RIKEN Accel. Prog. Rep. 50 (2017)

Ⅱ-2. Nuclear Physics (Theory)

Eﬀect of isoscalar spin-triplet pairings on spin-isospin responses†
H. Sagawa,∗1,∗2 T. Suzuki,∗3 and M. Sasano∗1
The spin-isospin response is a fundamental process
in nuclear physics and astrophysics. The GamowTeller (GT) transition induced by σ t± and, in a nocharge-exchange channel, magnetic dipole (M1) transitions are extensively observed in a broad region of
the mass table. Recent high-resolution proton inelastic scattering measurements at Ep = 295 MeV have revealed that the isoscalar (IS) quenching is substantiallysmaller than the isovector (IV) quenching in the spin
M1 excitations for several N = Z sd-shell nuclei.1) In
this paper, we study the eﬀect of IS spin-triplet pairing correlations on the IS and IV spin M1 responses
based on modern shell model eﬀective interactions forthe same set of N = Z nuclei as those in Ref. 1.
We consider the IS
and IV spin M1 operators,whichare given as ÔIS = i σ (i) and ÔIV = i σ (i)τz (i),respectively. The proton-neutron spin-spin correlation
is deﬁned as

Fig. 1. (Color online) Experimental and calculated protonneutron spin-spin correlation ΔS . See the text for details. Experimental data are taken from Ref. 1. See
Ref. 1 for a description of the experimental error bars.

1(S(σ ) − S(σ τz ))16  σn (i) + σp (i) σn (i) + σp (i)=i||f f ||i
44ii
ΔS =f−

fi|

 σn (i) − σp (i)i

n |i,p · S= i|S4|f f | σn (i) − σp (i)
i4|i

(1)

n =  sn (i). The corp =  sp (i) and S
where Si∈pi∈nrelation value is 0.25 and −0.75 for a proton-neutronpair with a pure spin triplet and a spin singlet, respectively. The former corresponds to the ferromagnet
limit of the spin alignment, while the latter is the antiferromagnetic one.
Shell model calculations are performed in the fullsd-shell model space with a USDB eﬀective interaction. In the results of USDB∗ , the IS spin-triplet interactions are enhanced by multiplying the relevant
matrix elements by a factor of 1.2 compared to theoriginal USDB interaction. For the results of the IV
spin-M1 transitions, a quenching factor q = 0.9 isused for USDB∗∗ . The calculations for 28 Si reproduce
quite well the experimental IS 1+ state with a strong
spin transition at Ex = 9.50 MeV. The enhanced IS
pairing has a quenching eﬀect of approximately 20%
on the transition strength [i.e., B(σ) = 6.82(5.63) inUSDB(USDB∗ )], but the excitation energies are lessaﬀected within a few hundred keV change. Two IV 1+†∗1∗2∗3

Condensed from the article in Phys. Rev. C 94, 041303(R)(2016)RIKEN Nishina Center
Center for Mathematics and Physics, University of Aizu
Department of Physics, Nihon Univeritystates with strong spin strengths of B(στ ) = 2.05 and0.92 are reported at Ex = 11.45 and 14.01 MeV, respectively. The shell model gives strong IV M1 statesat similar excitation energies. The enhanced IS pairing
reduces the IV spin transition strength, corresponding
to a renormalization factor of gseﬀ (IV)/gs (IV) = 0.87.
Figure 1 shows the experimental and calculated
proton-neutron spin-spin correlations (1). The results
calculated with the USDB interaction show poor agreement with the experimental data. The results withan enhanced IS spin-triplet pairing improve the agreement to some extent. A quenching factor close to unity,q = 0.9, for only the IV matrix elements, results eventually in a ﬁne agreement with the experimental values.
The positive value of the correlation indicates that thepopulation of spin triplet pairs in the ground state islarger than that of the spin singlet pairs.
In summary, we studied the IS and IV spin M1 transitions in even-even N = Z sd-shell nuclei using shellmodel calculations with USDB interactions in full sdshell model space. The quenching eﬀects on the spin
M1 transition matrices are larger in the IV case thanin the IS case. Positive contributions for the spin-spincorrelations are obtained via an enhanced isoscalar
spin-triplet pairing interaction. The eﬀect of the Δhole coupling is also examined on the IV spin transition, and the empirical spin-spin correlations in theground states are reproduced well by a combined eﬀectof the IS pairing and a quenching factor of q = 0.9 on
the IV spin transition matrix elements.
Reference1) H. Matsubara et al., Phys. Rev. Lett. 115, 102501(2015).

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