Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 47 (2014)

RIKEN Accel. Prog. Rep. 00 (0)Di-neutron correlation in pair-addition vibrational mode of theneutron-rich Sn isotopes†
H. Shimoyama∗1 and M. Matsuo∗2
the low-lying pair vibration in 134 Sn has a some degreeof collectivity.
(ad)
Figure 1 shows the transition density Pν0 (r) andthe partial sums of the decomposed transition densi∑
(ad)
(ad)
ties, Pν0,lcut (r) = ii′ ,l≤lcut Pν0,ii′ (r), for various values of the angular momentum cut-oﬀ lcut . Although(ad)the partial sums (Pν0,lcut (r)) of each high-l component
are very small, the inclusion of these small transition
densities is necessary to reproduce the total transition
density. The highest orbital angular momentum of theoccupied Hartree−Fock single particle orbit in 134 Sn
is locc = 5(1h11/2 ). However it is clear that the large
value of the orbital angular momentum contributes tothe total transition density. The coherent accumulation up to high-l contributions in the pair-addition vibrational mode suggests the di-neutron5) correlation
discussed in the same manner in Ref.[4, 6].
We ﬁnd that the di-neutron correlation in the lowlying pair vibration of 132−140 Sn is formed by large
numbers of weakly bound and unbound continuum
quasiparticle states. Therefore, even if the positionsof the quasiparticle states are varied for other Skyrme
parameter sets, this di-neutron character may be observed in the low-lying pair vibration or pair rotationof the neutron-rich Sn isotopes with N ≥ 82.

Recently, two-neutron transfer in unstable nuclei has
attracted attention since the experiments using radioactive ion beams became possible1,2) . Anticipating future experiments, we have been theortically investigating two-neutron transfer modes in heavy-mass
neutron-rich nuclei. A good example is of neutron-rich
Sn isotopes with A ≥ 132, for which we predict enhanced pair-addition transfer populating the groundstates (pair rotation) or the low-lying 0+ states (pairvibration) in the neighboring ∆N = 2 isotopes3) . In
this works we analyze in detail the microscopic structure of the two-neutron transfer modes, and we showthat di-neutron correlation appears in the pair vibrational mode of the neutron-rich Sn.
We describe the two-neutron transfer using theHartree−Fock−Bogoliubov (HFB) mean-ﬁeld theory
and the continuum quasiparticle random phase approximation (QRPA)3,4) . The Skyrme functional withthe parameter SLy4 is adopted. For pairing interaction, we choose the density-dependent delta interaction.
We analyze the microscopic structure of the twoneutron transfer modes in the Sn isotopic chain, especially the pair-addition vibrational mode in 132−140 Sn.
Within the QRPA theory, one can characterize anexcitation mode in terms of forward- and backwardpropagating amplitudes Xiiν ′ and Yiiν′ for the twoquasiparticle conﬁguration ii′ = (nlj) (n′ l′ j ′ ). Theindex ν is a label for QRPA normal modes, andexcitation energy is denoted as h̄ων . Concerning
the low-lying pair vibration state predicated to appear at h̄ων = 3.81 MeV in 134 Sn, for example,
the main two-quasiparticle conﬁgurations (|Xiiν ′ | >0.1) are [3p3/2 ]2 , [1h9/2 ]2 , [2f7/2 ]2 , [2f5/2 ]2 , [1i13/2 ]2 ,[3p1/2 ]2 , and [3p3/2 ][4p3/2 ]. These quasiparticle orbits
are weakly bound or unbound resonant quasiparticle(ad)states. Similarly, the transition density PνL=0 (r) forthe monopole (L = 0) pair-transfer operator can be de∑(ad)(ad)composed as Pν0 (r) = ii′ Pν0,ii′ (r) in terms of thetwo-quasiparticle conﬁgurations. For the main components, the amplitude of these decomposed transition
densities are signiﬁcantly smaller than that of the total transition density. Even if we sum the main decomposed transition densities, it reproduces approximately
half of the total transition density. This suggests that†∗1∗20.5(b)r P

2 (ad)-1(r) (fm )

0.4

134

lcut= 12
11
10
98
7
654
3
2
10

Sn−hων= 3.81 MeV

0.3
0.2
0.1
00

2

4

68r (fm)

10

121416Fig. 1. Decomposition of the pair-addition transition den(ad)sity Pν0,lcut (r) of the pair-addition vibrational mode in134
Sn with respect to the orbital angular momentum
cutoﬀ lcut = 0, 1, 2, · · · , 12. The√ arrow indicates theneutron rms radius RN,rms (= ⟨rn2 ⟩) = 4.93 fm.

References

1) I. Tanihata et al.: Phys. Rev. C 100, 192502 (2008).
2) K. Wimmer et al.: Phys. Rev. C 105, (2010).
3) H. Shimoyama and M. Matsuo: Phys. Rev. C 82,044317 (2011).
4) Y. Serizawa and M. Matsuo: Prog. Theor. Phys. 121,
97 (2009).
5) G. F. Bertsch and H. Esbensen, Ann. Phys. (NY) 209,327 (1991).
6) M. Matsuo, K. Mizuyama, Y. Serizawa: Phys. Rev. C71, 064326 (2005).

Condensed from the article in Phys. Rev. C 88, 054308(2013)
Department of Physics, Faculty of Science and Graduate
School of Science and Technology, Niigata University
Department of Physics, Faculty of Science, Niigata University- 57 -1