Definition of Anomalous Scattering Factors

Different authors use different definitions of anomalous scattering factors (see, below). Our scattering factors are defined in terms of how they are used to define our photon coherent scattering cross section, d[Sig(E,Z,cos)]/d[cos] = R(Z)*[1 + cos^2][{FF + f1}^2 + {f2)^2] where,d[Sig(E,Z,cos)]/d[cos]= Angular Distribution of Coherently Scattering PhotonsZ= Element Atomic NumberE= Photon Incident Energycos= Cosine of the Scattering AngleR(Z)= Element Dependent normalization[1 + cos^2]= Rayleigh Scattering FormulaFF= Form Factor = Z in the Forward directionf1= Real Anomalous Scattering Factor (or f’)f2= Imaginary Anomalous Scattering Factor or f’’) At low photon incident energy our f1 is defined to approach the negative of the Form Factor, i.e., the Form Factor (FF) Approaches Z and f1 approaches -Z. At very high energy the Anomalous Scattering factors approach zero, and the Angular Distribution of Coherently Scattered Photons approaches a simple limit defined only in terms of Form Factors, d[Sig(E,Z,cos)]/d[cos] = R(Z)*[1 + cos^2][FF]^2 WARNING - other authors use different definitions of Anomalous Scattering Factors, such as, d[Sig(E,Z,cos)]/d[cos] = R(Z)*[1 + cos^2][{FF - f1}^2 + {f2)^2] In which f1 approaches Z at low energy, which differs from our definition merely in sign. Another definition is, d[Sig(E,Z,cos)]/d[cos] = R(Z)*[1 + cos^2][{f1}^2 + {f2)^2] In which f1 approaches zero at low energy, which differs from our definition by Z.

Format of Anomalous Scattering Factors

Our Anomalous Scattering Factors are given here in a simple, tabulated, fixed field, text format, that can be read by any text editor, as well as any computer application code. Each field is 10 columns wide (WARNING - fields are all 10 columns wide and not blank or in any other way delimited). The format is illustrated below using the hydrogen data. The first line defines, 1) The Atomic Number of the Element (Z = 1 for hydrogen) 2) The Number of Tabulated Energy Points (361) 3) The Atomic Weight of the Naturally Occurring Element (1.008) 4) The STP Density in grams/cc (8.988e-5) 5) Definition of the Element in text (1-H -Nat) The Second Line contains titles for each Column 1) MeV - the units of Energy 2) F1-Total - Total f1 (sum of ionization and excitation) 3) Z+F1 - In this form it is easier to see FF+F1 approaching zero at low energy. 4) F1-Ionize - Contribution of Ionization to f1 5) F1-Excite - Contribution of Excitation to f1 6) F2-Total - Total f2 (sum of ionization and excitation) 7) F2-Ionize - Contribution of Ionization to f2 8) F2-Excite - Contribution of Excitation to f2 9) Coherent (barns) - Coherent Cross Section defined by integrating the above equation. The following lines contains data at a series of given energy points, in ascending energy order, from 1 eV up to 10 MeV. The number of lines (given energies) is defined by the number of tabulated energy points on the first line of the table. 1 361 1.00800+0 8.98800-5 1-H -Nat Mev F1-Total Z+F1 F1-Ionize F1-Excite F2-Total F2-Ionize F2-Excite Coherent (barns) 1.00000-6-1.00613+0-6.12925-3-4.35753-1-5.70376-1 0.0 0.0 0.0 1.23363-5 1.50000-6-1.00148+0-1.47720-3-4.37476-1-5.64001-1 0.0 0.0 0.0 1.66856-6 1.68750-6-9.99023-1 9.76798-4-4.38122-1-5.60901-1 0.0 0.0 0.0 9.64288-7 . . . 7.40374+0-2.66551-5 9.99973-1-2.66551-5 0.0 4.2773-12 4.2773-12 0.0 8.43954-8 8.90125+0-2.66551-5 9.99973-1-2.66551-5 0.0 3.5966-12 3.5966-12 0.0 5.83874-8 1.00000+1-2.66551-5 9.99973-1-2.66551-5 0.0 3.2284-12 3.2284-12 0.0 4.62616-8 This data is designed to be linearly interpolated between tabulated energies.

Example Simple FORTRAN code to Read a Table

IMPLICIT REAL*8 (A-H,O-Z) CHARACTER*10 SYMBOL, TITLES(9) DIMENSION DATA(8) C-----OPEN HYDROGEN FILE TO READ OPEN(10,FILE=’ZA001000’) C-----READ FIRST LINE READ(10,1000) IZ, NPOINT, ATWT, DENSITY, SYMBOL 1000 FORMAT(2I10,2D10.3,A10) C-----READ COLUMN TITLES READ(10,1010) TITLES 1010 FORMAT(9A10) C-----READ ALL DATA POINTS DO IPOINT = 1, NPOINT READ(10,1020) ENERGY,DATA 1020 FORMAT(9D10.3) . . (USE THE DATA IN ANY WAY THAT YOU WISH) . . ENDDO STOP END