Legendre polynomial expansion for the Klein-Nishina formula for nonstationary electrons

Webster, Joseph B.; Stephan, Brian G.; Bridgman, Charles J.

doi:10.1016/0021-9991(74)90003-5

Cited by 10 publications

(4 citation statements)

References 6 publications

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“…As before, for v --+ 0, (59) (6o) (63) Effective q-2 Kernel With a differential cross section dependency on inverse energy, n constant,…”

Section: V2r(3/2)+"-lr(5/2)]mentioning

confidence: 83%

“…Numerical techniques are requisite to generate the total effective cross, ~r~. Computer programs (62,63) are available to produce momemtum integrated differential and total photon electron cross sections. Turning to the effective differential cross, a number of interesting cases result for various forms of the background electron distribution, ~.…”

Section: K2(m/kt)mentioning

confidence: 99%

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Transport equations in moving material Part I: Neutrons and photons

Wienke

2005

Progress in Nuclear Energy

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“…As before, for v --+ 0, (59) (6o) (63) Effective q-2 Kernel With a differential cross section dependency on inverse energy, n constant,…”

Section: V2r(3/2)+"-lr(5/2)]mentioning

confidence: 83%

Section: K2(m/kt)mentioning

confidence: 99%

Transport equations in moving material Part I: Neutrons and photons

Wienke

2005

Progress in Nuclear Energy

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“…For inelastic scattering up to about 100 keV, the KN factor has a rapidly convergent Legendre series [24]. The total differential cross section is given by the sum of elastic and inelastic contributions, namely,…”

Section: Transfer Of Cross Section For Smoothingmentioning

confidence: 99%

“…The number may be estimated the rapidity with which the Legendre coefficients of the KN distribution approach zero. The formulas for these coefficients with numerical values were published over 50 years ago [24]. For 100 keV, the series is rapidly convergent, dropping off by about a factor of 10 for each .…”

Section: Transfer Of Cross Section For Smoothingmentioning

confidence: 99%

Scatter Corrections in X-Ray Computed Tomography: A Physics-Based Analysis

Levine

Blattner

Peskin

et al. 2019

J. RES. NATL. INST. STAN.

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Fundamental limits for the calculation of scattering corrections within X-ray computed tomography (CT) are found within the independent atom approximation from an analysis of the cross sections, CT geometry, and the Nyquist sampling theorem, suggesting large reductions in computational time compared to existing methods. By modifying the scatter by less than 1 %, it is possible to treat some of the elastic scattering in the forward direction as inelastic to achieve a smoother elastic scattering distribution. We present an analysis showing that the number of samples required for the smoother distribution can be greatly reduced. We show that fixed forced detection can be used with many fewer points for inelastic scattering, but that for pure elastic scattering, a standard Monte Carlo calculation is preferred. We use smoothing for both elastic and inelastic scattering because the intrinsic angular resolution is much poorer than can be achieved for projective tomography. Representative numerical examples are given.

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Maxwell: Exact photon cross-section processor for relativistic Maxwellian electrons

Lathrop

Wienke

1984

Computer Physics Communications

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Legendre polynomial expansion for the Klein-Nishina formula for nonstationary electrons

Cited by 10 publications

References 6 publications

Transport equations in moving material Part I: Neutrons and photons

Transport equations in moving material Part I: Neutrons and photons

Scatter Corrections in X-Ray Computed Tomography: A Physics-Based Analysis

Maxwell: Exact photon cross-section processor for relativistic Maxwellian electrons

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