Search for the 1 / 2 + intruder state in P 35

The excitation energy of deformed intruder states (specifically the 2p2h bandhead) as a function of proton number $Z$ along $N=20$ is of interest both in terms of better understanding the evolution of nuclear structure between spherical $^{40}\\mathrm{Ca}$ and the Island of Inversion nuclei, and for benchmarking theoretical descriptions in this region. At the center of the $N=20$ Island of Inversion, the $n\\mathrm{p}n\\mathrm{h}$ (where $n=2,4,6$) neutron excitations across a diminished $N=20$ gap result in deformed and collective ground states, as observed in $^{32}\\mathrm{Mg}$. In heavier isotones, $n\\mathrm{p}n\\mathrm{h}$ excitations do not dominate in the ground states but are present in the relatively low-lying level schemes. With the aim of identifying the expected $2\\mathrm{p}2\\mathrm{h}\\ensuremath{\\bigotimes}{\\mathrm{s}}_{1/{2}^{+}}$ state in $^{35}\\mathrm{P}$, the only $N=20$ isotone for which the neutron 2p2h excitation bandhead has not yet been identified, the $^{36}\\mathrm{S}(d,^{3}\\mathrm{He})^{35}\\mathrm{P}$ reaction has been revisited in inverse kinematics with the HELical Orbit Spectrometer (HELIOS) at the Argonne Tandem Linac Accelerator System (ATLAS). While a candidate state has not been located, an upper limit for the transfer reaction cross section to populate such a configuration within a 2.5 to 3.6 MeV energy range provides a stringent constraint on the wave function compositions in both $^{36}\\mathrm{S}$ and $^{35}\\mathrm{P}$.