Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 52 (2019)

Spin-singlet and spin-triplet pairing correlations on shape evolution insd-shell N = Z Nuclei†
E. Ha,∗1 M. -K. Cheoun,∗1 and H. Sagawa ∗2,∗3Pairing correlations play an important role in nuclear structure, and have an important eﬀect on nuclear electro-magnetic (EM) and weak transitions.
The pairing correlations are classiﬁed into like-pairing(neutron-neutron (nn) and proton-proton (pp)) andunlike-pairing (neutron-proton (np)) correlations. In
particular, for N = Z nuclei, the np pairing may become signiﬁcant because protons and neutrons occupy
the same orbital and have the maximum conﬁguration
overlap, which is important especially for the T = 0pairing. The nn and pp pairings have isovector (IV)spin-singlet (T = 1, J = 0) mode, while the np pairing correlations have peculiar isoscalar (IS) spin-triplet(T = 0, J = 1) as well as IV spin-singlet mode. Overthe last few decades, there have been many discussions
regarding the np pairing correlations, in particular, thecoexistence of IS and IV correlations and their competitions in some speciﬁc nuclear observables.
Recently, interesting experimental data have beenreported, which show more quenching in the IV M1
spin transition data for the N = Z sd-shell nuclei1)
than the IS data. These features are not expectedaccording to former theoretical discussions.2,3) It waspointed out in Ref. 4) that the T = 0 pairing plays
a signiﬁcant role to cause these features in the spin
dependent observables.
We studied the shape evolution of N = Z nuclei,
24Mg, 28 Si, and 32 S in the deformed Woods-Saxon(DWS) and deformed BCS (DBCS) approximations
taking into account both T = 0 and T = 1 pairingcorrelations. In the ﬁlling approximation for the DWS
potential, it is shown that the shape evolution strongly
correlates with the shell structure of s.p. energies near
the last occupied orbit (Fermi energy). The eﬀect of
two types of pairing correlations with isospin T = 0and T = 1 are studied by the DBCS model with Gmatrix-based pairing interactions. We adopted an enhanced T = 0 pairing interaction to clarity the eﬀect of
T = 0 pairing on the ground state energy. In Fig. 1, weused a stronger T = 0 interaction (50% stronger thanthe G-matrix results4) ), which makes the pairing correlations more transparent, especially at the large prolate
deformation and leads to the deep prolate deformation
minimum in 24 Mg. A drastic change in the pairing correlation energy is induced by the active T = 0 pairing
channel on top of the usual T = 1 channel, implying†∗1∗2∗3Fig. 1. The ground state energy (Etotal = EMF′ +Epair ) for24Mg by the DBCS model with Woods-Saxon potential.
Mean field energy by the DBCS is denoted as EMF′ .
Epair is the pairing energy in the right y-axis. The
pairing energies are estimated with enhanced T = 0
pairing in np channel.

that the two paring channels co-exist in the large deformation region.
In summary, we found a coexistent phase of twotypes of superconductors in the large deformation region |β2 | > 0.3 in 24 Mg, 28 Si and 32 S with the enhanced
T = 0 pairing. The competition between T = 0 andT = 1 pairing channels substantially aﬀect the energy
minima of 24 Mg, 28 Si and 32 S. Our model gives a reasonable deformation minima for these nuclei, i.e., prolate for 24 Mg and 32 S and oblate for 28 Si.
References

1) H. Matsubara et. al., Phys. Rev. Lett. 115, 102501(2015).
2) A. Arima , K. Shimizu, W. Bentz, H. Hyuga, Adv. Nucl.
Phys. 18, 1 (1987).
3) I. S. Towner, Phys. Rep. 155, 263 (1987).
4) H. Sagawa, C. L. Bai, G. Colo, Phys. Scr. 91, 083011(2016).

Condensed from the article in Phys. Rev. C 97, 024320(2018)
Department of Physics and Origin of Matter and Evolutionof Galaxy (OMEG) Institute, Soongsil University
RIKEN Nishina Center
Center for Mathematics and Physics, University of Aizu

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