. . 2ik r K or -i 

 '^ ^"^^ J 1 



^2^ 1/2 

 |-+2(inK)-^/^ 



1/2 "^ 2 2 ^/2 

 1 {[k„k+2(inK)^^^] -4k^k^} 



k2k 

 exp \ -1 — — X ) dk 



2ik, r K or I i 

 4 



exp I 1 -;; — X I dk 



1/2 "* 2 2 ^/2 

 1 {[k^k-2(mK) '^] -4k^k^} 



2ni 



^j 



K or i 



k k 



3 1/2 

 -^ -2(mK) ''^ 



, , ,^ exp i ^p— X dk for x > (120) 

 1/9 '^ o o 1/2 V 2m 

 o {[k„k-2(mK)-''^] -4kX> 



k^k 



,(3) ^ _ 1 



""" N (k) exp i - ^ [l-2(mK)-'"''^] x [exp ( - ^ 6kx 



2m 



2m 



[k(l-k) (6k+l) (6k+2)] 



1/2 



dk 



X exp l-[6(l-k) (6k+l)] 



1/2 



2m 



(121) 



In Equations (119) and (120), the first numerator is for n = 3 and the second for 

 n = 4. All other notations used in Equations (118) through (121) are as follows: 



R3(v) = K 



1/2 

 R, (v) = -i (mK) - mv sign x 



m, = (K-mv^) - (4 mK-1) v^ 



(122) 

 (cont . ) 



= 4 (mK) V (K-mv ) sign x 



33 



