Hoenl-London Factors

The Hoenl-London factors show the distribution of transition intensities over different rotational branches, i.e. how much the relative percentage of R; P; and Q-Branches is. For diatomic molecules (where Λ corresponds to the ground state and Λ' corresponds to the excited state, DL = Λ' − Λ) one will have:

DL = 0

SJR = | (J'' + 1 + Λ'') (J'' + 1 −Λ'')
J'' + 1
SJQ = | (2J'' + 1) Λ''²
J'' (J'' + 1)
SJP = | (J'' + Λ'') (J'' − Λ'')
J''

DL = +1

SJR = | (J'' + 2 + Λ'') (J'' + 1 + Λ'')
4 (J'' + 1)
SJQ = | (J'' + 1 Λ'') (J'' − Λ'') (2J'' + 1)
4 J'' (J'' + 1)
SJP = | (J'' − 1 − L'') (J'' − L'')
4 J''

DL = −1

SJR = | (J'' + 2 - L'') (J'' + 1 − Λ'')
4 (J'' - 1)
SJQ = | (J'' + 1 −Λ'') (J'' + Λ'') (2J'' + 1)
4 J'' (J'' +1)
SJP = | (J'' − 1 −Λ'') (J'' + Λ'')
4 J''