.. _gfactors_cena:

=================================
How to calculate g-factor for H
=================================


Introduction
============
G-factor is important in calculating the differential flux from count rate.
Details are written in the :download:`calibration report <../../../src/doc/cena_calibration_issue_1_revision_2.pdf>`.


Theory
======
Theory is written in the calibration report.
In the calibration report, several definition of the g-factor is defined.
Usually, the g-factor is :math:`G_{n,i}^m` (or :math:`G_{n,i}^H`).
This g-factor depends on both energy (i) and sector (n).
Using 3.15, the g-factor can be used to convert between the count rate and the differential flux.

The g-factor can be separated into two part.  Energy-dependent G-factor and sector-dependent part.
The energy dependent g-factor is defined in 3.19.

.. math::

        G_{n,i}^{H} = \sigma{\cdot}A{\cdot}e_{i,H}{\cdot}\Bigl(\frac{\Delta E_i}{E_i}\Bigr)
                {\cdot}[s_n{\cdot}\Delta\Omega_n] = G_i^H {\cdot} [s_n{\cdot}\Delta\Omega_n]


Energy dependent g-factor
=========================
Energy dependent g-factor, :math:`G_{i}^{H}`, can be derived by aggregating
all the parameters that affect to it.

:mod:`pyana.cena.gfactor` module contains two derived classes:
:class:`pyana.cena.gfactor.GFactorH_Table` and
:class:`pyana.cena.gfactor.GFactorH_Component`.
The difference is the way of calculation.
``GFactorH_Table`` trust ``Table 3.5`` in the calibration report,
while ``GFactorH_Component`` starts from primitive parameters.

The method :meth:`energyDependentGfactor <pyana.cena.gfactor.GFactorH_Base.energyDependentGfactor>`
returns the energy dependent g-factor as 16-element ``numpy.ma.MaskedArray``.

In the scripts folder, an example program is placed (cena_ene_gfactor.py).

.. literalinclude:: ../../../src/scripts/cena_ene_gfactor.py
   :linenos:

.. image:: ../../../src/scripts/cena_ene_gfactor.png


G-factor
========
G-factor, :math:`G_{n,i}^{H}`, can be calculated from the energy dependent g-factor.
The :meth:`geometricFactor <pyana.cena.gfactor.GFactorH_Base.geometricFactor>` method returns
the g-factor.  The returned type is ``numpy.ma.MaskedArray`` with element of [7] x [16].

There are a little confusion in the current version (issue 1 revision 1) in the calibration report.
There are three calculatable g-factor values.

1. Using the energy dependent g-factor first, and derive g-factor (:class:`pyana.cena.gfactor.GFactorH_Table`)
2. Using the energy dependent g-factor first, and derive g-factor (:class:`pyana.cena.gfactor.GFactorH_Component`)
3. Values listed in Table, only for CH-3. (Not implemented as module)

The methods 1 and 2 has little difference, while they
returns ~10% larger than the g-factor (3) listed in the last column in Table 3.15
(version ``v1.3+feature/cena_gfactor``).
This is to be investigated.


.. literalinclude:: ../../../src/scripts/cena_gfactor_ch3.py
   :linenos:

.. image:: ../../../src/scripts/cena_gfactor_ch3.png

Date
====
2011.01.06

See also
========
:ref:`gfactor_matrix` section for advanced g-factor analysis.