section with exact limits on the momentum transfer and with the parameter θ S corrected for the PSS effect and multiplied the result by the Coulomb deflection factor (therefore the acronym eRPWBA-CPSS).…”

Section: Resultsmentioning

confidence: 99%

“…This recipe was not followed in the early cross section tabulation by Cohen and Harrigan [19] and the original ISICS code by Liu and Cipolla [20]. At low projectile velocities, a marked discrepancy was soon observed between the tabulated values [19,20] and the ECPSSR cross sections [21,22]. It was even believed that all codes using exact integration limits are incorrect and that only the original ECPSSR theory using the f S -function should be used [22].…”

Section: Introductionmentioning

confidence: 99%

Energy loss in the ECPSSR theory and its calculation with exact integration limits

Šmit¹,

Lapicki²

2014

J. Phys. B: At. Mol. Opt. Phys.

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ECPSSR cross sections for inner-shell ionization are compared with numerical calculations that use correct and wrong expressions for exact limits of momentum transfer. For very adiabatic collisions, the employment of the wrong expression, as done in several popularly utilized computer codes, overestimates the cross sections up to two orders of magnitude. By contrast, even in such collisions the original ECPSSR approach of Brandt and Lapicki that approximates the effect of projectile energy loss by a multiplicative correction function f S and the relativistic effects by a relativistically corrected electron mass yields cross sections that are in agreement within a factor of two with respect to the calculation with hydrogenic Dirac wavefunctions and exact limits of integration with no relativistic correction. For plane-wave Born approximation calculations, the relativistic corrected expressions of the exact limits of integration are presented. The cross section calculated with such limits differs from the ECPSSR calculation using the f S-function by less than 2% in the region of lowest collision velocities covered by experiments. A straightforward modification of the existing computer codes with the correct expression for exact momentum transfer is suggested.

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Energy-Loss Effect in K-Shell Ionization

Cited by 5 publications

References 13 publications

The status of theoretical K‐shell ionization cross sections by protons

The status of theoretical K‐shell ionization cross sections by protons

K-shell ionization cross sections of atoms by muons and pions

Energy loss in the ECPSSR theory and its calculation with exact integration limits

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