Intermediate energy proton knockout to the “island of inversion” isotope ${}^{31}\mathrm{Mg}$

The “island of the inversion” isotope ${}^{31}\mathrm{Mg}$ was investigated using an intermediate energy proton knockout reaction from ${}^{32}\mathrm{Al}$ at 90 MeV/nucleon at the National Superconducting Cyclotron Laboratory. A negligible cross section to the ground state supports an intruder-dominant configuration in ${}^{31}\mathrm{Mg}$. The partial cross sections to excited final states preferentially populate configurations in the ${}^{31}\mathrm{Mg}$ residues which have no neutron excitations across the $N=20$ shell closure. There is strong evidence that the reaction populates the $3/2^{+}$ and $5/2^{+}$ states which correspond with the neutron-hole states predicted by the shell model with the model space truncated above the $\mathit{sd}$-shell.

Figure 1

The incoming particles identified by the time-of-flight from the A1900 focal plane to the object box of the S800 spectrograph.

Figure 2

Reaction products from the incoming beam of ${}^{32}\mathrm{Al}$ identified in the S800 spectrograph by their time of flight and energy loss in the ionization chamber.

Figure 3

(Line) Predicted momentum distribution from the knockout of a $d_{5/2}$ proton to the ${3/2}^{+}$ 673 keV state in ${}^{31}\mathrm{Mg}$ including effects from the target and the momentum acceptance of the incoming beam. (Points) The corresponding measured distribution for ions coincident with the 623 keV $\gamma$-ray.

Figure 4

Background subtracted gamma-ray spectrum coincident with the known $\gamma$-ray decays from the 221 keV state.

Figure 5

(Left) The level scheme observed in the present experiment with suggested spins and parities is shown including tentatively placed gammas (dashed). (Middle) AMD+GCM calculations from Ref. [13] with the 0p1h states in bold. (Right) The $0\hslash \omega$ states calculated by the USD shell model interaction. Theoretical calculations have a shift in excitation energy to match the $3/2^{+}$ single-hole state energy to the experiment.

Figure 6

Relative intensity of $\gamma$-rays emitted from the 221 keV state in ${}^{31}\mathrm{Mg}$ as determined by efficiency calibrations and proper Doppler reconstruction for the forward (dashed) and backward (solid) rings in SeGA.

Figure 7

Gamma-ray energy spectrum in the 90 degree ring of SeGA following Doppler reconstruction, showing several doublet structures at 1.1, 1.5, and 1.9 MeV.

Figure 8

The angular distribution coefficient $a_2$ determined from the experimental data (triangles) and theory (line) as a function of increasingly broader longitudinal momentum gates for a $3/2\to 3/2$ 623 keV $\gamma$-ray transition. The abscissa describes the percentage of central momentum counts included.

Figure 9

The Compton scattering of gamma rays relative to the reaction plane defined by the beam axis and the gamma ray propagation direction: (solid) scattering perpendicular to the plane, (dashed) scattering parallel to the plane, normalized to the intrinsic scattering from a gamma ray from a source with no spin alignment.