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We present highly correlated multi-configuration Hartree-Fock (MCHF) calculations of the hyperfine structure of the 3p5 2Po_J levels of {33}S- and {35,37}Cl. We obtain a good agreement with observation. The hyperfine structure of the neutral sulfur {33}S 3p4 3P_J lowest multiplet that has never been measured to the knowledge of the authors, is also estimated theoretically. We discuss some interesting observations made on the description of the atomic core in MCHF theory.

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