T+ /(M I I[1T+) ~ / K 2 and obtain
p2M JT 11 2 1- 1 ~ p2, ,1
2 (2 + (-3 10 o5)
1 lK 2 ( 2 i ') I 2 ,
Mi/ 2M Mi Mi.' ; ,
12 I 1(",," '",,) I M ,"+ .... ( '
R3 ~ 2I1
R4 r [
R,5 I K2
Combining the I s 0 en, Ioint contributions gives
2 2
-R- In R2 In I
K 2 + f.,2
in
A M + K2 K2 + ,1
I i M. M l
-ln 11 ^
I iK2 h K2 2
-. in (K2 I A
M. 1 Ai
3 4 I
In-
2 +
K2 1}
+ 11 Ki
In
IlK
In -
Ii i
A'
1 '. 'r
in
I} for < : 3-110)
For the other endpoint, 1M < 1 T, the roots of the p< :. :..' 1 (A I MT) H : roach
T -A/l/A/i and Ta "/. Which of these roots is ...... 1 d by T depends on the
S: values, but since the formulae are syrrmmetric under their interchange, we can
choose to use the first in place of T, and the second in place of T_. Since the denominator
M 1 1T = 0 in this limit, we need to carefi:1 evaluate
1 T1 MT K 2
dTI i
(3-107)
(3-108)
(3-109)