Determination of the $N=16$ Shell Closure at the Oxygen Drip Line

The neutron unbound ground state of ${}^{25}\mathrm{O}$ ($Z=8$, $N=17$) was observed for the first time in a proton knockout reaction from a ${}^{26}\mathrm{F}$ beam. A single resonance was found in the invariant mass spectrum corresponding to a neutron decay energy of ${770}_{-10}^{+20}\mathrm{keV}$ with a total width of 172(30) keV. The $N=16$ shell gap was established to be 4.86(13) MeV by the energy difference between the $\nu 1s_{1/2}$ and $\nu 0d_{3/2}$ orbitals. The neutron separation energies for ${}^{25}\mathrm{O}$ agree with the calculations of the universal $sd$ shell model interaction. This interaction incorrectly predicts an ${}^{26}\mathrm{O}$ ground state that is bound to two-neutron decay by 1 MeV, leading to a discrepancy between the theoretical calculations and experiment as to the particle stability of ${}^{26}\mathrm{O}$. The observed decay width was found to be on the order of a factor of 2 larger than the calculated single-particle width using a Woods-Saxon potential.

Figure 1

Measured ${}^{24}\mathrm{O}$ fragment kinetic energies (a), neutron kinetic energies (b), and their relative decay angle (c) are shown by the data points with their statistical errors. The results of Monte Carlo simulation are shown by the solid black lines which are comprised of the sum of the resonant (red, dotted) and nonresonant (blue, dashed) contributions to the decay spectrum (see text).

Figure 2

The reconstructed neutron decay energy spectrum of ${}^{25}\mathrm{O}$ is shown by the data points. The solid black line shows the simulated line-shape composed of a resonant (red, dotted) ($E_{\mathrm{decay}}=770\mathrm{keV}$, $\Gamma =172\mathrm{keV}$, $l=2$) and nonresonant (blue, dashed) contribution (ratio $3.25:1$). The inset shows a contour plot of the ${\chi }^2$ dependence ($N=19\mathrm{degrees}$ of freedom) of the Breit-Wigner parameters for decay energy ($E_{\mathrm{decay}}$) and total width ($\Gamma$). The red (dotted) and blue (dashed) contours represent the 1 and 2 $\sigma$ limits, respectively.

Figure 3

The experimental (data points) and theoretical [13, 14, 15] (lines) single-particle energies (SPE) for the $\nu 1s_{1/2}$ and $\nu 0d_{3/2}$ orbitals at $N=16$ are shown on the left. The difference between these SPEs is shown for $Z=8$, $N=15$ [12] and 16, giving the $N=16$ shell gap size. Errors are shown if they are larger than the symbol size.

Figure 4

The experimental [25, 26] (data points) and theoretical [13, 14, 15] (lines) one- and two-neutron separation energies for the $N=15–18$ oxygen isotopes. The experimental error is shown if it is larger than the symbol size.