content_image/310639.jpg content_image/310636.jpg content_image/310637.jpg content_image/310638.jpg
The following is its matrix form: 

<img src='content_image/310639.jpg'>

Here the order of matrix elements is m = 1 , 2, and then l = 3 ↑ , 3 ↓ , 4 ↑ , 4 ↓ etc.., V$_{±}$$_{x}$ = V e ± ik$_{x}$a 0 , V$_{±}$$_{y}$ = V e ± ik$_{y}$b 0 and s$_{i}$ = sin δθ$_{i}$ , c$_{i}$ = cos δθ$_{i}$ . It can be diagonalized and the eigen values are 

<img src='content_image/310636.jpg'>

<img src='content_image/310637.jpg'>

where ε$_{p}$ is six-fold degenerate and − → R$_{nn}$ and δθ$_{nn}$ = 2 δθ$_{l}$ are the position vector and spin angle difference between two nearest neighboring transition element 

<img src='content_image/310638.jpg'>

