Reduced Occupancy of the Deeply Bound $0d_{5/2}$ Neutron State in ${}^{32}\mathrm{A}\mathrm{r}$

The ${}^9\mathrm{B}\mathrm{e}({}^{32}\mathrm{A}\mathrm{r},{}^{31}\mathrm{A}\mathrm{r})X$ reaction, leading to the ${\frac{5}{2}}^{+}$ ground state of a nucleus at the proton drip line, has a cross section of 10.4(13) mb at a beam energy of $65.1\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{\text{nucleon}}$. This translates into a spectroscopic factor that is only 24(3)% of that predicted by the many-body shell-model theory. We introduce refinements to the eikonal reaction theory used to extract the spectroscopic factor to clarify that this very strong reduction represents an effect of nuclear structure. We suggest that it reflects correlation effects linked to the high neutron separation energy (22.0 MeV) for this state.

Figure 1

The two lower diagrams show the Woods-Saxon potentials for the valence nucleons of ${}^{22}\mathrm{O}$ and ${}^{32}\mathrm{A}\mathrm{r}$. Note the large asymmetry in the Fermi energies for these nuclei near the neutron and proton drip lines. The top diagrams show the corresponding radial number distributions of the residues (normalized to the number of nucleons divided by $4\pi$) obtained in a Hartree-Fock calculation with the Skyrme X (SKX) interaction [6].

Figure 2

Longitudinal momentum distribution for the unreacted projectile beam ${}^{32}\mathrm{A}\mathrm{r}$ fitted with a rectangular distri­bution folded with a Gaussian resolution function. The distribution of the ${}^{31}\mathrm{A}\mathrm{r}$ residues (left) is compared with theoretical calculations for $l=0$ (dashed line) and $l=2$ (solid line).

Figure 3

Measured reduction factors $R_s$ as a function of nucleon separation energy. The points, taken from the left, use data from ${}^8\mathrm{B}$, ${}^9\mathrm{C}$, ${}^{15}\mathrm{C}$, ${}^{57}\mathrm{N}\mathrm{i}$, ${}^{12}\mathrm{C}$, and ${}^{16}\mathrm{O}$ [4, 5, 26]. The labeled $N=14$ nuclei are discussed in the present Letter.