iData_Sqw2D: Bosify: apply the 'Bose' factor (detailed balance) to a classical data set.
The initial data set should obey S*=S(q,w) = S(q,-w), i.e. be 'classical'.
The resulting data set is 'quantum/experimental' and satisfies the detailed
balance. It contains the temperature effect (population).
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
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 and Q(w) defined below.
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]
References:
B. Hehr, http://www.lib.ncsu.edu/resolver/1840.16/7422 PhD manuscript (2010).
S. A. Egorov, K. F. Everitt and J. L. Skinner. J. Phys. Chem., 103, 9494 (1999).
P. Schofield. Phys. Rev. Lett., 4, 239 (1960).
J. S. Bader and B. J. Berne. J. Chem. Phys., 100, 8359 (1994).
T. D. Hone and G. A. Voth. J. Chem. Phys., 121, 6412 (2004).
L. Frommhold. Collision-induced absorption in gases, 1 st ed., Cambridge
Monographs on Atomic, Molecular, and Chemical Physics, Vol. 2,
Cambridge Univ. Press: London (1993).
syntax:
sqw_T = Bosify(sqw)
sqw_T = Bosify(sqw, T, type)
sqw_T = Bosify(sqw, 'T', T, 'type', type)
input:
sqw: Sqw data set (classical, symmetric in energy, no T Bose factor)
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. The temperature is in [K]. 1 meV=11.605 K.
type: 'Schofield' or 'harmonic' or 'standard' (default)
output:
sqw_T: quantum Sqw data set (non classical, iData_Sqw2D).
Example: s=iData_Sqw2D('SQW_coh_lGe.nc'); sb=Bosify(symmetrize(s), 1235);
See also: iData_Sqw2D/deBosify, iData_Sqw2D/symmetrize,
iData_Sqw2D/dynamic_range, iData_Sqw2D/scattering_cross_section
(c) E.Farhi, ILL. License: EUPL.