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Spin-other-orbit interaction

The subroutine SOOC investigates the spin-other-orbit operator, which according to (16) of P3 [5] has the tensorial form:

$\displaystyle H_{12}^{soo}$ $\textstyle \equiv$    
  $\textstyle \equiv$ $\displaystyle \displaystyle {\sum_k}\left\{
H_{soo}^{\left( k-1k1,101\right) } +H_{soo}^{\left( k-1k1,011\right)
}+H_{soo}^{\left( kk1,101\right) } \right.$  
  $\textstyle +$ $\displaystyle \left.
H_{soo}^{\left( kk1,011\right) }+H_{soo}^{\left( k+1k1,101\right)
}+H_{soo}^{\left( k+1k1,011\right) }\right\}.$  

This subroutine is used for all distributions except $\alpha\alpha\alpha\alpha$, $\alpha\beta\alpha\beta$, $\beta\alpha\beta\alpha$, $\alpha\beta\beta\alpha$, $\beta\alpha\alpha\beta$ and $\alpha\alpha\beta\beta$. For distributions $\alpha\alpha\alpha\alpha$, $\alpha\beta\alpha\beta$ and $\beta\alpha\beta\alpha$, according to (34), (39) and (40) of P3 [5], the tensorial form
$\displaystyle H_{12}^{soo}$ $\textstyle \equiv$    
  $\textstyle \equiv$ $\displaystyle \displaystyle {\sum_k}\left\{
H_{soo}^{\left( k-1k1,101\right) } +H_{soo}^{\left( k-1k1,011\right)
} \right.$  
  $\textstyle +$ $\displaystyle \left.
H_{soo}^{\left( k+1k1,101\right)
}+H_{soo}^{\left( k+1k1,011\right) }\right\}$  

is valid. Therefore instead of subroutine SSC the subroutines SOO1111, SOO1212, SOO1212 respectively are used. The distribution $\alpha\beta\beta\alpha$, $\beta\alpha\alpha\beta$ and $\alpha\alpha\beta\beta$ are also calculated according to separate expressions. These are treated by the subroutines SOO1221P, SOO1221P and SOO1122P.

The subroutines SOOA and SOOB investigate the submatrix elements of the spin-other-orbit interaction operator

\begin{displaymath}\left( n_i\lambda _in_j\lambda _j\vert\vert H_{ss}^{\left( k-...
... }\lambda _i^{\prime }n_j^{\prime }\lambda _j^{\prime }\right),\end{displaymath}


\begin{displaymath}\left( n_i\lambda _in_j\lambda _j\vert\vert H_{ss}^{\left( k ...
... }\lambda _i^{\prime }n_j^{\prime }\lambda _j^{\prime }\right),\end{displaymath}


\begin{displaymath}\left( n_i\lambda _in_j\lambda _j\vert\vert H_{ss}^{\left( k+...
...e }\lambda _i^{\prime }n_j^{\prime }\lambda _j^{\prime }\right)\end{displaymath}

according to the formulas (26), (27) and (28) of P3 [5] respectively. These subroutines are used for all distributions except $\alpha\alpha\alpha\alpha$. In the latter case instead of subroutines SOOA and SOOB the subroutine SOO1 is used.


next up previous
Next: Examples Up: SAI_DUDU Previous: Spin-spin interaction
2001-12-07