Sqw_deBosify: remove Bose factor (detailed balance) from an 'experimental' data set.
In principle the resulting data set is 'classical' that is S(q,w) = S(q,-w)
The S(q,w) is a dynamic structure factor aka scattering function.
input:
s: Sqw data set (non classical, including T Bose factor e.g from experiment)
e.g. 2D data set with w as 1st axis (rows, meV), q as 2nd axis (Angs-1).
T: when given, Temperature to use for Bose. When not given, the Temperature
is searched in the object.
type: 'Schofield' or 'harmonic' or 'standard' (default)
conventions:
omega = Ei-Ef = energy lost by the neutron, given in [meV]
omega > 0, neutron looses energy, can not be higher than Ei (Stokes)
omega < 0, neutron gains energy, anti-Stokes
Egelstaff, Eq (9.25) p189
S(q,-w) = exp(-hw/kT) S(q,w)
S(q,w) = exp( hw/kT) S(q,-w)
S(q,w) = Q(w) S*(q,w) with S*=classical limit
for omega > 0, S(q,w) > S(q,-w)
The semi-classical correction, Q, aka 'quantum' correction factor,
can be selected from the optional 'type' argument:
Q = exp(hw_kT/2) 'Schofield' or 'Boltzmann'
Q = hw_kT./(1-exp(-hw_kT)) 'harmonic' or 'Bader'
Q = 2./(1+exp(-hw_kT)) 'standard' or 'Frommhold' (default)
The 'Boltzmann' correction leads to a divergence of the S(q,w) for e.g. w above
few 100 meV. The 'harmonic' correction provides a reasonable correction but does
not fully avoid the divergence at large energies.
Bose factor: n(w) = 1./(exp(w*11.605/T) -1) ~ exp(-w*11.605/T)
w in [meV], T in [K]
Example: s = Sqw_deBosify(s, 300);
See also: Sqw_Bosify, Sqw_symmetrize, Sqw_dynamic_range, Sqw_scatt_xs
(c) E.Farhi, ILL. License: EUPL.