@@ -116,7 +116,9 @@ The sample data normalisation is the final step of data reduction of D7 sample,

There are three options for the normalisation; it uses either the input from a reference sample with a well-known cross-section, namely vanadium, or the output from the cross-section separation, either magnetic or spin-incoherent cross-sections. A relative normalisation of the sample workspace to the detector with the highest counts is always performed.

.. math:: S \text{(#,} \pm \text{, chn/t/meV)} = I \text{(#,} \pm \text{, chn/t/meV)} \cdot D \text{(#,} \pm \text{, chn/t/meV)},

.. math::

S (\#, \pm \text{, chn/t/meV)} = I (\#, \pm \text{, chn/t/meV)} \cdot D (\#, \pm \text{, chn/t/meV)},

where `I` is the sample intensity distribution corrected for all effects, and `D` is the normalisation factor.

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@@ -124,17 +126,17 @@ where `I` is the sample intensity distribution corrected for all effects, and `D

If the data is to be expressed in absolute units, the normalisation factor is the reduced vanadium data, normalised by the number of formula units in the sample :math:`N_{S}`:

.. math:: D \text{(#,} \pm \text{, chn/t/meV)} = \frac{1}{N_{S}} \cdot V \text{(#,} \pm \text{, chn/t/meV)}

.. math:: D (\#, \pm \text{, chn/t/meV)} = \frac{1}{N_{S}} \cdot V (\#, \pm \text{, chn/t/meV)}

If data is not to be expressed in absolute units, the normalisation factor depends only on the vanadium input:

This normalisation is not valid for TOF data, and requires input from XYZ or 10-point cross-section separation. The paramagnetic measurement does not need to have background subtracted, as the background is self-subtracted in an XYZ measurement.

.. math:: D \text{(#)} = \frac{2}{3} \frac{(\gamma r_{0})^{2} S(S+1)}{P \text{(#)}},

.. math:: D (\#) = \frac{2}{3} \frac{(\gamma r_{0})^{2} S(S+1)}{P (\#)},

where :math:`\gamma` is the neutron gyromagnetic ratio, :math:`r_{0}` is the electron's classical radius, and S is the spin of the sample.

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@@ -144,11 +146,11 @@ Similarly to the paramagnetic normalisation, it is also not valid for TOF data,

The data can be put on absolute scale if the nuclear-spin-incoherent (NSI) cross-section for the sample is known, then:

.. math:: D \text{(#)} = \frac{\text{d} \sigma_{NSI}}{\text{d} \Omega} \frac{1}{NSI \text{(#)}}.

.. math:: D (\#) = \frac{\text{d} \sigma_{NSI}}{\text{d} \Omega} \frac{1}{NSI (\#)}.

If only the detector efficiency is to be corrected, then it is sufficient to use only the nuclear-spin-incoherent cross-section input:

.. math:: D \text{(#)} = \frac{\text{max}(NSI \text{(#)})}{NSI \text{(#)}}.

.. math:: D (\#) = \frac{\text{max}(NSI (\#))}{NSI (\#)}.