  Purpose: Single-neutron adding data was collected in order to determine the
distribution of the single-neutron strength of the $0f_{7/2}$, $1p_{3/2}$,
$1p_{1/2}$ and $0f_{5/2}$ orbitals outside of $Z=16, N=18$, $^{34}$S.
  Methods: The $^{34}$S($d$,$p$)$^{35}$S reaction has been measured at 8 MeV/u
to investigate cross sections to excited states in $^{35}$S. Outgoing proton
yields and momenta were analyzed by the Super-Enge Split-Pole Spectrograph in
conjunction with the CeBrA demonstrator located at the John D. Fox Laboratory
at Florida State University. Angular distributions were compared with Distorted
Wave Born Approximation calculations in order to extract single-neutron
spectroscopic overlaps.
  Results: Spectroscopic overlaps and strengths were determined for states in
$^{35}$S up through 6 MeV in excitation energy. Each orbital was observed to
have fragmented strength where a single level carried the majority. The
single-neutron centroids of the $0f_{7/2}$, $1p_{3/2}$, $1p_{1/2}$ and
$0f_{5/2}$ orbitals were determined to be $2360^{+90}_{-40}$ keV,
$3280^{+80}_{-50}$ keV, $4780^{+60}_{-40}$ keV, and $\gtrsim7500$ keV,
respectively.
  Conclusion: A previous discrepancy in the literature with respect to
distribution of the neutron $1p_{1/2}$ strength was resolved. The integration
of the normalized spectroscopic strengths, up to 5.1 MeV in excitation energy,
revealed fully-vacant occupancies for the $0f_{7/2}$, $1p_{3/2}$, and
$1p_{1/2}$ orbitals, as expected. The spacing in the single-neutron energies
highlighted a reduction in the traditional $N=28$ shell-gap, relative to both
the $1p$ spin-orbit energy difference ($N=32$) and the lower limit on the
$N=34$ shell spacing.
