### 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.

### Input Arguments

spectra
Input structure, contains spin-spin correlation functions. Supported inputs are produced by spinw.spinwave, 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.