RIKEN Accel. Prog. Rep. 48 (2015)

Ⅱ-2. Nuclear Physics (Theory)

Correlated two-neutron emission in decay of unbound nucleus 26 O†
K. Hagino∗1 and H. Sagawa∗2,∗3We study the two-neutron decay of the unbound 26 O
nucleus with a three-body model assuming an inert 24 O
core and two valence neutrons. In order to describe thedecay properties of the neutron unbound nucleus, wetake into account the couplings to the contiuum byusing the Green’s function technique.
In the experiment of Ref.1) , the 26 O nucleus wasproduced in a single proton-knockout reaction from asecondary 27 F beam. Therefore, we ﬁrst construct theground state of 27 F with a three-body model, assuming the 25 F+n+n structure. We then assume a sudden proton removal; that is, the 25 F core changes to24O keeping the conﬁguration for the n+n subsystemof 26 O to be the same as that in the ground state of27F. This initial state, Ψi , is then evolved with theHamiltonian for the three-body 24 O+n+n system forthe two-neutron decay.
We consider two three-body Hamiltonians, one forthe initial state 25 F+n+n and the other for the ﬁnal
state 24 O+n+n. For both cases, we use the Hamiltonian
H = ĥnC (1) + ĥnC (2) + v(1, 2) +p⃗1 · p⃗2,Ac m(1)where Ac is the mass number of the core nucleus, m isthe nucleon mass, and ĥnC is the single-particle (s.p.)
Hamiltonian for a valence neutron interacting with thecore. We use a contact interaction between the valence
neutrons. See ref.2) for details of the parameters of Eq.
(1) and the contact interaciton between the neutrons.
With the initial wave function from the three-bodymodel, the decay energy spectrum can be computedas3)dP
1= ℑ⟨Ψi |G(E)|Ψi ⟩,dEπ(2)

with G(E) = G0 (E) − G0 (E)v(1 + G0 (E)v)−1 G0 (E),where ℑ denotes the imaginary part. G(E) is the perturbed Green’s function, while G0 (E) is the unperturbed Green’s function given byG0 (E) =∑ |(j1 j2 )(0+ ) ⟩⟨(j1 j2 )(0+ ) |1,2

e1 + e2 − E − iη,(3)where the sum includes all independent two-particle
states coupled to the total angular momentum J = 0with positive parity, as described by the three-body
Hamiltonian for 24 O+n + n.
Figure 1 shows the decay energy spectrum obtained†
∗1
∗2
∗3

Condensed from the article in Phys. Rev. C 89,014331(2014)
Department of Physics, Tohoku University
RIKEN Nishina Center
Center for Mathematics and Physics, University of Aizu

Fig. 1. (Color online) Decay energy spectrum for the twoneutron emission decay of 26 O. The solid line shows
the result with the full inclusion of the final–stateneutron-neutron (nn) interaction, while the dotted lineshows the result without the final–state nn interaction. The dashed line is obtained by including only+the (d3/2 d3/2 )(0 ) configurations in the unperturbed
Green’s function of Eq. (3). The theoretical curves
are drawn with a finite width of 0.21 MeV, which isthe same as the experimental energy resolution. The
experimental data are taken from Ref.1) .

with Eq. (2). The solid line shows the correlated spectrum, in which the ﬁnal–state nn interaction is fully
taken into account, while the dotted line shows the result without the ﬁnal–state nn interaction. The lattercorresponds to the term G0 (E) in G(E). Without theﬁnal–state nn interaction, the two valence neutrons in26
O occupy the s.p. resonance state of 1d3/2 at 770
keV, and the peak in the decay energy spectrum appears at twice this energy. When the ﬁnal–state nn interaction is taken into account, the peak is drasticallyshifted towards a lower energy and appears at 0.14
MeV, in good agreement with the experimental data.
The ﬁgure also shows with the dashed line the result+obtained by including only the (d3/2 d3/2 )(0 ) conﬁgurations in the unperturbed Green’s function of Eq.
(3). This corresponds to the case without the dineutron correlation in the ﬁnal state, as the dineutron correlation is caused by an admixture of several conﬁgurations with diﬀerent parities. The dineutron correlation
shifts the peak position further down, making the peak
appear at an energy close to the threshold, as shownby the solid line.
We discuss the role of neutron-neutron correlation in
the decay probability as well as in the energy and theangular distributions of the emitted neutrons in Ref.2)
References
1) E.Lunderberg et al.,Phys.Rev.Lett.108,142503 (21012).
2) K.Hagino and H.Sagawa, Phys.Rev.C89,014331(2014).
3) H.Esbensen and G.F.Bertsch, Nucl.Phys.A542, 310(1992).

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