Isobaric analog resonances of ${}^{31}\mathrm{Mg}$ and the border of the island of inversion

The evolution of the nuclear shell structure in the region of the neutron-rich shell-breaking nucleus ${}^{32}\mathrm{Mg}$ has been the subject of considerable interest. We present here the first determination of the overlap of the ground and two first excited states in ${}^{31}\mathrm{Mg}$ with a neutron coupled to the ground state in ${}^{30}\mathrm{Mg}$ based on studies of its isobaric analog resonances in ${}^{31}\mathrm{Al}$. The excitation function for proton resonant elastic scattering on ${}^{30}\mathrm{Mg}$ was measured close to $0^{\circ }$ in the laboratory frame by bombarding a thick polyethylene target with a ${}^{30}\mathrm{Mg}$ beam at an energy of 2.92 MeV/nucleon at the REX-ISOLDE facility at CERN. Three resonances were successfully resolved, and angular momenta and total and proton resonance widths were determined by using $R$-matrix analysis. The deduced spectroscopic factor for the ground state in ${}^{31}\mathrm{Mg}$ is consistent with the shell-model calculation, whereas those for the first and second excited states could not be reproduced. These results show that a drastic change in structure occurs between ${}^{30}\mathrm{Mg}$ and ${}^{31}\mathrm{Mg}$ and that the onset of structural change in this region therefore occurs between these two isotopes.

Figure 1

Correlation between $E_{\mathrm{c}.\mathrm{m}.}$ and the detection time ($T_{\mathrm{proton}}$) after each proton synchrotron impact. Resonance loci can be seen within 100 ms after the impact.

Figure 2

Excitation functions of the proton elastic scattering. Cross sections measured with the polyethylene target (diamonds) and the carbon target (crosses). The solid (dashed) line denotes the best-fit $R$-matrix calculation by assuming three (two) resonances. The region of $E_{\mathrm{c}.\mathrm{m}.}=2350–2660\mathrm{keV}$ is illustrated in the inset. The expected resonance energies are also presented. The IARs would appear higher than 2400 keV. See text for details.

Figure 3

Dependence of the matching radius for the spectroscopic factors of the three resonances. Solid, dashed, and dotted lines indicate the $S^{pp}$'s for $1/2^{+},3/2^{+}$, and $3/2^{-}$ resonances, respectively.

Figure 4

Spectroscopic factors of the low-lying states in $N=19$ isotopes. Solid, dashed, and dotted lines stand for the lowest $1/2^{+},3/2^{+}$, and $3/2^{-}$, respectively. The spectroscopic factors of the corresponding states in ${}^{35}\mathrm{S}$ [35] and ${}^{37}\mathrm{Ar}$ [34] were determined by $(d,p)$ reactions. Here, only the statistical error is presented, whereas we estimated the systematic error as 100% for the $1/2^{+}$ and $3/2^{+}$ states and 30% for the $3/2^{-}$ state.