RIKEN Accel. Prog. Rep. 48 (2015)

Ⅱ-2. Nuclear Physics (Theory)

Proton-neutron pairing vibrations in 40 Ca: Precursory soft mode ofthe isoscalar spin-triplet pairing condensation†
K. Yoshida∗1†∗1Condensed from the article in Phys. Rev. C 90, 031303(R)(2014)
Graduate School of Science and Technology, Niigata University80-1)" $&$!%$%&$!&
pair-transfer
strength (MeVThe pairing correlation plays a central role in lowenergy nuclear phenomena. The correlation is sostrong that the ﬂuctuations of the pairing gap aroundits zero equilibrium value develop in nuclei near theclosed shell, and the systems get deformed eventuallyin gauge space when more nucleons are added. The collective pairing vibration emerging in the closed-shell
nuclei is thus associated with the occurrence of thepairing condensation.
It is in the isovector and spin-singlet (T = 1, S = 0)channel that the pairing correlation has been extensively studied. With the advent of the radioactiveisotope beam technology, heavy proton-rich nuclei
along the N = Z line have received considerable attention. The isoscalar and spin-triplet (T = 0, S = 1)
pairing correlation is expected to be visible in N ∼ Z
nuclei because the shell structures around the Fermi
levels of both neutrons and protons are similar to eachother and the spatial overlap between the neutron andproton single-particle wave functions would be large toform a proton-neutron (pn) Cooper pair1) . Because of
the strongly attractive pn interaction in the 3 S1 channel, the possible T = 0 pairing condensate has been
discussed theoretically in heavy N ∼ Z nuclei2–4) .
I investigate the possibility of a collective T = 0 pnpairing vibrational mode in the “normal” phase where
the T = 0 pairing gaps are zero. The pn pair excitations are described microscopically based on the nuclear energy-density functional (EDF) method. Moreprecisely, the pn-pairing vibrational modes are obtained out of the solutions of the pn particle-particle
random-phase approximation (ppRPA) equation, andare described as elementary modes of excitation generated by two-body interactions acting between a protonand a neutron. Then, I show that the strongly collective T = 0 pn-pairing vibrational mode emerges when
the interaction is switched on.
Figure 1 shows the strength distributions for themonopole (L = 0) pn-pair-addition and removal trans†fer |⟨Z ± 1, N ± 1; λ|P̂T,S(P̂T,S )|Z, N ⟩|2 as functions ofthe RPA frequency ωλ in 40 Ca. In the present calculation, the SGII interaction is used for the particlehole (ph) channel. For the pp channel, the densitydependent contact interactions are employed. Thepairing strength in the T = 1 channel is ﬁxed as(T =1)
V0= −390 MeV fm3 . The pairing strength in(T =0)(T =1)
the T = 0 channel is given as V0= f × V0.

f=0
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f=1.0
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f=1.3
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f=1.7
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f=2.0
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60
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40
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42Sc 15
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(b)
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8

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(c)

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34Fig. 1. Monopole pn pair-addition strengths of 40 Ca →42
Sc and pair-removal strengths of 40 Ca → 38 K in theπJ = 1+ , T = 0 [(a), (b)] and J π = 0+ , T = 1 [(c),(d)] states smeared with a width of 0.1 MeV. For the(J, T ) = (1, 0) channel, the strengths obtained with factors f = 0, 1.0, 1.3, 1.7, and 2.0 are shown. For the(J, T ) = (0, 1) channel, the unperturbed single-particle
transition strengths are also shown by a dotted line.

Factor f is changed to see the eﬀect of the interactionin the T = 0 channel.
It is clearly visible that the RPA frequency of theT = 0 pn-pairing vibrational mode becomes lower on
increasing the pairing strength f . The pairing collectivity generated is sensitive to the shell structure aswell as to the interactions. The critical strength isfound to be fc = 2.04. A rapid lowering of the RPA frequency seen here indicates the occurrence of true vacuum giving the T = 0 pairing gaps ∆ ≡ ⟨P̂T =0,S=1 ⟩ ̸=0 in the limit of the strong pairing interaction f > fc .
Another direct measure of the collectivity is the pntransfer strength. One can also see an exponential enhancement in the transition strengths when approaching the critical strength fc . Therefore the 1+ state in38
K and 42 Sc can be considered as a precursory softmode of the T = 0, S = 1 pairing condensation.
References
1) A. L. Goodman: Phys. Rev. C 58, R3051 (1998).
2) W. Satula and R. Wyss: Phys. Lett. B 393, 1 (1997).
3) A. L. Goodman: Phys. Rev. C 60, 014311 (1999).
4) G. F. Bertsch and Y. Luo: Phys. Rev. C 81, 064320(2010).

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