⇤

2 2 6 6

6 12

2

�

⇤

2

2 6 6 6 12

µ

2 2

2

�↵e2/2r4

↵ e

�

� =4⇡

k2

1X

l=0

(2l + 1) sin2 ⌘l(k),

k l⌘l

l

tan ⌘l =m2 � tan2 �l +B%

l tan �l(m2 � 1)

tan �l(1�m2) +B%l (1�m2 tan2 �l)

,

�l = ⇡(v � l � 1/2)/2 m v

B%l (k)

B%l (k) ⇡ Bl(0) +

RlR⇤k2/2+ . . . Rl

R⇤ =p↵e2µ/~2

r�4

µ~

l = 0 B0(0) A sB0 = �R⇤/A

s p d

tan ⌘l(k) ⇡⇡↵k2

8(l � 1/2)(l + 1/2)(l + 3/2), l > 2.

2 2 6 6

6 12

2

2

2 2

A = 9.52a0 13.04a0

B0 a0

Eb = 1/(2A2)6 12 6 6

2

2 6 6 6 12

A = �R⇤/B0 B1 B2 R1

R2

A [a] R0 [a0] B1 R1 [a0] B2 R2 [a0] ↵ [a30]

2 �3.13 �0.12 �1.99 �0.90

�5.52 �4.34

2 �9.23 �22.67

6 12⇤ �0.05 �0.18

6 6⇤ �0.23 �0.29

⇤

��

Ze↵ = 4⇡⇢e�R⇣R2 +

�

4⇡+ 2RRe{f0}

⌘,

Ze↵ = �/(⇡r20cn) r0

c n⇢e

�R

R f0

s⌘0 Re{f0} = sin(2⌘0)/(2k)

⇢e�R

Ze↵

2

R = R⇤

4⇡⇢e�R

sZe↵

r�4 R = R⇤ = 3.35a0 3.40a0

4⇡⇢e�R = 0.51

2 4

4⇡⇢e�R R

Ze↵ �

A [a0] R [a0] 4⇡⇢e�R

⇤ �5.52⇤2 �9.23† �0.52† �0.61† �5.30† �10.4† �45.3

⇤ †

4⇡⇢e�R

4⇡⇢e�R ⇡ 0.5

2

Ze↵(k)2 6 6 6 12

r�4

6 12

6 6

2