last modified: 01-JUL-1964 | catalog | categories | new | search |

NESC0056 SUMMIT.

SUMMIT, Energy Transfer Diffusion Cross-Sections, Crystalline Moderator, Phonon Expansion

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1. NAME OR DESIGNATION OF PROGRAM:  SUMMIT.
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2. COMPUTERS
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Program name Package id Status Status date
SUMMIT NESC0056/01 Tested 01-JUL-1964

Machines used:

Package ID Orig. computer Test computer
NESC0056/01 IBM 7090 IBM 7090
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3. NATURE OF PHYSICAL PROBLEM SOLVED

The program evaluates the differential energy-transfer cross section for scattering by a crystalline moderator, utilizing the so-called phonon expansion. The scattering kernel for a 1-phonon change in energy is added to that for a 2-phonon energy exchange, and so on. This program has been used to determine scattering matrices for beryllium, graphite, and oxygen. Sigma(E(0) to E)/sigma(0)=(((M+1)/M)**2) * SQRT(E/E(0)) * 1/2 the integral from -1 to 1 of sigma(E(0) to E,cos(theta)) D(COS(theta)) where E(0) and E are the initial and final energies, theta is the angle of scattering, sigma(0) the free-atom cross section, and M the ratio of the mass of the scattering nucleus to that of the neutron.
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4. METHOD OF SOLUTION

The general method used to evaluate the scattering kernel involves two different expansions. The one that is to be used for given initial and final energies and for a given angle of scattering is determined by the magnitude of the free-atom recoil energy, (K*K)/2M. If (K*K)/2M is smaller than some quantity which is controlled by input, we use the phonon expansion. Each of the first N(PHO) terms in this expan- sion, where N(PHO) is an input number, is computed by numerically performing the convolution integral which determines the N-phonon cross section. The terms of order N greater than N(PHO) are approximated by means of the central-limit theorem. For larger values of (K*K)/2M, we use the short-collision-time approximation for the low-frequency modes, making the phonon expansion only for the high-frequency modes. In this case, the central-limit theorem is used to approximate the contributions from the high-frequency modes for all values of N.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM
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6. TYPICAL RUNNING TIME

  -----------------------------------------------------------
                no. of energy   temp.     time*     no. of
     type          points      (deg. K) (centihr.)  E(o) to E
  -----------------------------------------------------------
  L-dependent   10 to 0.50 eV    300       4.6        55
  isotropic
   crystal      10 to 0.50 eV    300       1.9        55
  -----------------------------------------------------------
        *total time to load = 36 seconds
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7. UNUSUAL FEATURES: UNUSUAL FEATURES OF THE PROGRAM
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8. RELATED OR AUXILIARY PROGRAMS: RELATED AND AUXILIARY PROGRAMS
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9. STATUS
Package ID Status date Status
NESC0056/01 01-JUL-1964 Tested at NEADB
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10. REFERENCES

- Joan Bell:
  SUMMIT - An IBM-7090 Program for the Computation of Crystalline Scattering Kernels.
  GA-2492, February 1962.
- D.E. Parks:
  The Calculation of Thermal Neutron Scattering Kernels in Graphite.   GA-2438, October 10, 1961
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11. HARDWARE REQUIREMENTS: MACHINE REQUIREMENTS
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0056/01 FORTRAN+FAP
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13. SOFTWARE REQUIREMENTS: OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM IS EXECUTED
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

ANY OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS
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15. NAME AND ESTABLISHMENT OF AUTHOR

                 Joan Bell
                 Gulf General Atomic Incorporated
                 P. O. Box 608
                 San Diego, California  92112
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16. MATERIAL AVAILABLE
NESC0056/01
File name File description Records
NESC0056_01.001 SOURCE & DATA 3397
NESC0056_01.002 OUTPUT 5017
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17. CATEGORIES
  • A. Cross Section and Resonance Integral Calculations

Keywords: beryllium, cross sections, crystals, graphite, moderators, oxygen, scattering.