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The structure of $^{35,37,39}$S isotopes is described by performingcomprehensive shell model calculations with SDPF-U and SDPFMW interactions.Protons and neutrons are restricted to the $sd$-shell for $N < 20$, neutronsstart to fill the $pf$-shell for $N > 20$. Natural parity states are describedby only in-shell mixing, unnatural parity states with 1p-1h inter-shell neutronexcitations. With SDPF-U interaction, reported are the results for naturalparity states only because this interaction is not suitable for cross shellexcitations. Calculated energy levels, electromagnetic properties andspectroscopic factors are in good agreement with the recently availableexperimental data.

$^{35,37,39}$S isotopes in $sd-pf$ space : Shell-model interpretation