Hyperfine structure of extremely high Rydberg msns1S0and msns3S1series in odd alkaline-earth isotopes

In extremely high Rydberg states of odd alkaline-earth isotopes, the Fermi constant ams is comparable to the energy separation between levels belonging to different principal quantum numbers n and hyperfine interactions dominate the structure of the levels. The multichannel quantum defect theory of fine structure has been developed and applied to hyperfine structure and thus the HFS can be analysed directly by MQDT. A two-channel quantum defect model for extremely high Rydberg msns 1S0 and msns 3S1 series in odd alkaline-earth isotopes for F=I is described. The Ui(F)i matrix is given analytically and the relationship between the eigenquantum defects of HFS and the quantum defects of fine structure is derived. The HFS of two extremely high Rydberg 5sns 1S0 and 3S1 series in 87Sr has been calculated by the model and an excellent agreement between the theoretical and experimental results has been achieved. The HFS of extremely high Rydberg msns 1S0 and 3S1 series in 43Ca, 135Ba and 137Ba are also analysed by the model.