.. _sec-a-distribution:

Definition of angular distribution
--------------------------------------------------

When **dir = data** is specified, an angular-distribution subsection starting with **a-type =** as shown below is required.
Items with (D=***) are omissible.

a-type = 1, (11)
^^^^^^^^^^^^^^^^^

An arbitrary angular distribution is specified by giving angular boundary points **a(i)** and the integrated value of the source particle generation probability **w(i)** in each bin.
The boundary points are given in :math:`\cos` for 1 and in degrees for 11.
The integral number of particles generated in each bin is proportional to **w(i)**.
For continuous energy distribution with double differential type (e-type = 41, 42, 51, 52), if all w(i) are set to 0, the angular distribution specified by the e-type is used as is.

**na =**: Number of angular groups.
Data are given in free format as follows.

``(a(i), w(i), i = 1, |na|), a(|na|+1)``

a-type = 4, (14)
^^^^^^^^^^^^^^^^^

The same angular distribution as **a-type = 1, (11)** is generated.
However, whereas **a-type = 1, (11)** represents the angular distribution by adjusting the number of generated particles, **a-type = 4, (14)** represents it by generating the same number of particles in all angular bins and making the integrated particle weight in each bin equal to **w(i)**.
For continuous energy distribution with double differential type (e-type = 41, 42, 51, 52), if all w(i) are set to 0, the angular distribution specified by the e-type is used as is.
The boundary points are given in :math:`\cos` for 4 and in degrees for 14.
The integral number of particles generated in each bin is proportional to **q(i)**.

**na =**: Number of angular groups.
Data are given in free format as follows.

``(a(i), w(i), i = 1, |na|), a(|na|+1)``

By default, **q-type = 0**, the same number of particles is generated in each bin.
When **q-type = 1** and **q(i)** is specified, the integrated number of generated particles in each bin is proportional to those values.

**q-type = 0, 1**: Generation-number option, D = 0.

- For 0, **q(i)=1** in all bins, and there is no following data.
- For 1, the generation number ratio **q(i)** in each bin is given in the following line.

(q(i), i = 1, na)

a-type = 5, (15)
^^^^^^^^^^^^^^^^^

The angular distribution, :math:`d\varphi/d\Omega`, is given by an arbitrary function **g(x)**.
The boundary points are given in :math:`\cos` for 5 and in degrees for 15.

**g(x) =**: A function written in Fortran format.
Here, **x** represents the angle.
Internal variables and constants can be used.
Example: **g(x) = exp(-c1*x**2)**.

**nn =**: Number of angular groups.

**ag1 =**: Lower cutoff value of the angular distribution.

**ag2 =**: Upper cutoff value of the angular distribution.

a-type = 6, (16)
^^^^^^^^^^^^^^^^^

The same angular distribution as **a-type = 5, (15)** is generated.
However, whereas **a-type = 5, (15)** represents the angular distribution by adjusting the number of generated particles, **a-type = 6, (16)** represents it by generating the same number of particles in all angular bins and changing particle weights in proportion to the arbitrary function :math:`g(x)`.
The boundary points are given in :math:`\cos` for 6 and in degrees for 16.

**g(x) =**: A function written in Fortran format.
Here, **x** represents the angle.
Internal variables and constants can be used.
Example: **g(x) = exp(-c1*x**2)**.

**nn =**: Number of angular groups.
By default, **q-type = 0**, the same number of particles is generated in each bin.
When **q-type = 1** and **q(i)** is specified, the integrated number of generated particles in each bin is proportional to those values.

**ag1 =**: Lower cutoff value of the angular distribution.

**ag2 =**: Upper cutoff value of the angular distribution.

**q-type = 0, 1**: Generation-number option, D = 0.

- For 0, **q(i)=1** in all bins, and there is no following data.
- For 1, the generation number ratio **q(i)** in each bin is given in the following line.

(q(i), i = 1, nm)