Resonant Inelastic X-ray Scattering(RIXS)

Using the option -x and -xa the RIXS cross section can be calculated by mcdisp. Option -x calculates resonant inelastic x-ray intensities maximized with respect to azimuth. Option -xa calculates resonant inelastic x-ray intensities with complete azimuth dependence for each reflection.

The formalism is based on [31, equ.8 ff], e.g. the observables $\hat \mathcal O_{\alpha}$ are the 9 components ($\alpha$ =xx xy xz yx yy yz zx zy zz) of the tensor $\mathbf R$, which is related to the operator $R_{\omega,j}^{\epsilon_i\epsilon_o}$ in [31] by

  $$R_{\omega,j}^{\epsilon_i\epsilon_o}=\mathbf \epsilon _o^{\star} \cdot \mathbf R \cdot \mathbf \epsilon _i$$ (62)

Here the vector $\mathbf \epsilon$ describes the polarisation of the incoming / outgoing photon beam (linear (real) or circular polarized (complex) light). Vector components (e.g. $\hat \mathbf S$ to the xyz coordinate system, where $y\vert\vert b$, $z\vert\vert(a \times b)$ and $x$ perpendicular to $y$ and $z$.

For the isotropic ion the scattering operator $R_{\omega,j}^{\epsilon_i\epsilon_o}$ is given by

	$$R_{\omega,j}^{\epsilon_i\epsilon_o}$$	$=$	$$\mathbf \epsilon _o^{\star} \cdot \mathbf R \cdot \mathbf \epsilon _i$$	(63)
		$=$	$$\sigma^{(0)} \mathbf \epsilon _i \cdot \mathbf \epsilon _o^{\star... ...1)}}{s} \mathbf \epsilon _o^{\star} \times \mathbf \epsilon _i \hat \mathbf S_j$$
			$$\frac{\sigma^{(2)}}{s(2s-1)} \left ( \mathbf \epsilon _i \cdot \h... ...athbf \epsilon _i \cdot \mathbf \epsilon _o^{\star} \hat \mathbf S_j^2 \right )$$	(64)

In order to use this expression, the conductivities $\sigma$ have to be entered in the sipf file, e.g.

SIGMA0r=1.32
SIGMA1r=1.32
SIGMA2r=1.32
SIGMA0i=1.32
SIGMA1i=1.32
SIGMA2i=1.32

('r' and 'i' stand for real and imaginary part, respectively).

Note: in module so1ion the scattering operator is given in terms of the total angular momentum $\hat \mathbf J$ instead of $\hat \mathbf S$.

If a more complex tensor $\mathbf R$ is required, it's components can be defined in the sipf file using the perlparse option.