II-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 54 (2021)

RIKEN Accel. Prog. Rep. 54 (2021)

Dineutron and eﬀective pairing forces in momentum space
M. Yamagami ∗1cmqrel

The spatial two-neutron correlation, called dineutron
correlation, is one of the unique features around the neutron drip line. The dineutron correlation has been discussed extensively in light-mass nuclei such as 11 Li,1,2)
but it is considered to be a universal phenomenon over
all mass-number regions.3)
We propose a new eﬀective pairing force by focusing on the spatial structure of a neutron pair.
First, we discuss the necessity by performing a threebody model calculation with the density-dependentzero-range force (DD δ(r)-force),1,2) Vδ (r 1 , r 2 ) =V (0) {1 − η[ρ(r 1 )/ρ0 ]} δ(r 1 − r 2 ). The DD δ(r)-force iswidely used in nuclear structure calculations.1–3) It mustbe supplemented with a cutoﬀ in the two-particle spectrum, ε1 + ε2 ≤ Ecut . The parameters V (0) and η are
adjusted for each Ecut so as to reproduce the propertiesof low-energy neutron-neutron (nn) scattering and thetwo-neutron energy E2n of ﬁnite nuclei. The parameterρ0 = 0.16 fm−3 is the saturation density.
In Fig. 1, the root-mean-square (rms) values krel andqcm of the relative and center of mass (cm) momenta ofpaired neutrons in 11 Li and 12 Be are shown. krel converges, while qcm diverges as a function of Ecut owing toundesirable coupling to high-momentum components ofsingle-particle states in the continuum.
In order to overcome the diﬃculties, we consider
a new eﬀective pairing force in momentum space (kspace) that has a non-local separable form (k-SEP(0)force), VSEP = − 2π1 2 Vk g(k)g(k′ )h(q)h(q ′ ). Here, theYamaguchi-type form factor g(k) = 1/(k2 + Λ2 ) and√
22the Gaussian distribution h(q) = ( πq0 )−3 e−q /q0 for
the relative momentum k and the cm momentum q of(0)paired neutrons are adopted. The parameters Vk andFig. 2. Two-neutron energies E2n obtained with the k-SEPforce (q0 = 0.209 and 0.171fm−1 ) and the DD δ(r)-force
with fixed Ecut = 40 MeV and η = 0.849, in comparison
with the experimental data.

Λ are ﬁxed so as to reproduce the properties of lowenergy nn scattering.4) The parameter q0 is ﬁxed by thetwo-neutron energy E2n of ﬁnite nuclei.
The krel and qcm obtained with the k-SEP force areshown in Fig. 1. They converge well above Ecut =100 MeV. Here, the parameter q0 = 0.209 fm−1
(0.171 fm−1 ) is used for 11 Li (12 Be). The small cm momentum qcm indicates that the pairing correlation occurs
only around the nuclear surface region in real space. The
relative momentum krel in 12 Be becomes larger than thatin Borromean 11 Li owing to the high-momentum component in the bound 1p1/2 state.
The two-neutron energies E2n of three-body systems
can be classiﬁed into two categories as shown in Fig. 2.
The Borromean nuclei (6 He, 22 C, 11 Li) are well described with q0 = 0.209 fm−1 , while q0 = 0.171 fm−1
for non Borromean nuclei. Because the parameter q0
introduces a cutoﬀ for correlations in the opening angleθk between k1 and k2 as cos θk ≲ q02 /(2k1 k2 ) in h(q),the pairing correlations have a more collective nature in
calculation with a larger q0 .
In conclusion, we proposed a new eﬀective pairing
force that describes well the structure of the neutronpair. It is also easily utilizable in various frameworks
such as the density functional theory in k space.5)
References

Fig. 1. Relative momentum krel and cm momentum qcm of
the neutron pair in 11 Li and 12 Be. The results using thek-SEP force and the DD δ(r)-force are shown.
∗1

Department of Computer Science and Engineering, Universityof Aizu

1) G. F. Bertsch, H. Esbensen, Ann. Phys. (NY) 209, 327(1991).
2) H. Esbensen, G. F. Bertsch, K. Hencken, Phys. Rev. C
56, 3054 (1997).
3) M. Matsuo, K. Mizuyama, Y. Serizawa, Phys. Rev. C 71,064326 (2005).
4) H. Tajima, T. Hatsuda, P. van Wyk, Y. Ohashi, Sci. Rep.
9, 18477 (2019).
5) M. Yamagami, Phys. Rev. C 100, 054302 (2019).

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