RIKEN Accel. Prog. Rep. 50 (2017)

Ⅱ-2. Nuclear Physics (Theory)

Quasi-particle random phase approximation (QRPA) withquasi-particle-vibration coupling (QPVC): application to the
Gamow-Teller response of a superﬂuid nucleus 120 Sn†∗1,∗2∗1∗5,∗6G. Colò,∗3,∗1 , E.
E. Vigezzi,Vigezzi,∗1C.L.
L.Bai,Bai,∗4∗4andandH.
H.Sagawa
Sagawa∗5,∗6
Y. Y.
F. Niu,Niu,∗1,∗2C.

The RPA+PVC approach is obviously limited to thecase of magic nuclei. In this paper we propose theQRPA+QPVA formalism for spherical superﬂuid nuclei, describing the nuclear ground state within theHartree-Fock-Bogoliubov (HFB) approximation, andthe collective excitations of the system within QRPA.
We consider the Gamow-Teller transitions in a wellbound super-ﬂuid nucleus 120 Sn in this study. As aunique feature in GT transitions of superﬂuid nuclei,
both isovector (IV) and isoscalar (IS) pairing are expected to play a relevant role. While the usual IV
pairing determines the ground-state structure, the IS
pairing is present in the QRPA residual interaction forGamow-Teller transitions.
The GT strength associated with QRPA+QPVC, isgiven by
11S(E) = Im,(1)ν|ÔGT± |02πE−Ω+i( Γ2ν + Δ)ννA
where the GT operator is ÔGT± = i=1 σ(i)t± (i) andΔ is a smearing parameter. In our calculation, we
will only focus on the GT− excitations. |ν denotes
the eigenstates associated with the complex eigenvalues Ων − i Γ2ν obtained by diagonalizing the energydependent complex QRPA matrix.
The four theoretical strength functions are compared with experimental results in Fig. 1. We usea smearing parameter Δ = 0.5 MeV in the QRPA andQRPA+QPVC calculation. In Fig. 1, the (3 He, t) experimental low-energy strength distribution is well reproduced by including isoscalar pairing, while the (p,n)
data are better reproduced without it. The spreading
width and lineshape of the giant resonance region arevery well reproduced by the inclusion of the QPVC
eﬀect.
HFB+QRPA is an appropriate tool for neutronrich and neutron-deﬁcient, nuclei, especially for weakly
bound nuclei. The QRPA+PVC calculation in thesecases is a new research line which is still in its infancy. Improving the theoretical predictive power ofsuch calculations is not only beneﬁcial for our progress
†∗1
∗2
∗3
∗4
∗5
∗6

Condensed from the article in Phys. Rev. C 94, 064328(2016)
Istituto Nazionale di Fisica Nucleare (INFN)
ELI-NP, ”Horia Hulubei” National Institute for Physics andNuclear Engineering, Bucharest-Magurele
Dipartimento di Fisica, Università degli Studi di Milano
School of Physical Science and Technology, Sichuan University, Chengdu
RIKEN Nishina Center
Center for Mathematics and Physics, University of Aizu

- 98 -Fig. 1. (Color online) Gamow-Teller strength distributionsfor 120 Sn calculated by QRPA and QRPA+QPVC models, with [panel (a)] and without [panel (b)] isoscalarpairing, using the Skyrme interaction SkM*. The excitation energy is with respect to the ground state of120
Sn. The smearing parameter Δ = 0.5 MeV is used.
The experimental results from (3 He, t) and (p,n) reactions are shown for comparison. The cross section fromthe (3 He, t) experiment is scaled by a factor of 1.6 sothat the main GTR strength exhausts 65% of the Ikeda
sum rule1) . The cross section from the (p,n) reaction isnormalized by the unit cross section2)

in understanding nuclear structure, but also of essential interest understanding weak-interaction processes
in particle physics and astrophysics. Accordingly, weenvisage the study of weak-interaction processes ofastrophysical interest in our future research of theQRPA+QPVC model.
References
1) K. Pham et al., Phys. Rev. C51, 526 (1995).
2) M. Sasano et al., Phys. Rev. C79, 024602 (2009).