Itinerant Spin Dynamics in Structures of ... - Jacobs University

Appendix C: Cooperon and Spin Relaxation 145
And for n > 0,n ′ > 0, we get
( ) Pπ
a = R {2,+} sin(Pπ)+4K x R {1,−} cos , (C.59)
2
b = −2R {2,+} sin(Pπ),
(C.60)
( ) Pπ
c = R {2,+} sin(Pπ)−4K x R {1,−} cos , (C.61)
2
d = R {2,+} sin(Pπ),
(C.62)
f = − √ (
( )) Pπ
2 R {2,−} cos(Pπ)+2K x R {1,+} sin , (C.63)
g =
√
2
(
R {2,−} cos(Pπ)−2K x R {1,+} sin
2
( Pπ
2
))
, (C.64)
with the functions
R {1,±} =
R {2,±} =
(
1±(−1) n+n′) (n 2 +n ′2 −P 2 )
((n−n ′ )−P)((n+n ′ )−P)((n−n ′ )+P)((n+n ′ )+P) ,
(
1±(−1) n+n′) (n 2 +n ′2 −(2P) 2 )
((n−n ′ )−2P)((n+n ′ )−2P)((n−n ′ )+2P)((n+n ′ )+2P) . (C.66)
(C.65)