D Rydberg Series of Ca, Sr, and Ba

Spin-Orbit Coupling and Hyperfine Structure of Pure msnd Rydberg States 

For Rydberg states of pure msnd configuration, the Hamiltonian Hq, which takes Coulomb and spin-orbit interactions of the valence electrons into account, can be written as 

Since for Rydberg states of pure msnd character both and A st( ) decrease proportional to n, is expected to be essentially independent of 

Comparing Eqs. (53)-(56) with the usual expression for the hyperfine components Ep in terms of the hyperfine splitting factor A 

In Eqs. (58)-(61) the hyperfine coupling constant of the ms valence electron has been taken to be independent of the principal quantum number n. On the assumptions made, the hyperfine coupling constants A Di) and A( Di) do not contain any mixing coefficients. On the contrary, from the measured splitting factors AC Dj), the amplitudes fiso and Aso can 

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