Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 50 (2017)

Decay dynamics of the unbound 25 O and 26 O nuclei†∗1∗2,∗3and H.
H. Sagawa
Sagawa∗2,∗3
K. Hagino,Hagino∗1andTable 1. Comparison of the energies of the 3/2+ state of25
O and the 2+ state of 26 O obtained with several methods. These values, given in units of MeV, are measured
from the thresholds.

We study the ground and excited resonance statesin 26 O with a three-body model by taking into accountthe coupling to the continuum. The main aim of ourstudy is to extract the di-neutron correlations and thehalo nature of the ground state of 26 O from the twoneutron decay spectrum with updated empirical inputs
for the model Hamiltonian. In the present 24 O +n +n three-body model, the neutron-core potential as wellas the strength of the pairing interaction between thevalence neutrons is calibrated using new experimental data from Ref.1)1 and the calculations performed inRefs.2)2 are reﬁned. With the same model input, wealso discuss the structure of the excited 2+ resonancestate.
We discuss the ﬁrst 2+ state in 26 O. One of the mostimportant ﬁndings in the recent experiment reportedin Ref.1)1 is a clear second peak at E = 1.28+0.11−0.08 MeV,
which is likely attributed to the 2+ state. Because of
the pairing interaction between the valence neutrons,
the energy of the 2+ state is slightly shifted towards
lower energies from the unperturbed energy, whereas
the energy shift is much larger for the 0+ state due tothe larger overlap between the wave functions of thetwo neutrons in the three-body model. The 2+ peakappears at 1.282 MeV, which agrees perfectly with theexperimental data, as shown in Table 1.
While we achieve an excellent agreement with theexperimental data for the energy of the 2+ state, it isstriking that most theoretical calculations performed
so far overestimate the energy. We summarize otherresults in Table I together with the energy of the 3/2+state in 25 O for each calculation. The 2+ state should
certainly appear at an energy slightly lower than theunperturbed state, as long as the three-body structure
is reasonable. In this sense, the ab-initio calculation
with chiral N N and 3N interactions shows the opposite trend, and the shell model (SM) calculations, except for the continuum SM calculations of Ref. 4)4 andRef.5)5,, seem to overestimate the correlation.
We next discuss the angular correlation of the emitted neutrons from the ground state of 26 O. Figure 1
shows the angular distributions thus obtained. In theabsence of the correlation between the valence neutrons, the angular distribution is symmetric with respect to θ12 = π/2 (see the dotted line). On theother hand, in the presence of the interaction between
the valence neutrons, the angular distribution becomes
highly asymmetric, with an enhancement of the back†∗1∗2∗325 25+ + 26 26 +MethodO (3/2) ) O (2O )(2+ ) Ref. Ref.
MethodO (3/2
Shellmodel(USDA)
1.301
1.9 1.9 3) 3)
Shell model (USDA)
1.301
Shell
1.303
2.1 2.1 3) 3)
Shell modelmodel(USDB)(USDB)
1.303
chiral0.742
1.641.64 3) 3)
chiralNN
NN++3N3N
0.7424)
continuum SM
1.002
1.8continuum SM
1.002
1.8 5) 4)
continuum-coupled SM
0.86
1.66
continuum-coupled SM0.86
1.66 6) 5)
3-body model?
1.66)
3-bodymodel
model?
3-body0.749 (input)
1.2821.6 this work
3-bodymodel
0.749(10)(input)1.28+0.11
1.282 1) this work
Experiment
0.749
−0.08

Experiment

0.749 (10)1.28+0.11−0.081)

Fig. 1. (Color online) Angular correlations between theemitted neutrons from the two-neutron decay of 26 O.
The solid and dotted lines show the correlated and uncorrelated distributions, respectively.

to-back emission,2,7) as shown by the solid line. This isa natural consequence of the dineutron correlation in
the momentum space, which has an opposite trend tothe correlation in the coordinate space; the di-neutron
correlation has a strong peak at the small correlation
angle in the coordinate space and Heisenberg’s uncertainty principle converts the backward correlations in
the momentum space.
References
1) Y. Kondo et al., Phys. Rev. Lett.116, 102503 (2016).
2) K. Hagino and H. Sagawa, Phys. Rev. C89, 014331(2014) ; Phys. Rev. C90, 027303 (2014).
3) C. Caesar et al., Phys. Rev. C88, 034313 (2013).
4) A. Volya, V. Zelevinsky, Phys. Rev. C74, 064314 (2006).
5) K. Tsukiyama, T. Otsuka, R. Fujimoto, Prog. Theor.
Exp. Phys. 2015, 093D01 (2015).
6) L.V. Grigorenko, M.V. Zhukov, Phys. Rev. C91, 064617(2015).
7) L.V. Grigorenko, I.G. Mukha, M.V. Zhukov, Phys. Rev.
Lett. 111, 042501 (2013).

Condensed from the article in Phys. Rev. C 93, 034330(2016)
Department of Physics, Tohoku University
RIKEN Nishina Center
Center for Physics and Mathematics, University of Aizu

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