Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 56 (2023)
RIKEN
Accel. Prog. Rep. 56 (2023)

Momentum-space structure of dineutron in 11 Li†
M. Yamagami ∗1
A recent knockout-reaction experiment for the Borromean nucleus 11 Li measured the mean correlation angle between the momenta of emitted neutrons n1 and n2
in the reaction channel 11 Li(p, pn1 )10 Li∗ → 9 Li + n2 .1)
The dependence on the missing momentum k of n1 is
considered to reﬂect the spatial structure of dineutron.
Here, the reﬂection of the spatial structure of dineutron to the mean opening angle between the momenta
k1 and k2 of the valence neutrons at the ground state of11
Li is discussed. Further, the similarities with the mean
correlation angle are highlighted.
A three-body model calculation is performed in themomentum space using a ﬁnite-range n–n interaction,
which reproduces the two-neutron (2n) separation energy and the matter radius of 11 Li. Further, the 2n
density, ρ2 (k1 , k2 , θk ), is calculated using k1 = |k1 |,k2 = |k2 |, and the opening angle between k1 and k2 ,
θk . Figure 1(a) shows ρ2 (k1 , k2 , θk ) as a function of both
k1 = k2 = kn and θk . Figure 1(b) shows the 2n density inreal space via the Fourier transformation, ρ2 (r1 , r2 , θr ),using the radial coordinates, r1 = r2 = r, and opening
angle, θr .

of k1 = kn as follows[∫ kcut∫ πcos ⟨θk ⟩ ≡k22 dk2 2π sin θk dθk00]
× ρ2 (kn , k2 , θk ) cos θk /ρk (kn ),(1)where ρk (kn ) is the one-neutron density distribution.
Figure 2(a) shows ⟨θk ⟩ using the cutoﬀ momenta ofkcut = ∞ (no cutoﬀ) and kcut = ksurf = 0.62 fm−1 .

Fig. 2. (a) Mean opening angle ⟨θk ⟩ as a function of k1 = kn
for 11 Li. “Surface” indicates the cutoﬀ of kcut = ksurf . (b)Same as (a) but for 6 He, 22 C, and 19 B.

Fig. 1. (a) 2n density for 11 Li as functions of k1 = k2 = kn
and the opening angle θk . It is weighted with a factor of8π 2 kn4 sin θk . (b) Same as (a) but 2n density in real spaceas functions of r1 = r2 = r and the opening angle θr . It
is weighted with a factor of 8π 2 r4 sin θr .

The dineutron conﬁguration is obtained at the lowmomentum of (kn , θk ) = (0.18 fm−1 , 128◦ ). It is accompanied by the broad angular distribution, and the longkn -tail indicates the strong dineutron correlation (thehigh n–n relative momentum).
The mean opening angle ⟨θk ⟩ is deﬁned as a function†∗1Condensed from the article in Phys. Rev. C 106, 044316 (2022)
Department of Computer Science and Engineering, Universityof Aizu⟨θk ⟩ (no cutoﬀ) exhibits a peak at kn = 0.27 fm−1 ;however, it gradually increases above kn ≈ 0.5 fm−1 .
ksurf characterizes the low-momentum halo region by
k1 , k2 < ksurf . ⟨θk ⟩ using kcut = ksurf exhibits a peakat kn = 0.31 fm−1 and a plateau of ⟨θk ⟩ ≈ 82◦ abovekn ≈ 1.0 fm−1 . These features are consistent with theobserved k dependence of the mean correlation angle (thepeak at k ≈ 0.3 fm−1 and the plateau of approximately
87◦ above k ≈ 0.9 fm−1 ),1) which is considered to reﬂect
the 2n correlations in the surface region.2)
In conclusion, the manner in which the mean opening
angle reﬂects the 2n density in 11 Li was discussed. For⟨θk ⟩, the importance of the surface eﬀect and the similarities with the mean correlation angle in the knockout
reaction were highlighted. The same conclusion was obtained for 6 He, 22 C, and 19 B (see Fig. 2(b)), wherein
the measurement of the momentum dependence of theangular correlations between the halo neutrons can provide useful information on dineutron correlations at lowdensity.
References
1) Y. Kubota et al., Phys. Rev. Lett. 125, 252501 (2020).
2) J. Casal et al., Phys. Rev. C 104, 024618 (2021).

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