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We, however, should take care of the property of the E i1 function which has the logarithmic
singularity.
We consider now the lattice cell system where a unit cell is divided into N regions and the
collision region j lies periodically. A sum of such terms as Eq.(7.1-26) gives
P
ij
=
1
2λ
∑{
i l=
0
l1
l1
Ei3 ( λij
) − Ei3
( λij
+ λi
) − Ei3
( λij
+ λ j ) + Ei3
( λij
+ λi
+ λ j ) +
E
l 2
l2
l2
l 2
i3 ij i3
ij i i3
ij j i3
ij i j
l1
( λ ) − E ( λ + λ ) − E ( λ + λ ) + E ( λ + λ + λ
(7.1-32)
l1
)}
where
λ
λ
l1
ij
l 2
ij
=
=
j−1
∑
i−1
∑
λ + l ×
∑
∑
k
k = i+
1 k = 1
λ +
N
N
λ +
k
k
k = 1 k = j+
1
λ
k
i−1
∑
k = 1
λ
k
+ l ×
N
∑
k = 1
λ
k
(7.1-33)
The summation over l is achieved separately by or series until or exceeds the
fixed optical length, say, 6, respectively. For the case where j