Oxygen, with eight protons, is the heaviest isotope for which the neutron drip line has been experimentally established; it occurs at ²⁴O which has 16 neutrons. A Hamiltonian called USDB [1] for the sd (0d_5/2,1s_1/2,0d_3/2) shell that was derived in 2006 made predictions for the energies and spectroscopic properties of neutron unbound states in nuclei near ²⁴O.

The results are shown in the figure. We plot the energies of states relative to ¹⁶O vs mass number. States in a nucleus with A nucleons are bound to neutron decay if their energy is lower than that in the nucleus with A-1 nucleons. The blue dots in the figure are bound-state energies that were known in 2006 and were used (together with about 600 other energy data) to determine the properties of the USDB Hamiltonian.

The horizontal black lines are the predicted energies obtained with the USDB Hamiltonian. ²⁴O is at the neutron drip line since the energies of states in heavier nuclei are smaller than that of ²⁴O and neutrons added to ²⁴O will literally drip off. The black arrows show the neutron decay pattern expected for the neutron unbound states.

Since 2006 many experiments have been carried out to observe the centroids and widths of these neutron unbound states which can be compared to the theoretical predictions. The experimental centroids are shown by the red dots.

In 2007 a level in ²³O consistent with a 3/2⁺ assignment was observed at RIKEN [2] that is in good agreement with the prediction. Also in 2007 a low energy neutron from the decay of ²³O was observed at the NSCL which was associated with the predicted 5/2⁺ state just above the neutron-decay threshold [3] From the observed the neutron-decay centroid energy of 40 keV one predicts a neutron-decay width of 10 eV (much smaller than the experimental resolution). This is perhaps the smallest neutron decay width predicted so far for any nucleus.

In 2008 the neutron decay of ²⁵O was observed [4] which was associated with the predicted 3/2⁺ state. There are two problems in comparison with theory. The energy is about 500 keV lower than predicted. The other problem is that the experimental decay width is about two times larger that predicted. Perhaps the lowest state in ²⁵O is the 1p_3/2, or perhaps there is a doublet of 0d_3/2 and 1p_3/2. We may expect a crossing of the 0f_7/2 and 1p_3/2 [5] in the isotones with N=15 as the single-particle energies become loosely bound. The pattern of 0d_3/2, 1p_3/2 and 0f_7/2 single-particle states for N=15 may be analogous to the better known experimental and theoretical properties of the 0p_1/2, 1s_1/2 and 0d_5/2 orbitals for N=7 [6].

In 2009 the decay of two excited state of ²⁴O were observed [7] This experiment showed that the first excited state in ²⁴O was high (4.0 MeV) confirming the doubly closed-shell nature of ²⁴O predicted by USDB. The centroid of the two states observed are 200 to 600 keV lower than those predicted (2⁺ and 1⁺). There are four states that have a large 0d_3/2 component, 3/2⁺ in ²³O, 2⁺ and 1⁺ in ²⁴O and 3/2⁺ in ²⁵O. Since the USDB Hamiltonian is determined by neutron-bound states, one might expect some dissagrement with the predictions when the state becomes unbound. But it is not clear why there is agreement with theory for ²³O but an energy lowering compared to theory for ²⁴O and ²⁵O.

For the future, the decay of ²⁶O provides the exciting prospect of observing the fist di-neutron decay. As seen the figure, from the centroid energies, ²⁶O is bound to one-neutron decay but unbound to two-neutron decay. But there may also be some sequential process for neutron decay through the tail of the unbound state in ²⁵O.

References

[1] B. A. Brown and W. A. Richter, Phys. Rev. C {\bf 74}, 034315 (2006). link to paper

[2] Z. Elekes et al., Phys. Rev. lett. {\bf 98}, 102502 (2007). link to journal

[3] A. Schiller et al., Phys. Rev. Lett. {\bf 99}, 112501 (2007). link to journal

[4] C. R. Hoffman et al., Phys. Rev. Lett. {\bf 100}, 152592 (2008). link to journal

[5] I. Hamamoto, Phys. Rev. C {\bf 76}, 054319 (2007). link to journal

[6] H. Sagawa, B. A. Brown and H. Esbensen, Phys. Lett. {\bf B309} 1, (1993). link to paper

[7] C. R. Hoffman et al., Phys. Lett. B 672, 17 (2009). link to journal