Isoscalar spin-triplet pairing and tensor correla1ons on Spin-Isospin response Osaka,Japan, November 16-19,

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1 Isoscalar spin-triplet pairing and tensor correla1ons on Spin-Isospin response Osaka,Japan, November 16-19, Hiroyuki Sagawa RIKEN/University of Aizu Skyrme tensor interac1ons Shell evolu1on in medium-mass nuclei Tensor interac1on in mean-field and density Spin-triplet Spin-isospin excita1ons and sum rules func1onal and theory spin-singlet approaches pairing to nuclear correla1ons structure In Pairing correla1ons T=1,S=0 and T=0,S=1 pairs Progress Spin-Isospin Par1cle excita1ons and Nuclear Physics Bohr-Mo_elson Energy spectra of N=Z odd-odd nuclei. Volume 76, May Novel 2014, Prize pp th anniversary (2014) memorial issuse Physics Gamow-Teller excita1ons in N=Z+2 pf- shell nuclei H. Sagawa Scripta and (2015) G. Colo H. Sagawa, interplay C. L. between Bai and G. T=0 Colo pairing and tensor correla1ons

2 Skyrme-type tensor interac1ons :Triplet-even :Triplet-odd Two Advantages 1. A simple formula for spin-orbit splidng 2. Analy1c formulas for mul1pole expansion for spin-dependent excita1ons T.H.R. Skyrme, Nucl.Phys. 9,615(1959). F.L. Stancu, D. M. Brink and H. Flocard, PLB68,108 (1977). T.Lesinski, M. Bender, K. Bennaceur, T. Duguet, J. Meyer, Phys. Rev.C76, (2007). G.Colo, H. Sagawa, S. Fracasso, P.F. Bortignon, Phys. Lett. B 646 (2007) 227. B.A.Brown, T. Duguet,T. Otsuka, D. Abe and T. Suzuki, Phys. Rev. C74(2006) (R)

3 Two par1cle systems T=1, S=0 pair (L = S = 0)J = 0,T =1 ( j = j ' )J = 0,T =1 p(n) p(n) T=0, S=1 pair (L = 0, S =1)J =1,T = 0 p n a (l = l ' j = j ' )J =1,T = 0 + b ((l = l ' ) j, j ' = j ±1)J =1,T = 0 If there is strong spin-orbit splidng, it is difficult to make (T=0,S=1)pair. But, T=0 J= 1 + state could be Gamow-Teller states in nuclei with N~Z è strong GT states in N=Z+2 nuclei SU(4) supermul1plet in spin-isospin space Well-known in light p-shell nuclei (LS coupling dominance)

4 0.2 Pairing Correlation Energy (MeV) l=1 with T=0 l=3 with T=0 l=1 with T=1 l=3 with T= f=g T=0 /G T=1 HS, Y. Tanimura and K. Hagino, PRC87, (2013) Pairing correla1on energy of (J,T)=(0,1) and (1,0) states in pf shell Even with large spin-orbit splidng for f -orbits, the spin-triplet correla1ons will be larger than the spinsinglet one for f>1.5 Diagonalise the Hamiltonian V (T=1,S=0) +V (T=0,S=1) +V (spin-orbit) G.F. Bertsch and Y. Luo, PRC81, (2010)

5 Coopera1on of T=0 and T=1 pairing in Gamow-Teller states in N=Z nuclei C. L. Bai, H.S., M.Sasano, T. Uesaka, K. Hagino, H.Q. Zhang, X.Z. Zhang,F.R.Xu Phys. Le_. B719, pp (2013) HFB+QRPA with T=1 and T=0 pairing T=1 pairing in HFB T=0 pairing in QRPA How large is the spin-triplet T=0 pairing corela1on? As a possible manifesta1on of T=0 S=1 pairing correla1ons in nuclei N=Z. Ô(GT ) = στ ±

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7 B = (Xu π v ν Yu ν v π ) π Ô(GT ) ν C = X 2 Y 2

8 EXP: Sasano et al., PRL107 (2011)

9 Gamow-Teller Transi1ons in nuclei with N=Z+2 C.L. Bai, HS, G. Colo, Y. Fujita et al., PRC90, (2014) HFB+QRPA with T=1 and T=0 pairing T=1 pairing in HFB T=0 pairing in QRPA Ô(GT ) = στ ± σ, τ and στ are generators of SU(4) Supermul1plet : Wigner SU(4) symmetry (E. Wigner 1937, F. Hund 1937) (T=1, S=0) à(t=0, S=1) GT transi1on is allowed and enhanced.

10 Supermul1plet : Wigner SU(4) symmetry (T=1, S=0) à(t=0, S=1) GT transi1on is allowed and enhanced. Spacial symmetry is the same between the ini1al and final states p n σ τ n n (T=0,S=1) (T=1,S=0) B(GT)=6 What happens in pf shell nuclei with strong spin-triplet pairing interac1ons?

11 Gamow-Teller transi1ons in in N=Z+2 BCS vacuum pf nuclei Ô(GT ) = στ ± p-h type excita1on Fermi energy 1f 5/2 2p 1/2 2p 3/2 1f 7/2 T=0 S=1 T=1 S=0 1d 3/2 BCS vacuum p-p type excita1on v 2 v 2 protons neutrons 42 Ca A pair of SU(4) supermul1plet

12 Spin-triplet p-h spin-isospin T=0 paring interac1on is a_rac1ve is strongly and repulsive shipdown è GT higher strength energy near IAS collec1ve à SU(4) Gamow-Teller symmetry restora1on states. IAS f =IS/IV pairing Y. Fujita et al., PRL112, (2014) HFB+QRPA with T=1 and T=0 pairing T=0 pairing strength in QRPA is changed by a factor f=spin-triplet/spin-singlet

13 Effect of tensor correla1ons is small in 42 Ca.

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15 Tensor effect is seen in 50 Cr!

16 Tensor effect

17 Summary 1. Corpera1ve effct of T=0 and T=1 pairing correla1ons enhance the low-energy GT strength in N=Z and N=Z+2 nuclei. è Restora1on of supermul1plet symmetry in (T=1,J=0) and (T=0,J=1) states in pf shell nuclei 2. A coopera1ve effect of T=0 pairing and tensor interac1ons are found in nuclei at the middle of pf shell. 3. The T=0 pairing strength is determined to be almost the same strength as the T=1 pairing from the observed rela1ve energies of IAS and the low-energy GT states; f=strength(t=0)/(t=1)~1.0 irrespec1ve of the adopted interac1ons. Theory a. Further study of Par1cle-vibra1on coupling: Yifei Niu, Gianluca Colo b. Fine fidngs of energy density func1ons for RPA and QRPA (which was done already for Shell model interac1ons: Toshio Suzuki, Michio Honma