1. Anomalous two-neutron transfer in neutron-rich Ni and Sn isotopes studied with continuum QRPA H.Shimoyama, M.Matsuo Niigata University 1 Dynamics and Correlations in Exotic Nuclei (DCEN2011) Yukawa Institute for Theoretical Physics One-day workshop IV Oct. 24

2. Outline Outline Anomalous pairing vibration state in neutron-rich 132-140 Sn ・ Introduction ・ Framework ・ Results Skyrme Hartree-Fock-Bogoliubov mean-field + continuum Quasiparticle Random Phase Approximation Giant pairing vibration in stable Sn isotopes Pairing vibration in Ni isotopes ・ Conclusion (Monopole pair transfer in Sn and Ni isotopes ) Pairing vibration in Sn isotopes 2 relation to the anomalous pairing vibration state beyond N=82 weak-binding feature

3. Outline Outline Anomalous pairing vibration state in neutron-rich 132-140 Sn ・ Introduction ・ Framework ・ Results Skyrme Hartree-Fock-Bogoliubov mean-field + continuum Quasiparticle Random Phase Approximation Giant pairing vibration in stable Sn isotopes Pairing vibration in Ni isotopes ・ Conclusion (Monopole pair transfer in Sn and Ni isotopes ) Pairing vibration in Sn isotopes 3 relation to the anomalous pairing vibration state beyond N=82 weak-binding feature

4. 2n-addition2n-removal A → A+2 2-neutron transfer 11 Li + p → 9 Li + t Example ） 03+03+ 02+02+ A A + 2A - 2 energy + 2n - 2n 0 gs + 0 + gs 03+03+ 02+02+ 0 gs + A → A-2 ( t, p ) ( p, t ) 4

5. D. R. Bes, et. al, NP(1966) R. A. Broglia, at. Al, NP(1973) Pairing vibration Re ⊿ Im ⊿ superfluid phase open-shell nuclei E Pairing rotation 02+02+ 02+02+ 02+02+ 0 gs + Pairing vibration A + 2 A - 2 A Pairing rotation weak strong Collective two-neutron transfers in surperfulid nuclei This is a standard picture of the two-neutron transfer modes. 5

6. Δ F /e F Lombardo et. al, (2001) Margueron et. al, PRC (2008) M.Matsuo PRC73 (2006) E. Khan et. al, PRC69 (2004); ibid PRC80 (2009) Recent study B. Avez, et. al, PRC78 (2008) M. Matsuo, Y.Serizawa (2010) neutron-rich O, Sn r [fm] proton neutron density neutron-skin Two-neutron transfer in neutron-rich nuclei ～ for unstable nuclei ～ I. Tanihata et al. PRL 100, (2008) 11 L + p → 9 L +t Experiments The neutron-rich nuclei often accompany low density distributions of neutrons surrounding the nucleus. The pairing in low-density neutron matter is predicted to be stronger. ρ/ρ 0 If the neutron pairing becomes strong around the surface, we can expect a large probability for a neutron pair to be added or removed from a nucleus by a transfer process. 10 0 10 -1 10 -2 10 -3 10 -4 30 Mg + t → 32 Mg + p K. Wimmer et al. PRL 105,(2010) 6

7. Linear response equation particle-hole densitypair -addition densitypair -removal density The densities describing the pair transfer is provided: ・ Skyrme interaction parameter ： SLy4 ・ Pairing interaction parameter ： Density Dependent Delta Interaction （ ph channel of cQRPA → Landau-Migdal approximation ） Two-neutron transfer in QRPA The parameter set reproduces the scattering length of the nn-interaction Skyrme Hartree-Fock-Bogoliubov mean-field + continuum Quasiparticle Random Phase Approximation DDDI-bare (surface type) a nn =-18.5 fm strong @ outside weak @ inside 7

8. Pair-removal operator Pair-addition operator strength function transition density Monopole pair transfer mode QRPA calc. of excitation modes Hartree-Fock-Bogoliubov mean-field calc. ground–ground pair transfer Pair transfer to excited 0 + states strength 8

9. Outline Outline Anomalous pairing vibration state in neutron-rich 132-140 Sn ・ Introduction ・ Framework ・ Results Skyrme Hartree-Fock-Bogoliubov mean-field + continuum Quasiparticle Random Phase Approximation Giant pairing vibration in stable Sn isotopes Pairing vibration in Ni isotopes ・ Conclusion (Monopole pair transfer in Sn and Ni isotopes ) Pairing vibration in Sn isotopes 9

10. Monopole neutron pair transfer Monopole neutron pair transfer addition removalstrength The pair addition strength to the pair vibration 0 + state in 134 Sn is large. The pair vibrational state of 134 Sn is a narrow resonance though it is located above the one-neutron separation energy. strength addition removal E ( MeV) Strength function for the pair transfer As we explain below, this pairing vibrational mode in 134 Sn is quite anomalous. E ( MeV) 0202 A-2AA+2 0202 0 gs 10

11. Sn isotopes Pair addition strength of pairing vibrational mode 0 gs 0202 0202 2n-add AA+2 gs-gs Ratio ( 0 2 + vs gs ) 60-90 ％ A A Large strength twice or more strength Anomalous Pairing Vibration 11 ratio less than 10 % in stable nuclei R. A. Broglia, O. Hansen, and C. Riedel (1973)

12. Transition density of pairing vibrational mode 120-130 Sn 132-140 Sn r [fm] r 2 P (ad) 00 (r) [fm -1 ] Anomalous Pairing Vibration 0 -5 -2.14 -0.36 (0.27) (0.66) -7.68 e s.p. The transition densities to the pair vibrational mode of 132-140 Sn have a long tail. By adding two-neutrons in the weakly bound p orbits, we can have a long tail. Very long tail r ～ 15 fm The weakly bound p orbits play an important role !! 2N-add f 7/2 p 3/2 p 1/2 h 11/2 Hartree-Fock single-particle energy in 134 Sn N= ８２ [MeV] 12

13. Strength of ground state transfer Pair addition strength Relation to the ground state transfer A p orbits occupied in excited states p orbits occupied in ground states Sn isotopes 0 gs 0202 0202 2n-add AA+2 gs-gs 13 0 -5 -0.84 -0.23 (0.01) -7.68 e s.p. 2N-add N=82 f 7/2 p 3/2 p 1/2 h 11/2 [MeV] -2.62 Hartree-Fock single-particle energy in 142 Sn The anomalous pairing vibration in 132-140 Sn appears as a precursor of large enhancement of the ground state transfer beyond A=140.

14. Outline Outline ・ Introduction ・ Framework ・ Results Skyrme Hartree-Fock-Bogoliubov mean-field + continuum Quasiparticle Random Phase Approximation Giant pairing vibration in stable Sn isotopes Pairing vibration in Ni isotopes ・ Conclusion (Monopole pair transfer in Sn and Ni isotopes ) 14 relation to the anomalous pairing vibration state beyond N=82 Pairing vibration in Sn isotopes

15. Low-lying Pairing Vibration Giant Pairing Vivration Pair addition strength function 2nd-GPV 1st-GPV Giant Pairing Vibration (GPV) in stable Sn isotopes E [MeV] 2nd-GPV Gs-gs transfer Pairing Vibration Hartree-Fock single-particle energy in 122 Sn 0 -5 -0.84 -0.23 (0.01) -7.68 e s.p. 2N-add N=82 f 7/2 h 11/2 [MeV] -2.62 p 3/2 p 1/2 15 E [MeV] Pair addition strength function 2nd- GPV Anomalous pairing vibration

16. E [MeV] Giant Pairing Vibration (GPV) in stable Sn isotopes Pair addition transition density r 2 P (ad) 00 (r) [fm -1 ] 2nd- GPV in 122-130 Sn Anomalous pairing vibration in 132-140 Sn The transition densities of 2nd-GPV have a long tail. However the collectivity of the anomalous pairing vibration is much stronger. 122 Sn Same character of the anomalous pairing vibration. r [fm] Pair addition strength function 2nd- GPV Anomalous pairing vibration 16

17. Outline Outline ・ Introduction ・ Framework ・ Results Skyrme Hartree-Fock-Bogoliubov mean-field + continuum Quasiparticle Random Phase Approximation Giant pairing vibration in stable Sn isotopes Pairing vibration in Ni isotopes ・ Conclusion (Monopole pair transfer in Sn and Ni isotopes ) 17 Pairing vibration in Sn isotopes weak-binding feature

18. Pair addition strength function Pairing vibration in neutron-rich Ni isotopes E [MeV] The pairing vibration appears both isotopes, but the strength in 80 Ni is not large. E [MeV] Pair addition strength 18

19. Pairing vibration in neutron-rich Ni isotopes Strength of pair addition transfer to pairing vibration and ground state transfer ratio 10-20 ％ A A Ni isotopes Pair addition strength pair addition strength function Pair - add strength E (MeV) GPV The pairing vibrational states which are as large as ground state transfer are not appeared in neutron-rich region. 19

20. Pairing vibration in neutron-rich Ni isotopes 0 -5 -1.36 -0.28 e s.p. g 9/2 d 5/2 s 1/2 N=50 [MeV] (0.27) d 3/2 -5.60 The transition densities of neutron-rich 78-84 Ni have a long tail ( r ～ 15fm ) because the relevant weakly bound orbit is an s orbit. The collectivity is small. 2n-add Hartree-Fock single-particle energy in 80 Ni 78-84 Ni 58-66 Ni Pair addition transition density f [fm] 20 80 Ni Pair addition strength

21. 132 Sn 134 Sn 136 Sn 138 Sn 140 Sn 100-130 Sn 0 gs 0202 0202 0202 0202 0202 0202 142-150 Sn strong very strong strong weak strong weak strong The neutron-rich 132-140 Sn have the anomalous pair vibrational state. ～ as same value as the ground state transfer ～ ・ the pair addition strength is very large, ・ the transition density has a long tail extending to the outside, ～ weakly bound p orbits play an important role ～ Conclusion The ground state transfers is significantly enhanced beyond A=140, due to the weakly bound p orbits occupied in ground state. The anomalous pairing vibration is a precursor of this strong transfer. We found the pairing vibration beyond 78 Ni. They have a weak- bound feature because the relevant weakly bound orbit is an s orbit. However the collectivity is smaller. It is also related to the giant pairing vibration in stable Sn isotopes. 21 ( t, p )

22. 22

23. 23 DDDI mix DDDI volume DDDI bare’ Density Dependent Delta type Interaction No dependent on the density > Density Dependent delta Interaction parameter Acts by a low density strong >

24. 24 0 gs + ―0 gs + r 2 P (ad) gs (r) [fm -1 ] 0 -5 -0.84 -0.23 (0.01) -7.68 e s.p. 2n-add N=82 f 7/2 p 3/2 p 1/2 h 11/2 [MeV] -2.62 Hartree-Fock single-particle energy in 142 Sn ｒ [fm] 120-130 Sn 132-140 Sn 142-150 Sn Relation to the ground state transfer Strength of ground state transfer The anomalous pairing vibration in 132-140 Sn appears as a precursor of large enhancement of the ground state transfer beyond A=140.

25. 0 -5 -2.14 -0.36 (0.27) (0.66) e s.p. 2n-add f 7/2 p 3/2 p 1/2 N= ８２ [MeV] 0 -5 -1.58 -0.43 e s.p. 2n-add g 9/2 d 5/2 s 1/2 N=50 [MeV] 0 -5 -5.73 -3.56 -1.60 e s.p. 2n-add p 3/2 p 1/2 f 5/2 [MeV] (0.43) d 3/2 -6.02 N=2 ８ Not weakly bound r 2 P (ad) gs (r) [fm -1 ] 48-54 Ca 42-46 Ca-GPV 134-140 Sn 80-84 Ni 58-64 Ni 120-130 Sn [ ｆｍ ] Weak-bound featur

26. E [MeV] Giant Pairing Vibration (GPV) in stable Sn isotopes Pair addition transition density r 2 P (ad) 00 (r) [fm -1 ] 1st- GPV in 122-130 Sn ground state transfer in 132-140 Sn 122 Sn Same character of the ground state transfer of neutron-rich Sn isotopes. r [fm] Pair addition strength function 1st- GPV ground state transfer 26

27. 27 Giant Pairing Vibration (GPV) in stable Sn isotopes 0 -5 e s.p. 2n-add f 7/2 p 3/2 p 1/2 h 11/2 Pairing Vibration 0 -5 e s.p. 2n-add f 7/2 p 3/2 p 1/2 2nd-GPV 1st-GPV h 11/2 g.s. transfer Pairing Vibration Neutron-rich 132-140 SnStable area 120-130 Sn Hartree-Fock single-particle energy N=82

28. 28 GPV strength Sn isotopes

29. 29 Ni isotopes GPV strength

30. 30 strength Ca isotopes GPV

31. 31 82 Ni r 2 P (ad) gs (r) [fm -1 ] Pair addition strength function

32. Pairing vibration in neutron-rich Ni isotopes Strength of pair addition transfer to pairing vibration and ground state transfer ratio A A Ni isotopes Pair addition strength The pairing vibrational states which are as large as ground state transfer are not appeared in neutron-rich region. 32

33. Strength of the ground state transfer[Pairing gap] 2 GRPUND STATE PROPERTIES AND THE PARING ROTATION DDDI-bare’ mix volume DDDI-bare’ mix volume 33 AA strength

34. Transition density of the ground state transfer 120-130 Sn 132-140 Sn 142-150 Sn GRPUND STATE PROPERTIES AND THE PARING ROTATION r 2 P (ad/rm) gs (r) [fm -1 ] f [fm] 34

35. 102 Sn 120 Sn 134 Sn 142 Sn Pair addition Pair removal strength E [MeV] PAIRING VIBRATION ( strength function ) 35

36. 102 Sn 120 Sn 134 Sn 142 Sn Pair addition Normal N Pair removal Pair addition Normal N Pair removal Pair addition Normal N Pair removal Pair addition Normal N Pair removal (Transition density)×r 2 f [fm]r [fm] f [fm]r [fm] PAIRING VIBRATION ( transition density ) 36

37. 134 Sn 142 Sn pairing vibration [f7/2] 2 [p3/2] 2 pairing vibration [f7/2] 2 [p3/2] 2 Pair additionPair removal full QRPA unperturbed full QRPA unperturbed 134 Sn 142 Sn PAIRING VIBRATION ( Microscopic origin ) strength (Transition density)×r 2 f [fm] E [MeV] 37

38. Pair addition mode Excitation energyStrength E [MeV] A A strength DDDI-bare’ mix volume DDDI-bare’ mix volume PAIRING VIBRATION ( systematics ) 38

39. Pair removal mode Excitation energyStrength DDDI-bare’ mix volume PAIRING VIBRATION ( systematics ) E [MeV] strength DDDI-bare’ mix volume 39 AA

40. Ratio Pair additionPair removal PAIRING VIBRATION ( comparison with the ground state transfer ) 40 AA

41. DDDI-bare’ mix volume 134 Sn SENSITIVITY TO DENSITY-DEPENDENT PARING 41 E [MeV] strength

42. 42 B(Pad0)Ground state trensfer 0 gs + 2n-add A A+2 gs-gs 0 gs + 02+02+ 21+21+ AA strength 02+02+ 0 gs + 21+21+

43. 21+21+ 02+02+ 43 0 gs + 2n-add A A+2 gs-gs 0 gs + 02+02+ 21+21+ r 2 P (ad) 00 (r) [fm -1 ]r 2 P (ad) gs (r) [fm -1 ]

44. Transition density of pair vibration mode 120-130 Sn 132-140 Sn 142-150 Sn PAIRING VIBRATION ( systematics ) r 2 P (ad) 00 (r) [fm -1 ] f [fm] 44

45. 45

46. Pair-removal operator Pair-addition operator strength function transition density Monopole pair transfer mode QRPA calc. of excitation modes Hartree-Fock-Bogoliubov mean-field calc. ground–ground pair transfer Pair transfer to excited 0 + states strength transition density

47. 47 [ fm ] r 2 P (ad) (r) [fm -1 ] 2nd-GPV in 122-130 Sn Giant Pairing Vibration (GPV) in stable Sn isotopes 1st-GPV in 122-130 Sn r 2 P (ad) (r) [fm -1 ] [ fm ] g.s. transfer in 132-140 Sn Anomalous pairing vibration in 132-140 Sn Pair addition transition density E [MeV] Transition densities have a same character. Transition densities of 2nd-GPV have a long tail ( r ~ 15fm ).

48. Pairing vibration in neutron-rich Ni isotopes 0 -5 -1.36 -0.28 e s.p. g 9/2 d 5/2 s 1/2 N=50 [MeV] (0.27) d 3/2 -5.60 The transition densities of neutron-rich 78-84 Ni have a long tail ( r ～ 15fm ) because the relevant weakly bound orbit is an s orbit. The collectivity is small. 2n-add Hartree-Fock single-particle energy in 80 Ni 78-84 Ni 58-66 Ni Pair addition transition density f [fm] 48

49. 49