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NEA-0593 FPSPH. DFPSPH.

FPSPH DFPSPF, Line Shape Function for Doppler Broadened Resonance Cross-Sections Calculation

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1. NAME OR DESIGNATION OF PROGRAM:  FPSPH, DFPSPH. (FPSPH (single- precision), DFPSPH (double precision)).
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2. COMPUTERS
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Program name Package id Status Status date
FPSPH/DFPSPH NEA-0593/01 Tested 28-JUN-1982

Machines used:

Package ID Orig. computer Test computer
NEA-0593/01 IBM 370 series IBM 370 series
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3. DESCRIPTION OF PROBLEM OR FUNCTION

In the computation of Doppler-  broadened resonance cross sections, use is made of the symmetric and anti-symmetric line shape functions. These functions usually denoted as Psi and Phi (Psi and Chi in Anglo-Saxon formalism) are defined in terms of the real and imaginary parts of the error function for complex arguments. They are the product of the convolution of a Gaussian function with the symmetric and anti-symmetric Breit-Wigner functions, respectively.  FPSPH and DFPSPH compute these functions.
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4. METHOD OF SOLUTION

For (1+x**2) > 20 Beta**2, the calculation is based upon the asymptotic expansion:

Psi+(i*Phi) = 1/(1-ix)*(1-t+3t**2-3.5t**3+3.5+7t**4---)

with:  t = 1/(2z**2)   z = (1-ix)/Beta

The half-plane (Beta,x) is split in several parts, and use is made of PADE approximants.

For 1 + x**2 < 20 Beta**2, the calculation is based upon the relation with the erf function:

Psi + i*Phi = SQRT(Pi)/Beta*(e**(z**2))*(1-erf(z))

(z = (1-ix)/Beta, and erf(z) being calculated from its analytic expansion:

erf(z) = 2/SQRT(Pi)*z*e**(-z**2)*(1+z**2/3+z**4/(3*5)
         +z**6/(3*5*7)+---)

PADE approximants are used to compute the expansion and e**z**2.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:  No restriction.
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6. TYPICAL RUNNING TIME

Very much depending upon the values of (Beta,x).  See report.
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7. UNUSUAL FEATURES OF THE PROGRAM:
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8. RELATED AND AUXILIARY PROGRAMS

Related programs are MC2-2 and FSDP-3 which treat the same kind of problem.
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9. STATUS
Package ID Status date Status
NEA-0593/01 28-JUN-1982 Screened
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10. REFERENCES

- For FPSPH, DFPSPH,
  Rapport interne SERMA-T-382-CEN-Saclay (revised November 1979).
- D.R. Mathews:
  "FSDP3. A Computer Program for Computing Cross Sections for
  Resonance Parameters"
  Gulf-GA-A12052 (1972).
- H. Henryson II et al.:
  "MC2-2.  A Code to Calculate Fast Neutron Spectra and Multigroup
  Cross Sections"
  ANL-8144 (ENDF 239) (1976).
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11. MACHINE REQUIREMENTS:
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NEA-0593/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:
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15. NAME AND ESTABLISHMENT OF AUTHOR: , P. Ribon, CEN/Saclay, France.
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16. MATERIAL AVAILABLE
NEA-0593/01
File name File description Records
NEA0593_01.001 FPSPH SUBROUTINE 220
NEA0593_01.002 DFPSPH SUBROUTINE 246
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17. CATEGORIES
  • A. Cross Section and Resonance Integral Calculations
  • P. General Mathematical and Computing System Routines

Keywords: Breit-Wigner formula, Doppler broadening, Gauss function, cross sections, error function, resonance absorption, resonance scattering.