# NRIXS Calculation

Non-Resonant Inelastic X-ray Scattering (NRIXS) is determined by the momentum transfer dependent dynamic structure factor $S(\overrightarrow{q},E)$ (DFF). feff NRIXS calculations output the DF for a given $\overrightarrow{q}$ over a range of E. From this quantity, the NRIXS signal is obtained by simply adding a multiplicative factor containing beam energies and polarization. (See references.) NRIXS calculations are controlled by the following cards : NRIXS, LJMAX, and LDEC. In addition, one must use either the XANES and FMS cards for the near-edge region ; or the EXAFS and RPATH cards for the extended region. Note that for NRIXS, if xkmax < 0 in the XANES or EXAFS card, then an energy grid of approximately constant energy step is used (instead of the usual constant k-step).

Although the code has been tested for wide range of momentum transfers the code is most stable for the medium region of momentum transfer values. This typically means 0.1 < q < 14a.u. for light elements or shallow edges, i.e. binding energy less than 400 eV. Higher momentum transfers are possible for more tightly bound electrons (see examples below). The small momentum transfers can cause numerical instabilities at near edge region and large momentum transfers also in the extendend energy range. There is no default value for the momentum transfer.

NRIXS produces two main output files. xmu.dat contains the total spectrum in the usual 6-column format. xmul.dat contains:

• col 1: the excitation energy (in eV).
• col 2: the value of k (in Angstrom) at this energy.
• col 3: the atomic background value $S_0\overrightarrow{q}, E)$
• col 4 - 4+ld: the next ld + 1 columns give the contribution to the atomic background $S_l^0\overrightarrow{q},E)$ for the final state electron angular momentum values l = 0,...,ld :

$S_l^0\overrightarrow{q}, E) = (2l + 1)|M_l\overrightarrow{q}, E)|^2\rho^0_l (E)$

• col 4+ld+1 - end: the next (ld+1)(ld+1) columns give the decomposition of fine structure. i.e.

$\chi_\overrightarrow{q}^{ll'} = \frac{1}{S_0(\overrightarrow{q}, E)}\sum_{mm'}M_L(-\overrightarrow{q}, E)\rho_{LL'}^{sc}(E)M_{L'}(\overrightarrow{q}. E)$

To plot the contribution of only s-type (l = 0) final states one would do in gnuplot (ld = 2):

> plot xmul.dat u 1:($4+$3*$7) and for only p-type: > plot xmul.dat u 1:($5+$3*$11)

To get the s-p non-diagonal contribution to $S_0\overrightarrow{q},E)\chi_{\overrightarrow{q}}(k)$:

> plot xmul.dat u 1:($3*($10+\$8))