1520 
This expansion is valid in the region which gives the major 
contribution to the integral (76). Since the integrand is 
small outside this region, we can use the first two terms of 
the expansion over the entire range. 
Taking O = 0, equation 
(76) becomes 
Co 
bs exp | r(t-4/c) + 2X Aac3 
pt) = = exp| rte wie) + 20¢e/oel| d 
: t+A (78) 
<te 
For convenience, we define the parameters: 
a= 2x /3c* 
a= ie. 2/76 
600 Z 
Le exp (¢7 ray?) d (79) 
Lee tral es A 
ra 
— 600 
Combining petacions (78) and (79): 
of Tt plat) =f (80) 
Differentiating I with respect to @ it is evident that: 
loo 
T+ AL =- at a 
2 9 exp (¢t+ 3) Af- me 
— lod 
and completing the square of the exponent in the integrand: 
60d 
wat - -t/4a* y+ 2)* 
ee =° ep (Hae) ep je (r a!) dp (82) 
-¢ob 
-~ 4b. 
