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The excitation energy of deformed intruder states (specifically the 2p2hbandhead) as a function of proton number $Z$ along $N=20$ is of interest bothin terms of better understanding the evolution of nuclear structure betweenspherical $^{40}$Ca and the Island of Inversion nuclei, and for benchmarkingtheoretical descriptions in this region. At the center of the $N=20$ Island ofInversion, the npnh (where n=2,4,6) neutron excitations across a diminished$N=20$ gap result in deformed and collective ground states, as observed in$^{32}$Mg. In heavier isotones, npnh excitations do not dominate in the groundstates, but are present in the relatively low-lying level schemes. With the aimof identifying the expected 2p2h$\otimes\mathrm{s}_{1/2^+}$ state in $^{35}$P,the only $N=20$ isotone for which the neutron 2p2h excitation bandhead has notyet been identified, the $^{36}$S(d,$^3$He)$^{35}$P reaction has been revisitedin inverse kinematics with the HELical Orbit Spectrometer (HELIOS) at theArgonne Tandem Linac Accelerator System (ATLAS). While a candidate state hasnot been located, an upper limit for the transfer reaction cross-section topopulate such a configuration within a 2.5 to 3.6\,MeV energy range, provides astringent constraint on the wavefunction compositions in both $^{36}$S and$^{35}$P.

Search for the $1/2^+$ intruder state in $^{35}$P