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The Dispersion_relation Component

Identification

• Author: Daniel Lomholt Christensen and Kim Lefmann
• Origin: NBI
• Date: 22.06.23

Description

Single-cylinder shape.
Absorption included.
No multiple scattering.
No incoherent scattering emitted.
No attenuation from coherent scattering. No Bragg scattering.
Any crystal system: the unit cell is given either by its lengths and angles
(a, b, c, aa, bb, cc) or by its real-space lattice vectors (ax ... cz).



Algorithm:
0. Always perform the scattering if possible (otherwise ABSORB)
1. Choose a dispersion mode, a scattering point and a direction within a
focusing solid angle
2. Calculate the zeros of (E_i-E_f-hbar omega(kappa)) as a function of k_f
3. Choose one value of k_f (always at least one is possible!)
4. Perform the correct weight transformation

Dispersion files:
folder_path holds one file per dispersion mode. Each file has the columns
h  k  l  E  I
on a regular grid covering one unit cell in reciprocal lattice units: h, k, l
are the coordinates of q along the reciprocal lattice vectors a*, b*, c*,
h = a.q/(2 pi) and so on. For a cell with 90 degree angles and no vectors
given, a*, b*, c* lie along the sample x, y, z axes, as a, b, c do in
SpinWave_BCO and Phonon_simple. E [meV] is the mode energy and
I [barn/sr per unit cell of the given lattice] is the partial differential
scattering cross section of the mode, as the factor in front of the delta
function:
d2sigma/dOmega dE_f = (k_f/k_i) * DW * I(q) * n_B * delta(hbar omega - E(q)).
The component adds k_f/k_i, the Debye-Waller factor DW and the Bose factor
n_B = n(omega) + 1 for neutron energy loss and n(omega) for energy gain, so
I should not include them. I is looked up at the scattering vector folded
into the unit cell.

Weight:
p *= exp(-mu l) * dOmega * l_full * m * n_modes * rho_cell
* (k_f/k_i) * DW * I(q) * n_B * |dE_f/d(E(q) - |E_i - E_f|)|
with l the path length in the sample, dOmega the focusing solid angle,
l_full the path length without scattering, m the number of final
velocities found, n_modes the number of dispersion files and rho_cell the
density of unit cells.

Input parameters

Links

• Source code for Dispersion_relation.comp.
• The test instrument Test_Dispersion_relation_TAS.instr.

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