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

TL;DR

This study searches for the 2p2h intruder state in $^{35}$P to understand nuclear structure evolution near the Island of Inversion, setting limits on its existence through a specific transfer reaction experiment.

Contribution

It provides the first upper limit on the cross-section for populating the 2p2h state in $^{35}$P, constraining theoretical models of nuclear wavefunctions.

Findings

No candidate state was observed within the energy range.

An upper limit for the transfer cross-section was established.

Results constrain wavefunction compositions in $^{36}$S and $^{35}$P.

Abstract

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 $^{40}$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 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 ground states, but are present in the relatively low-lying level schemes. With the aim of 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 not yet been identified, the $^{36}$S(d,$^3$He)$^{35}$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 wavefunction compositions in both $^{36}$S and $^{35}$P.