(sw-neutron)=

# sw_neutron

## Syntax
  
`spectra = sw_neutron(spectra,Name,Value)`
  
## Description
  
`spectra = sw_neutron(spectra,Name,Value)` calculates the neutron
scattering cross section for polarised and unpolarised neutrons. The
function reads the calculated spin-spin correlation function
$\mathcal{S}^{\alpha\beta}(\mathbf{Q},\omega)$ and calculates the neutron
scattering cross section for unpolarized neutrons using the formula:
 
$$S_\perp(Q,\omega)=\sum_{\alpha\beta}(1-\hat{q}^\alpha\hat{q}^\beta)\cdot S^{\alpha\beta}(Q,\omega)$$
   
It also calculates spin-spin correlation function in the Blume-Maleev
coordinate system and the complete polarised neutron scattering cross
section.
  
{% include note.html content=" The Blume-Maleev coordinate system is a cartesian coordinate
system with $x_{BM}$, $y_{BM}$ and $z_{BM}$ basis vectors defined as:
<br> $x_{BM}$    parallel to the momentum transfer $Q$,
<br> $y_{BM}$    perpendicular to $x_{BM}$ in the scattering plane,
<br> $z_{BM}$    perpendicular to the scattering plane.
" %}
 
## Input Arguments
  
`spectra`
: Input structure, contains spin-spin correlation functions. Supported
  inputs are produced by [spinw.spinwave](#spinw-spinwave), [spinw.powspec](#spinw-powspec) and
  [spinw.scga].
  
## Name-Value Pair Arguments
  
`'n'`
: Normal vector to the scattering plane, in real space ($xyz$
  coordinate system), stored in a row vector with 3 elements. Default
  value is `[0 0 1]`.
 
`'uv'`
: Cell, that contains two vectors defining the scattering 
  plane in rlu. If given overwrites the `n` parameter value. For example:
  `{[1 0 0] [0 1 0]}` stands for the $(h,k,0)$ scattering plane.
  
`'pol'`
: If `true` the cross sections in the Blume-Maleev
  coordinate system will be also calculated (`inP`, `Pab` and `Mab`
  fields of the output `spectra`). Default value is `false`.
  
## Output Arguments
  
`spectra`
: Same as the input `spectra` plus the following additional fields:
  * `param`   Input parameters.
  * `Sperp`   $S_\perp(i_{mode},\mathbf{Q})$ unpolarised neutron 
              scattering cross section, stored in a matrix with
              dimensions of $[n_{mode}\times n_{hkl}]$.
  * `intP`    $I_P(P_i,i_{mode},\mathbf{Q})$ polarised neutron scattering 
              cross section, when only the incident neutron polarization
              is analyzed. It is stored in a matrix with dimensions of
              $[3\times n_{mode}\times n_{hkl}]$.
  * `Pab`     $I_{Pab}(P_f,P_i,i_{mode},\mathbf{Q})$ complete polarised 
              neutron scattering cross section, when the polarisation of
              both the incident ($P_i$) and the scattered ($P_f$)
              neutrons are analyzed. Stored in a matrix with dimensions
              of $[3\times 3\times n_{mode}\times n_{hkl}]$.
  * `Mab`     $M_{ab}(P_f,P_i,i_{mode},\mathbf{Q})$ components of the 
              spin-spin correlation function in the blume-Maleev
              coordinate system, stored in a matrix with dimensions of
              $[3\times \times3 n_{mode}\times n_{hkl}]$.
 
If several domains exist in the sample, `Sperp`, `intP`, `Pab` and `Mab`
will be packaged into a cell, that contains $n_{twin}$ number of
matrices.
 
The meaning of the indices above:
* $P_i$: index of incident polarisation ($1=x_{BM}$, $2=y_{BM}$ or $3=z_{BM}$),
* $P_f$: index of final polarisation ($1=x_{BM}$, $2=y_{BM}$ or $3=z_{BM}$),
* $i_{mode}$: index of spin wave mode,
* $\mathbf{Q}$: index of momentum transfer.
 
  
## See Also
  
[sw_egrid](#sw-egrid) \| [spinw](#spinw) \| [spinw.spinwave](#spinw-spinwave)
 
*[rlu]: reciprocal lattice units