**14. 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
interactions. 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 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.

![](media/image1.wmf)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 energy 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,

![](media/image2.wmf)

where

μ = cosine of the reaction angle in the lab system,

E = energy of the incident neutron in the laboratory system,

> σ~k~^γ^(E) = photon production cross section for the discrete photon
> or photon continuum specified by k, as given in either File 13 or in
> File 2, 3, and 12 combined,

*l* = order of the Legendre polynomial,

dσ~k~^γ^/dΩ = differential photon production cross section in
barns/steradian,

> a*~l~*^k^(E) = the *l*‑th Legendre coefficient associated with the
> discrete photon or photon continuum specified by k. (It is understood
> that a*~0~*^k^(E) ≡ 1.0.)

![](media/image3.wmf)Angular distributions may be given in File 14 by
tabulating as a function of incident neutron energy either the
normalized probability distribution function, p~k~(μ,E), or the Legendre
polynomial expansion coefficients, a*~l~*^k^(E). Provision is made in
the format for simple flags to denote isotropic angular distributions,
either for a block of individual photons within a reaction type or for
all photons within a reaction type taken as a group.

Note that File 14 assumes separability of the photon energy and angular
distributions for the ***continuum*** spectrum. If this is not the case,
File 16 (analogous to File 6) must be used instead of Files 14 and 15.
(Since File 14 implicitly specifies an energy‑angle distribution for
discrete photons, File 16 is required only for the continuum spectrum).

**14.1. Formats**

As usual, sections are ordered by increasing reaction type (MT) numbers.
The following definitions are required.

+----------+-----------------------------------------------------------+
| **LI**   | LI=0, distribution is not isotropic for all photons from  |
|          | this reaction type, but may be for some photons.          |
|          |                                                           |
|          | LI=1, distribution is isotropic for ***all*** photons     |
|          | from this reaction type.                                  |
+----------+-----------------------------------------------------------+
| **LTT**  | LTT=1, data are given as Legendre coefficients, where     |
|          | a*~0~*^k^(E) ≡ 1.0 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, *i.e.*, a section |
|          | with at least one anisotropic distribution.               |
+----------+-----------------------------------------------------------+
| **NE**   | Number of neutron energy points given in a TAB2 record.   |
+----------+-----------------------------------------------------------+
| *        | Highest value of *l* required at each neutron energy      |
| *NL~i~** | E~i~.                                                     |
+----------+-----------------------------------------------------------+
| *        | Energy of the level from which the photon originates.     |
| *ES~k~** |                                                           |
|          | If the level is unknown or if a continuous photon         |
|          | spectrum is produced, then ES~k~=0.0 should be used.      |
+----------+-----------------------------------------------------------+
| *        | Photon energy as given in File 12 or 13.                  |
| *EG~k~** |                                                           |
|          | For a continuous photon energy distribution, EG~k~,=0.0   |
|          | should be used.                                           |
+----------+-----------------------------------------------------------+

**a. 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:

\[MAT, 14, MT/ ZA, AWR, LI, 0, NK, 0\] HEAD (LI=1)

\[MAT, 14, 0 / 0.0, 0.0, 0, 0, 0, 0\] SEND

**b. LI=0: Anisotropic Distribution**

If LI=0, there are two possible structures for a section, depending upon
the value of LTT.

**i. LTT=1: Legendre Coefficient Representation**

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

\[MAT, 14, MT/ ZA, AWR, LI, LTT, NK, NI\] HEAD (LI=0, LTT=1)

\<subsection for k=1\>

\<subsection for k=2\>

\...\...\....

\...\...\....

\...\...\....

\<subsection for k=NK\>

\[MAT, 14, 0/ 0.0, 0.0, 0, 0, 0, 0\] SEND

The structure of each record in the first block of NI subsections, which
is for the NI isotropic photons, is

\[MAT, 14, MT/ EG~k~, ES~k~, 0, 0, 0, 0\] CONT

There is just one CONT record for each isotropic photon. (The set of
CONT records is empty if NI=0). The subsections are ordered in
decreasing magnitude of EG~k~ (photon energy), and the continuum, if
present and isotropic, appears last, with EG~k~=0.0.

This block of NI subsections is then followed by a block of NK‑NI
subsections for the anisotropic photons in decreasing magnitude of
EG~k~. The continuum, if present and anisotropic, appears last, with
EG~k~=0.0. The structure for the last NK‑NI subsections is

\[MAT, 14, MT/ EG~k~, ES~k~, 0, 0, NR, NE/ E~int~ \] TAB2

\[MAT, 14, MT/ 0.0, E~1~, 0, 0, NL~1~, 0/ a~l~^k^(E~1~)\] LIST

\[MAT, 14, MT/ 0.0, E~2~, 0, 0, NL~2~, 0/ a~l~^k^(E~2~)\] LIST

> **\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--**
>
> **\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--**
>
> **\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--**

\[MAT, 14, MT/ 0.0, E~NE~, 0, 0, NL~NE~, 0/ a~l~^k^(E~NE~)\] LIST

Note that lists of the a*~l~*^k^(E) start at *l*=1 because a*~0~*^k^(E)
≡ 1.0 is always understood.

**ii. LTT=2: Tabulated Angular Distributions**

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

\[MAT, 14, MT/ ZA, AWR, LI, LTT, NK, NI\] HEAD (LI=0, LTT=2)

\<subsection for k=1\>

\<subsection for k=2\>

> \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--
>
> \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--
>
> \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

\<subsection for k=NK\>

\[MAT, 14, 0/ 0.0, 0.0, 0, 0, 0, 0\] SEND

The structure of the first block of NI subsection (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 magnitude of EG~k~. The continuum, if present and isotropic,
appears last, with EG~k~ ≡ 0.0.

# The structure of the first Ni subsections is

\[MAT, 14, MT/ EG~k~, ES~k~, 0, 0, 0, 0\] CONT

This block of NI subsections is then followed by a block of NK‑NI
subsections for the anisotropic photons, again in decreasing magnitude
of EG~k~, with the continuum, if present and anisotropic, appearing
last, with EG~k~ ≡ 0.0.

## The structure of the last NK‑NI subsections is

\[MAT, 14, MT/ EG~k~, Es~k~, 0, 0, NR, NE/ E~int~ \] TAB2

\[MAT, 14, MT/ 0.0, E~1~, 0, 0, NR, NP/ μ~int~ / p~k~(μ,E~1~)\] TAB1

\[MAT, 14, MT/ 0.0, E~2~, 0, 0, NR, NP/ μ~int~ / p~k~(μ,E~2~)\] TAB1

\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

\[MAT, 14, MT/ 0.0, E~NE~, 0, 0, NR, NP/ μ~int~ / p~k~(μ,E~NE~)\] TAB1

**14.2. Procedures**

1\. The subsections are given in decreasing magnitude of EG~k~ within
each of the isotropic and anisotropic blocks.

2\. The convention is that the subsection for the continuous photon
spectrum, if present, appears last in its block. In this case, EG~NK~ ≡
0.0.

3\. The values of EG~k~ should be consistent within four significant
figures with the corresponding EG~k~ values in File 12 or 13. File 12,
Option 2 (transition probability arrays), the values of EG~k~ are
implicitly determined by the level energies.

4\. ES~k~ is the energy of the level from which the photon originates,
if known. Otherwise, ES~k~=0.0 (as is always the case for the
continuum).

5\. Data should not appear in File 14 for photons that do not have
production data given in File 12 or 13. Conversely, for every photon
appearing in File 12 or 13 an angular distribution must be given in File
14. The neutron energy range for which the angular distributions are
given should be the same as that for which the photon production data
are given in File 12 or 13.

6\. For LTT=1 (Legendre coefficients), the value of NL should be the
minimum number of coefficients that will reproduce the angular
distribution with sufficient accuracy and be positive everywhere. In all
cases, NL should be an even number, ≤20.

7\. The TAB1 records for the p~k~(μ,E~i~) within a subsection are given
in increasing order of neutron energy, E~i~.

8\. The tabulated probability functions, p~k~(μ,E~i~), should be
normalized within four significant figures (to unity).

9\. The interpolation scheme for p~k~(μ,E) with respect to E must be
linear‑linear or log‑linear (INT=2 or 4) to preserve normality of the
interpolated distributions. It is recommended that the interpolation in
μ be linear‑linear (INT=2).

10\. For Li=1 (isotropic distribution), the parameter NK is the number
of photons in that section and should be consistent with the NK values
in Files 12 and 13.

11\. The minimum amount of data should be used that will accurately
represent the angular distribution as a function of both m and E.

12\. If all photons for a reaction type (MT number) are isotropic, the
LI=1 flag should be used. The use of LI=0 and NI=NK is strongly
discouraged. Likewise, isotropic distributions should not be entered
explicitly as a tabulation or as a Legendre expansion with a*~l~*^k^(E)
≡ 0, *l* ≥ 1.

13\. Angular distributions for photons must be given for all discrete
and continuum photons. This can be done by specifying the data
explicitly (by giving distributions) or implicitly by using a flag
meaning that all photons for a particular reaction (MT number) are
isotropic. Isotropic angular distributions should be specified unless
the anisotropy is ≥ 20%.