Structure ne et interactions magnétiques

n
n
n~ J2
~
J=~ L+~ S
n= 2−−n= 3 n= 2
J= 1/2
J= 3/2
L= 0 L= 1 S= 1/2n= 3
J= 1/2J= 3/2J= 5/2
∆J=−1,0,+ 1
n= 3,J = 1/2→n= 2,J = 1/2
n= 3,J = 1/2→n= 2,J = 3/2
n= 3,J = 3/2→n= 2,J = 1/2
n= 3,J = 3/2→n= 2,J = 3/2
n= 3,J = 5/2→n= 2,J = 3/2
n= 2,J = 1/2n= 2,J = 3/2
n= 3

α
n= 3
n= 2
λ= 589,0λ= 589,6
J= 3/2J= 1/2
1s22s22p63p1 2P J = 1/2 1s22s22p63s1
2S
2p3Po

~
Mspin
~
Mspin =−gsµB~s
µB=e¯h/2m
gs= 2,00...
~
Borbite
HSO =−~ Mspin.~ Borbite
~
Borbite
~
Borbite
e−~v
~
E
~
Borbite =−~v
c2×~
E/q1−v2/c2∼−~v
c2×~
E
~
E
U(r)
~
E=−dU
dr ~ur
~r =r~ur
m
~
Borbite =−~r ×m~v. 1
mc2.1 r.dU dr
~
l¯h
~
Borbite =−1
r.dU dr .¯h mc2.~
l

HSO =−gs.µB.¯h
mc2.1 r.dU dr .~
l.~s
HSO =A(r)~ l.~s
~s
Borbite
HSO
A(r) = −gs
2.µB.¯h mc2.1 r.dU dr
A~
l ~s
HSO
A
< ψnl|A(r)|ψnl >=−gs
2.µB.¯h mc2. < ψnl|1 r.dU dr |ψnl >
U(r) = Ze/(4π²0r)e > 0
dU/dr =−Ze/(4π²0r2)
< ψnl|A(r)|ψnl >=gs
2.µB.¯h mc2.Ze 4π²0
< ψnl|1
r3|ψnl >
< ψnl|1
r3|ψnl >=Z3
n3l(l+ 1/2)(l+ 1)a3
0
a0=¯h2
m(e2/4π²0)
EH=mc2
2α2

α
α=e2
4π²0¯hc =1 137,04...
A
< ψnl|A(r)|ψnl >=gs
2α2EH
Z4
n3l(l+ 1/2)(l+ 1)
∼5.10−5EH
Z4
n3
1
l(l+ 1/2)(l+ 1)
l= 0 l= 0
~
l.~s HSO
n(l= 0)
n−3Z4
n
Z
l Anl
<1/r3>
1/r3
HSO
Hel.st. HSO
Hel.st. Z4Zeff
α
n= 2 n= 3
1/n3
n= 2
<2p|A|2p >∼5.10−5.13,6.1
23.3= 2,8.10−5eV = 0,23cm−1
≡−1