Single-Photon Atomic Cooling - Raizen Lab - The University of ...

where mnuc is the nuclear mass. This value differs slightly from 1 due to finite
nuclear mass and is correct to lowest order in me/mnuc [54]. The value of gI
accounts for the complicated structure of the nucleus and is an experimental
value [45]. Finally, the values listed for gJ are all experimental values [45], the
exception being the value given for the state 5 2 P1/2 which is calculated from
theory.
gS 2.002 319 304 3622(15)
gL 0.999 993 69
gI −0.000 995 141 4(10)
gJ(52S1/2) 2.002 331 13(20)
gJ(52P1/2) 2/3
gJ(52P3/2) 1.336 2(13)
Table 2.3: 87 Rb D2 Transition “g-factors”
The expression for gJ given in Eq. 2.29 can be simplified by taking the
approximate values gS ≈ 2 and gL ≈ 1 yielding,
gJ ≈ 3
2
S(S + 1) − L(L + 1)
+ . (2.31)
2J(J + 1)
Likewise a simplification the expression for gF, given in Eq. 2.28, can be made
by neglecting the nuclear term
gF ≈ gJ
F(F + 1) − I(I + 1) + J(J + 1)
, (2.32)
2F(F + 1)
yielding an expression which is still correct to the 0.1% level.
As an example consider the F = 1 manifold in ground state 87 Rb (see
Fig. 2.1). In this state S = 1/2, L = 0, J = 1/2, I = 3/2 and F = 1 so
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