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Anomalous two-neutron transfer in neutron-rich Ni and Sn isotopes studied with continuum QRPA

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

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Anomalous two-neutron transfer in neutron-rich Ni and Sn isotopes studied with continuum QRPA

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

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

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

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

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

  6. Two-neutron transfer in neutron-rich nuclei The neutron-rich nuclei often accompany low density distributions of neutrons surrounding the nucleus. neutron proton density neutron-skin r [fm] ΔF/eF The pairing in low-density neutron matter is predicted to be stronger. Lombardo et. al, (2001) Margueron et. al, PRC (2008) M.Matsuo PRC73 (2006) 10-4 10-3 10-2 10-1 100 ρ/ρ0 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. ～ for unstable nuclei～ Recent study E. Khan et. al, PRC69 (2004); ibid PRC80 (2009) B. Avez, et. al, PRC78 (2008) neutron-rich O, Sn M. Matsuo, Y.Serizawa (2010) 11L + p → 9L +t Experiments I. Tanihata et al. PRL 100, (2008) 30Mg + t → 32Mg + p K. Wimmer et al. PRL 105,(2010)

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

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

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

  10. Monopole neutron pair transfer 02 02 Strength function for the pair transfer 0gs 0gs 0gs A-2 A A+2 134Sn 120Sn addition addition strength strength removal removal E ( MeV) E ( MeV) The pair addition strength to the pair vibration 0+ state in 134Sn is large. The pair vibrational state of 134Sn is a narrow resonance though it is located above the one-neutron separation energy. As we explain below, this pairing vibrational mode in 134Sn is quite anomalous.

  11. AnomalousPairing Vibration Pair addition strength of pairing vibrational mode Ratio (02+ vs gs ) less than 10 % in stable nuclei R. A. Broglia, O. Hansen, and C. Riedel (1973) Sn isotopes Large strength twice or more ratio 138Sn 136Sn 134Sn strength 140Sn 132Sn 60-90％ A A 02 02 2n-add 0gs 0gs A A+2 gs-gs

  12. AnomalousPairing Vibration Hartree-Fock single-particle energy in 134Sn Transition density of pairing vibrational mode es.p. 2N-add (0.66) p1/2 (0.27) 0 p3/2 Very long tail r～ 15 fm -0.36 -2.14 f7/2 120-130Sn [MeV] -5 N=８２ 132-140Sn r2P(ad)00(r) [fm-1] h11/2 -7.68 The transition densities to the pair vibrational mode of 132-140Sn have a long tail. By adding two-neutrons in the weakly bound p orbits, we can have a long tail. r [fm] The weakly bound p orbits play an important role !!

  13. Relation to the ground state transfer 02 02 2n-add 0gs 0gs Strength of ground state transfer A A+2 gs-gs Hartree-Fock single-particle energy in 142Sn Sn isotopes es.p. 2N-add (0.01) p1/2 0 -0.23 p orbits occupied in excited states p3/2 -0.84 p orbits occupied in ground states Pair addition strength -2.62 f7/2 Ground state transfer [MeV] N=82 -5 pairing vibration h11/2 -7.68 A The anomalous pairing vibration in 132-140Sn appears as a precursor of large enhancement of the ground state transfer beyond A=140.

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

  15. Giant Pairing Vibration (GPV) in stable Sn isotopes Pair addition strength function Pair addition strength function Giant Pairing Vivration 2nd- GPV 122Sn Hartree-Fock single-particle energy in 122Sn 122Sn | 124Sn 122Sn | 126Sn 122Sn | 130Sn 122Sn 122Sn | 128Sn 1st-GPV es.p. 2nd-GPV 2N-add 2nd-GPV (0.01) Low-lying Pairing Vibration p1/2 0 -0.23 E [MeV] p3/2 -0.84 -2.62 f7/2 Anomalous pairing vibration [MeV] N=82 -5 134Sn h11/2 -7.68 Pairing Vibration Gs-gs transfer E [MeV] E [MeV]

  16. Giant Pairing Vibration (GPV) in stable Sn isotopes Pair addition transition density Pair addition strength function 2nd- GPV 122Sn Anomalous pairing vibration in 132-140Sn r2P(ad)00(r) [fm-1] 2nd- GPV in 122-130Sn E [MeV] 122Sn Anomalous pairing vibration r [fm] 134Sn The transition densities of 2nd-GPV have a long tail. Same character of the anomalous pairing vibration. However the collectivity of the anomalous pairing vibration is much stronger. E [MeV]

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

  18. Pairing vibration in neutron-rich Ni isotopes Pair addition strength function 62Ni 80Ni Pair addition strength Pair addition strength E [MeV] E [MeV] The pairing vibration appears both isotopes, but the strength in 80Ni is not large.

  19. Pairing vibration in neutron-rich Ni isotopes pair addition strength function Strength of pair addition transfer to pairing vibration and ground state transfer Ni isotopes ratio 74Ni Ground state transfer Pair - add strength GPV Pair addition strength 10-20％ pairing vibrational 02+ A A The pairing vibrational states which are as large as ground state transfer are not appeared in neutron-rich region. E (MeV)

  20. Pairing vibration in neutron-rich Ni isotopes Pair addition transition density Hartree-Fock single-particle energy in 80Ni 58-66Ni es.p. 2n-add d3/2 78-84Ni (0.27) 0 s1/2 -0.28 Pair addition strength -1.36 d5/2 [MeV] 80Ni N=50 -5 g9/2 -5.60 f [fm] The transition densities of neutron-rich 78-84Ni have a long tail ( r ～ 15fm ) because the relevant weakly bound orbit is an s orbit. The collectivity is small.

  21. Conclusion (t , p ) (t , p ) (t , p ) (t , p ) (t , p ) 02 02 strong strong strong strong 02 02 strong 02 weak weak 02 weak 0gs 0gs 0gs 0gs 0gs 0gs 0gs strong strong strong strong strong very strong 140Sn 132Sn 134Sn 136Sn 138Sn 100-130Sn 142-150Sn The neutron-rich 132-140Sn havethe anomalous pair vibrational state. ・ the pair addition strength is very large, 　～ as same value as the ground state transfer　～ ・ the transition density has a long tail extending to the outside, 　～ weakly bound p orbits play an important role ～ 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. It is also related to the giant pairing vibration in stable Sn isotopes. We found the pairing vibration beyond 78Ni. They have a weak-bound feature because the relevant weakly bound orbit is an s orbit. However the collectivity is smaller.

  22. end

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

  24. Relation to the ground state transfer Strength of ground state transfer Hartree-Fock single-particle energy in 142Sn es.p. 2n-add 120-130Sn 0gs+―0gs+ (0.01) 132-140Sn p1/2 0 -0.23 p3/2 142-150Sn -0.84 r2P(ad)gs(r) [fm-1] -2.62 f7/2 [MeV] N=82 -5 h11/2 -7.68 ｒ [fm] The anomalous pairing vibration in 132-140Sn appears as a precursor of large enhancement of the ground state transfer beyond A=140.

  25. 120-130Sn 42-46Ca-GPV 58-64Ni 2n-add 134-140Sn 48-54Ca 80-84Ni 2n-add es.p. es.p. es.p. r2P(ad)gs(r) [fm-1] (0.66) p1/2 d3/2 2n-add (0.43) 0 0 (0.27) 0 p3/2 s1/2 -0.43 -0.36 d5/2 f5/2 -1.58 -1.60 -2.14 f7/2 [ｆｍ] [ｆｍ] [ｆｍ] [MeV] p1/2 -3.56 [MeV] [MeV] N=８２ N=50 -5 -5 -5 p3/2 -5.73 g9/2 -6.02 N=2８ Weak-bound featur Weak-bound featur Not weakly bound

  26. Giant Pairing Vibration (GPV) in stable Sn isotopes Pair addition transition density Pair addition strength function 1st- GPV ground state transfer in 132-140Sn 122Sn 1st- GPV in 122-130Sn r2P(ad)00(r) [fm-1] E [MeV] 122Sn ground state transfer r [fm] 134Sn Same character of the ground state transfer of neutron-rich Sn isotopes. E [MeV]

  27. Giant Pairing Vibration (GPV) in stable Sn isotopes Hartree-Fock single-particle energy Stable area 120-130Sn Neutron-rich 132-140Sn es.p. es.p. 2n-add 2n-add 2nd-GPV Pairing Vibration p1/2 p1/2 0 p3/2 0 p3/2 f7/2 f7/2 1st-GPV g.s. transfer N=82 -5 N=82 -5 Pairing Vibration h11/2 h11/2 g.s. transfer

  28. Sn isotopes GPV strength

  29. Ni isotopes strength GPV

  30. Ca isotopes strength GPV

  31. Pair addition strength function r2P(ad)gs(r) [fm-1] 82Ni

  32. Pairing vibration in neutron-rich Ni isotopes Strength of pair addition transfer to pairing vibration and ground state transfer Ni isotopes ratio Ground state transfer Pair addition strength 3rd 0+ A A The pairing vibrational states which are as large as ground state transfer are not appeared in neutron-rich region.

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

  34. GRPUND STATE PROPERTIES AND THE PARING ROTATION Transition density of the ground state transfer 120-130Sn 132-140Sn 142-150Sn r2P(ad/rm)gs(r) [fm-1] f [fm]

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

  36. PAIRING VIBRATION ( transition density ) 102Sn 120Sn Pair addition Pair addition Pair removal Pair removal (Transition density)×r2 (Transition density)×r2 Normal N Normal N f [fm] r [fm] 134Sn 142Sn Pair addition Pair addition Pair removal Pair removal Normal N Normal N (Transition density)×r2 (Transition density)×r2 f [fm] r [fm]

  37. PAIRING VIBRATION ( Microscopic origin ) Pair addition Pair removal full QRPA full QRPA unperturbed unperturbed strength strength 134Sn 142Sn E [MeV] E [MeV] 134Sn pairing vibration pairing vibration 142Sn [f7/2]2 [f7/2]2 [p3/2]2 [p3/2]2 (Transition density)×r2 (Transition density)×r2 f [fm] f [fm]

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

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

  40. PAIRING VIBRATION ( comparison with the ground state transfer ) Ratio Pair addition Pair removal A A

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

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

  43. 0gs+ 02+ r2P(ad)gs(r) [fm-1] r2P(ad)00(r) [fm-1] 21+ 2n-add 21+ 02+ 0gs+ 0gs+ A A+2 gs-gs 43

  44. PAIRING VIBRATION ( systematics ) Transition density of pair vibration mode 120-130Sn 132-140Sn 142-150Sn r2P(ad)00(r) [fm-1] f [fm]

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

  46. Giant Pairing Vibration (GPV) in stable Sn isotopes Pair addition transition density 1st-GPV in 122-130Sn r2P(ad)(r) [fm-1] 122Sn g.s. transfer in 132-140Sn E [MeV] 134Sn [ fm ] E [MeV] Anomalous pairing vibration in 132-140Sn r2P(ad)(r) [fm-1] 2nd-GPV in 122-130Sn Transition densities have a same character. Transition densities of 2nd-GPV have a long tail ( r ~15fm ). [ fm ]

  47. Pairing vibration in neutron-rich Ni isotopes Pair addition transition density Hartree-Fock single-particle energy in 80Ni es.p. 2n-add 58-66Ni d3/2 (0.27) 0 78-84Ni s1/2 -0.28 -1.36 d5/2 [MeV] N=50 -5 g9/2 -5.60 f [fm] The transition densities of neutron-rich 78-84Ni have a long tail ( r ～ 15fm ) because the relevant weakly bound orbit is an s orbit. The collectivity is small.

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