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moments=Sqw_moments(sqw, M, T, classical): compute Sqw moments (harmonic frequencies)


function sigma=Sqw_moments(data, M, T, classical)


 moments=Sqw_moments(sqw, M, T, classical): compute Sqw moments (harmonic frequencies)

   Compute the structure factor (moment 0), recoil energy (moment 1) and the
     collective, harmonic and mean energy transfer dispersions.

 The result is given as an iData array with data sets:
   S(q) = \int S(q,w) dw = <S(q,w)>                 structure factor [moment 0]
   Er   = \int w*S(q,w) dw = <wS(q,w)> = h2q2/2M       recoil energy [moment 1]
   Wc   = sqrt(2kT*Er/S(q))                    collective/isothermal dispersion
   Wl                                          harmonic/longitudinal excitation
   Wq   = 2q*sqrt(kT/S(q)/M)                               mean energy transfer
   M2   = <w2S(q,w)>                                                 [moment 2]
   M3   = <w3S(q,w)>                                                 [moment 3]
   M4   = <w4S(q,w)>                                                 [moment 4]

   data: Sqw data set e.g. 2D data set with w as 1st axis (rows, meV), q as 2nd axis (Angs-1).
   M: molar weight of the material atom/molecule in [g/mol].
     when omitted or empty, it is searched 'weight' or 'mass' is the object.
   T: when given, Temperature to use. When not given or empty, the Temperature
      is searched in the object. The temperature is in [K]. 1 meV=11.605 K.
   classical: 0 for non symmetric S(q,w) [with Bose, from exp.], 1 for symmetric (from MD)
     when omitted or empty, this is guessed from the data set when possible

   moments=[ sq M1 wc wl wq M2 M3 M4 ] as iData array

   Helmut Schober, Journal of Neutron Research 17 (2014) pp. 109
   Lovesey, Theory of Neutron Scattering from Condensed Matter, Vol 1, p180 eq. 5.38 (w0)
   J-P.Hansen and I.R.McDonald, Theory of simple liquids Academic Press New York 2006.

 Example: moments = sqw_moments(iData(fullfile(ifitpath,'Data','SQW_coh_lGe.nc')))
 (c) E.Farhi, ILL. License: EUPL.


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