Direct experimental evidence for a multiparticle-hole ground state configuration of deformed ${}^{33}\mathrm{Mg}$

The first direct experimental evidence of a multiparticle-hole ground state configuration of the neutron-rich ${}^{33}\mathrm{Mg}$ isotope has been obtained via intermediate energy (400 A MeV) Coulomb dissociation measurement. The major part $\sim (70\pm 13)\%$ of the cross section is observed to populate the excited states of ${}^{32}\mathrm{Mg}$ after the Coulomb breakup of ${}^{33}\mathrm{Mg}$. The shapes of the differential Coulomb dissociation cross sections in coincidence with different core excited states favor that the valence neutron occupies both the $s_{1/2}$ and $p_{3/2}$ orbitals. These experimental findings suggest a significant reduction and merging of $sd-pf$ shell gaps at $N\sim 20$ and 28. The ground state configuration of ${}^{33}\mathrm{Mg}$ is predominantly a combination of ${}^{32}\mathrm{Mg}(3.0,3.5\mathrm{MeV};2^{-},1^{-})⨂{\nu }_{s_{1/2}}$, ${}^{32}\mathrm{Mg}(2.5\mathrm{MeV};2^{+})⨂{\nu }_{p_{3/2}}$, and ${}^{32}\mathrm{Mg}(0;0^{+})⨂{\nu }_{p_{3/2}}$. The experimentally obtained quantitative spectroscopic information for the valence neutron occupation of the $s$ and $p$ orbitals, coupled with different core states, is in agreement with Monte Carlo shell model (MCSM) calculation using 3 MeV as the shell gap at $N=20$.

Figure 1

Total inclusive differential CD cross section with respect to the excitation energy ($E$*) of ${}^{33}\mathrm{Mg}$. The smooth curve is the cross section on the basis of a direct breakup model using a plane wave approximation for the $s$ (left panel) and the $p$ orbital (right panel) neutrons, respectively. The inset of the each panel of the figure shows the ${\chi }^2/N$ for the fit of the direct breakup model calculation to the experimental differential CD.

Figure 2

(Top) The observed sum-energy spectrum of $\gamma$-ray transitions from the excited states of ${}^{32}\mathrm{Mg}$ after Coulomb breakup of ${}^{33}\mathrm{Mg}$. The inset shows a partial scheme of levels in ${}^{32}\mathrm{Mg}$ and the population of those states after Coulomb breakup. (Bottom) The solid black line represents the sum of simulated sum-energy spectra of $\gamma$ rays decaying from various core excited states and experimental atomic background. The experimental atomic background is represented by spectrum I. Spectrum II, spectrum III, and spectrum IV represent the simulated sum-energy spectra of $\gamma$ rays decaying from the 2.5-MeV excited state and combinations of the 3.5- and 3.0-MeV states and the 4.78- and 4.82-MeV states, respectively.

Figure 3

Partial differential CD cross section of ${}^{33}\mathrm{Mg}$ with respect to ($E^{*}-E_{\gamma }$) in coincidence with ${}^{32}\mathrm{Mg}$ in the excited states $\sim 3.0$, 3.5 MeV ($I^{\pi }=1^{-},2^{-}$). The smooth curve is the cross section on the basis of the direct breakup model using a plane wave approximation for the $s$-wave (left) and the $p$-wave (right) neutron, respectively. The inset of each panel of the figure shows the ${\chi }^2/N$ for the fit.

Figure 4

Partial differential CD cross section of ${}^{33}\mathrm{Mg}$ with respect to ($E^{*}-E_{\gamma }$), in coincidence with ${}^{32}\mathrm{Mg}$ in the excited state $\sim 2.5$ MeV ($I^{\pi }=2^{+}$). The smooth curve is the cross section on the basis of the direct breakup model using a plane wave approximation for the $s$ orbital (left panel) and $p$ orbital (right panel). The inset of each panel of figure shows the ${\chi }^2/N$ for the fit.

Figure 5

The total experimental inclusive (black filled-circle data) differential CD cross section of ${}^{33}\mathrm{Mg}$ is overlaid with the sum of calculated exclusive CD cross sections (red solid line) for four components of the ground state. The (red online) mesh shaded region is the associated errors obtained from the various contributions. Other shaded regions as mentioned in the figure represent different calculated exclusive CD cross sections with errors. The error of each component is obtained from the respective error of the spectroscopic factor of valence neutron(s), occupying a particular orbital coupled with the core excited state as shown in the figure.