Changes
Page history
Update theory
authored
Jan 30, 2025
by
Johannes Wasmer
Show whitespace changes
Inline
Side-by-side
kkrsusc/theory.md
View page @
6a18439b
...
...
@@ -28,10 +28,12 @@ $R_{i\ell}\^\sigma(r;E)$ is regular at the center of the ASA
sphere, and $H_{i
\e
ll}
\^\s
igma(r;E)$ diverges there.
The Korringa-Kohn-Rostoker Green function is given by
```
math
G_{ij}^\sigma(\vec{r}\,,\vec{r}\,';E) &=& \sum_{LL'}Y_L(\hat{r}) \big(\sqrt{E}\,R_{i\ell}^\sigma(r_<;E)\,H_{i\ell}^\sigma(r_>;E)\delta_{ij}\delta_{LL'} \nonumber\
&&\hspace{-4em} + R_{i\ell}^\sigma(r;E)\,G^{\sigma,\text{str}}_{iL,jL'}(E)\,R_{j\ell'}^\sigma(r';E)\big) Y_{L'}(\hat{r}') \; ,
```
where $r_
\<
=
\m
in(r,r
\'
)$ and $r_
\>
=
\m
ax(r,r
\'
)$, and $G
\^
{
\s
igma,
\t
ext{str}}_{iL,jL
\'
}(E)$ is the
structural GF, describing backscattering effects.
...
...
...
...