File 14 - Photon Angular Distributions

The purpose of File 14 is to provide a means for representing the angular distributions of secondary photons produced in neutron reactions. Angular distributions should be given for each discrete photon and photon continuum appearing in Files 12 and 13, even if the distributions are isotropic.

The structure of File 14 is, with the exception of the isotropic flag (LI), closely analogous to that of File 4. Angular distributions for a specific reaction type (MT number) are given for a series of incident neutron energies in order of increasing neutron energy. The energy range covered should be the same as that for the data given under the corresponding reaction type in File 12 or File 13. The data are given in ascending order of MT number.

The angular distributions are expressed as normalized probability distributions, that is,

where p_k(μ,E) is the probability that an incident neutron of energy E will result in a particular discrete photon or photon continuum (specified by k and MT number) being emitted into unit cosine about an angle whose cosine is μ. Because the photon angular distribution is assumed to have azimuthal symmetry, the distribution may be represented as a Legendre series expansion,

where

Angular distributions may be given in File 14 by tabulating as a function of incident neutron energy either the normalized probability distribution function

Formats

The following quantities are defined:

ZA,AWR: standard material charge and mass parameters
NI: NI=0, distribution is not isotropic for all photons from this reaction type, but it may be for some photons.
NI=1, distribution is isotopic for all photons from this reaction type.
LTT: LTT=1, data are given as Legendre coefficents, where a₀^k=0 is understood.
LTT=2, data are given as a tabulation.
NK: number of discrete photons including the continuum (must equal the value given in File 12 or 13).
NI: number of isotropic photon angular distributions given in a section (MT number) for which LI=0, a section with at least one anistropic distribution.
NE: number of neutron energy points given in a TAB2 record.
NLI: highest value of l required at each neutron energy EI.
ESK: energy of the level from which photon K originates. If the level is unknown, or if a continuous photon spectrum is produced, then ESK=0.0 should be used.
EGK: photon energy as given in File 12 or 13. For a continuous photon energy distribution, EGK=0.0 should be used .
ALK: Legendre coefficients for photon K, extending from l=1 through NLI. The zeroth coefficient is understood to equal 1.
PK(MU,EI): tabulated angular distribution vs MU for incident energy EI for photon K.

LI=1: Isotropic Distribution

If LI=1, then all photons for the reaction type (MT) in question are assumed to be isotropic. This is a flag that the processing code can sense, and thus needless isotropic distribution data are not entered in the file. In this case, the section is composed of a HEAD card and a SEND card as follows:

     [MAT, 14, MT/ ZA, AWR, LI=1, 0, NK, 0] HEAD
     [MAT, 14, 0/ 0.0, 0.0, 0, 0, 0, 0] SEND

LI=0, LTT=1: Anisotropic Legendre Distribution

The structure of a section with LI=0 and LTT=1 is

     [MAT, 14, MT/ ZA, AWR, LI=0, LTT=1, NK, NI] HEAD
        NK subsections, for K=1, 2, ...,NK
     [MAT, 14, 0/ 0.0, 0.0, 0, 0, 0, 0] SEND

The structure of a subsection in the first block of NI subsections, which is for the NI isotropic photons, is

     [MAT, 14, 0/ EGK, ESK, 0, 0, 0, 0] CONT

There is just one CONT record for each isotropic photon. (The set of CONT records is empty if NI=)). The subsections are ordered in decreasing magnitude of EGK (photon energy), and the continuum, if present and isotropic, appears last with EGK=0.

This block of NI subsections is followed by a block of NK-NI subsections for the anisotropic photons in decreasing magnitude of EGK. The continuum, if present and anisotropic, appears last with EGK=0. The structure for the last NK-NI subsections is

     [MAT, 14, MT/ EGK, ESK, 0, 0, NR, NE/Eint] TAB2
     [MAT, 14, MT/ 0.0, 0.0, 0, 0, NL1, 0/ALK(E1)] LIST
     [MAT, 14, MT/ 0.0, 0.0, 0, 0, NL2, 0/ALK(E2)] LIST
         continue for NE incident energies

Note that ALK(E) starts at l=1 because the zeroth coefficient is always understood to be 1.

LI=0, LTT=1: Anisotropic Tabulated Distribution

The structure of a section with LI=0 and LTT=2 is

     [MAT, 14, MT/ ZA, AWR, LI=0, LTT=2, NK, NI] HEAD
        NK subsections, for K=1, 2, ...,NK
     [MAT, 14, 0/ 0.0, 0.0, 0, 0, 0, 0] SEND

The structure of the first block of NI subsections (where NI may be zero) is the same as for the case of a Legendre representation; i.e., it consists of one CONT record for each of the NI isotropic photons in decreasing order of EGK. The continuum, if present and isotropic, appears last with EGK=0. The structure of the first NI subsections is

     [MAT, 14, 0/ EGK, ESK, 0, 0, 0, 0] CONT

     [MAT, 14, MT/ EGK, ESK, 0, 0, NR, NE/Eint] TAB2
     [MAT, 14, MT/ 0.0, 0.0, 0, 0, NR, NP/MUint/PK(MU,E1)] TAB1
     [MAT, 14, MT/ 0.0, 0.0, 0, 0, NR, NP/MUint/PK(MU,E2)] TAB1
         continue for NE incident energies

Procedures

1. All subsections are given in decreasing magnitude of EGK within each of the isotropic and anisotropic blocks.

2. The convention is that the subsection for the continuum photons, if present, appears last in its block. In this case, EGK=0.0.

3. The values of EGK should be consistent to within four significant figures with the corresponding EGK values in Files 12 and 13. For File 12, Option 2 (transition probability arrays), the values of EGK are implicitly determined by the level energies. 4. ESK is the energy of the level from which the photon originates, if known. Otherwise, ESK=0.0 (as is always the case for the continuum.

See ENDF102, Sections 14.1 and 14.2