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