1. Saclay, October 13-15, 2008 Nucleon-nucleon correlations probed via heavy ion transfer reactions L.Corradi Laboratori Nazionali di Legnaro – INFN, Italy

2. outlineoutline Hystorical background - (p,t) reactions and the pairing vibration model (years 70’s) - (C,O) reactions and simultaneous vs sequential transfer (80’s) - Heavy ion reactions and enhancement factors (late 80’s - 90’s) Recent experimental and theoretical developments with heavy ions - inclusive data - particle-gamma coincidences (pairing vibrations) - sub-barrier transfer studies

3. J.Ball et al., PRC4(1971)196 90 Zr(p,t) 88 Zr The enhancement factor ε has been used to compare the experimental intensities with those calculated on the basis of specific assumptions about the nuclear wave function involved. Disagreement between theory and experiment is indicated by deviations of ε from unity. transition amplitude isospin coefficient normalization factor (zero range approx.) spectroscopic amplitude enhancement factor

4. Scheme levels from the harmonic pairing model

5. R.C. Ragaini et al., PRC2(1970)1020 L=0 transitions 92 Zr(p,t) 90 Zr 86 Sr(t,p) 88 Sr Pairing vibrations : (p,t) reactions

6. W.Mayer et al.,PRC26(1982)500 Two nucleon transfer reactions studied with Q3D spectrographs problems : - isotopic trend of g.s to g.s. cross sections reproduced by DWBA but a (common) scale factor needed - different scale factors needed to reproduce cross sections of excited levels of the same isotope - fixing the strength to the g.s., excited states are strongly underpredicted

7. Two nucleon transfer : simultaneous vs successive contributions

8. E.Maglione et al., PLB162(1985)59 Two nucleon transfer : simultaneous vs successive contributions

9. (multi) nucleon transfer with heavy ions (inclusive)

10. Distinguishing between gs. and 2qp band in 1 and 2 nucleon transfer X.T.Liu et al., PRC43(1991)R1 F = P 2n / (P 1n ) 2

11. ‘ A A’ a’ a Transfer reactions (multinucleon) among heavy ions The quasi-elastic regime is governed by - form factors (structure) - optimum Q-values (dynamics) degrees of freedom single particle states surface vibrations pair modes couplings inelastic: collective ff transfer: single particle ff pair ff (macroscopic)

12. Multinucleon transfer reactions : quasi-elastic regime pure neutron pick-up pure proton stripping N/Z equilibrization

13. Differential cross sections forward part : mainly reflects the behaviour of the form factors backward part : mainly reflects the absorption

14. The semiclassical theory

16. S.Szilner et al, Phys.Rev.C71(2005)044610 successive transfer + simultaneous transfer GRAZING code CWKB theory Pure neutron and proton transfers neutronsprotons

17. successive transfer+ simultaneous transfer + evaporation effects L.Corradi et al, PRC66(2002)024606 Pure neutron and proton transfers in 58 Ni+ 208 Pb E lab =328.4 MeV GRAZING code CWKB theory

18. multinucleon transfer : experiment vs. theory multinucleon transfer : experiment vs. theory data : LNL theory : GRAZING code and CWKB

19. L.Corradi et al, PRC63(2001)021601R g.s. Q-values histograms: exp. lines: CWKB theory Strong population close to the g.s.Q-values up to +4n channels in 62 Ni+ 206 Pb

20. Search for a possible odd-even staggering effect (pair modes)

21. THE PRISMA SPECTROMETER + CLARA GAMMA ARRAY

22. IC MWPPAC A physical event is composed by the parameters: position at the entrance x, yposition at the entrance x, y position at the focal plane X, Yposition at the focal plane X, Y time of flight TOFtime of flight TOF energy DE, Eenergy DE, E A physical event is composed by the parameters: position at the entrance x, yposition at the entrance x, y position at the focal plane X, Yposition at the focal plane X, Y time of flight TOFtime of flight TOF energy DE, Eenergy DE, E PRISMA spectrometer – trajectory reconstruction

23. ΔE-E q A/q Mass

24. Evaporation processes in multinucleon transfer reactions Evaporation processes directly identified with PRISMA+CLARA An example: 40 Ca+ 96 Zr at 152 MeV 40 Ca+ 96 Zr E=152 MeV 40 Ca+ 96 Zr E=152 MeV

25. TKEL distributions – Prisma vs. Prisma+Clara

26. TKEL distributions pure proton stripping

27. Pair transfer Search for pairing vibrations Measurements at sub-barrier energies

28. How the residual interaction acts in transfer processes How the residual interaction acts in transfer processes

29. S.Szilner et al, Eur.Phys.J. A21, 87(2004) strength function (shell model calculations) Strong population close to the pairing vibrational region in 40 Ca+ 208 Pb Strong population close to the pairing vibrational region in 40 Ca+ 208 Pb S.Szilner et al, Phys.Rev.C76(2007)024604

30. Multineutron and multiproton transfer channels near closed-shell nuclei PRISMA spectrometer data GRAZING code calculations Mass [amu] pure neutron pick-up channels 90 Zr+ 208 Pb E lab =560 MeV L.Corradi et al, Nucl.Phys.A787(2007)160

31. 2240 1874 33083842 Population of states close to the pairing vibrational region vibrational region Population of states close to the pairing vibrational region vibrational region

32. 2+ [2067] 2+ [2820] 2+ [1848] 2+ [3058] 0+ [4283] strong in (t,p) 2+ [3500] 0+ [2903] weak in (t,p) 0+ [3992] strong in (t,p) 0+ [3589] strong in (t,p) 2+ [934] 0+ [g.s.] 1132 12251463 990 934 1848 492 972 934 1742 912 439 837 1970 L=2 (t,p) new identified and known identified but in overlap with other known existing ? non tab (n,n’) 208 Pb( 90 Zr, 92 Zr) 206 Pb E=560 MeV (4000) (50) (1000) (4000) (245) (120) (1100) wide peak at 893

33. Sub-barrier transfer reactions

34. - few reaction channels are opened, i.e. W(r) very small - one has a much better control on the form factors F(r) inel has a decay length ~ 0.65 fm F(r) tr has a decay length ~ 1.3 fm nuclear couplings are dominated by transfer processes - Q-value distributions get much narrower than at higher energies - one can probe nucleon correlation close to the g.s. At energies lower than the Coulomb barrier : data are very scarse or almost non existing absorptive potential form factor Q-value window

35. Absolute cross sections for one and two-nucleon transfer reactions B.F.Bayman and J.Chen, PRC26(1509)1982 E ~ E b direct successive direct E << E b one+two step calculations undepredict the data by a factor ~ 2 one+two step calculations undepredict the data by 25-30% 208 Pb( 16 O, 18 O g.s. ) 206 Pb

36. R.Betts et al., PRL59(1987)978 58 Ni + x Sn detection of (heavy) target like ions with recoil mass spectrometers RMS measurements have been performed at subbarrier energies but for only one nucleon transfer and with very poor Q-value resolution

37. Detection of (light) target like ions in inverse kinematics with PRISMA PRISMA measurements have been performed for multinucleon transfer channels and at energies well below the barrier beam direction 20 o 94 Zr 40 Ca SSBD (rutherford sc.)

38. GRAZING code calculations for 40 Ca+ 94 Zr transfers differential cross sections total cross sections A.Winther, program GRAZING http://www.to.infn.it/~nanni/GRAZING Prisma acceptance

39. 94 Zr+ 40 Ca, E lab =330 MeV, θ lab =20 o, inverse kinematics

40. Mass distributions for pure neutron pick-up channels

41. TKEL distributions for pure neutron pick-up channels Q gs

42. Mass vs Q-value matrix for (-1p) channels channels (E l =315 MeV) background free spectra with transfer products at very low excitation energy : no evaporation effects and cleanest conditions for comparison with theory

43. Experimental vs Theoretical cross sections for +1n and -1p channels very preliminary

44. with neutron rich beams...

45. As the N/Z ratio increases many nuclear observables deviate from “normal” behaviour. In particular the fermi surface of neutrons is close to the continuum and properties like the pairing interaction is modified. G.Pollarolo et al, Phys.Rev.C59(1999)1534 The particles close to the Fermi surface are moving in a region of a very diffuse distribution of matter; it is convenient to replace the previous form with a contact force that is density dependent J.Dobaczewski et al., Phys.Rev.C53,2809 (1996)

46. C.H.Dasso, G.Pollarolo and A.Winther, Phys.Rev.Lett.73, 1907 (1994) neutron pick-up and proton stripping equal directions neutron stripping and proton pick-up Change of population pattern in going from neutron poor to neutron rich nuclei (theoretical) poor to neutron rich nuclei (theoretical) Change of population pattern in going from neutron poor to neutron rich nuclei (theoretical) poor to neutron rich nuclei (theoretical)

47. with (moderately n-rich) heavy ions one can populate (nn), (pp) and (np) channels with comparable strength Multinucleon transfer reactions

48. GRAZING code

49. One needs to learn whether and to what extent the degrees of freedom and the corresponding matrix elements tested with stable beams can hold with radioactive beams. In particular whether the form factors for one and two particle transfer and their strength need to be modified neutron-proton correlations (np channel) Multinucleon transfer reactions with radioactive beams 140 Sn onset of supercurrents (neutron rich nuclei)

50. A.M.Stefanini, E.Fioretto, A.Gadea, B.Guiot, N.Marginean, P.Mason, R.Silvestri, G.de Angelis, D.R.Napoli, J.J.Valiente- Dobon Laboratori Nazionali di Legnaro – INFN, Italy S.Beghini, G.Montagnoli, F.Scarlassara, E.Farnea, C.A.Ur, S.Lunardi, S.Lenzi, D.Mengoni, F.Recchia, F.della Vedova Universita’ di Padova and INFN, Sezione di Padova S.Szilner, N.Soic, D.Jelavec Ruđer Bošković Institute, Zagreb, Croatia G.Pollarolo Universita’ di Torino and INFN, Sezione di Torino, Italy F.Haas, S.Courtin, D.Lebhertz, M.-D.Salsac IReS, Strasbourg, France + CLARA collaboration

52. Elastic scattering – using Prisma and Clara information elastic scattering is the first important ingredient for nuclear reaction studies. It provides information on the (outer part of) nuclear potential grazing code

53. Total cross sections successive transfer S.Szilner et al, Phys.Rev.C76(2007)024604

54. Multinucleon transfer reactions with neutron-rich beams possibility to populate nuclei via pick-up and stripping of both neutrons and protons probing (nn), (pp) and (np) correlations. Important for studies on pairing vibrations/rotations, nuclear superfluidity C.H.Dasso, G.Pollarolo, A.Winther, PRL73(1994)1907 GRAZING code calculations production of neutron rich isotopes

55. K.Sapotta et al., PRC31(1985)1297 linear diffusion : strong correlation between proton and neutron transfer uncorrelated N and Z diffusion Interpretation of massive transfer via diffusion models the region with small energy loss is where nuclear structure properties play a major role

56. Mass distributions for proton stripping channels channels (E l =315 MeV) Ar isotopes (-2p) K isotopes (-1p) background free spectra with transfer products at very low excitation energy : no evaporation effects and cleanest conditions for comparison with theory

57. Evaporation processes directly identified with PRISMA+CLARA an example : 40 Ca+ 96 Zr reaction at 152 MeV an example : 40 Ca+ 96 Zr reaction at 152 MeV Evaporation processes directly identified with PRISMA+CLARA an example : 40 Ca+ 96 Zr reaction at 152 MeV an example : 40 Ca+ 96 Zr reaction at 152 MeV heavy partner light partner -2p+2n channel

58. Elastic scattering Inelastic scattering

59. G.Pollarolo and A.Winther, PRC62(2000)054611 GRAZING code calculations G.Montagnoli et al., EPJA15(2002)351 Transfer and fusion cross sections for 40 Ca+ 90,96 Zr

60. H.Esbensen et al, PRC57(1998)2401 exp. neutron transfer yield coupling scheme sub-barrier fusion near and sub-barrier transfer Evap.Res. Fusion Fusion+Deep Inel. Transfer Tr+Inel 2 +,3 - +Multiphonon 1-dim. 58 Ni+ 124 Sn C.L.Liang et al, PRC57(1998)2393

61. The transfer components and what the Grazing code can compute

62. E. Fioretto - LNL62 AGATA Dem - PRISMA Workshop - LNL, 15-16 Nov 2007 70 Zn+ 238 U 450 MeV 70 Zn+ 238 U 450 MeV 96 Zr+ 124 Sn 575 MeV 96 Zr+ 124 Sn 575 MeV 136 Xe+ 208 Pb 950 MeV 136 Xe+ 208 Pb 950 MeV 40 Ar+ 208 Pb 450 MeV 40 Ar+ 208 Pb 450 MeV Z=18 Z=30 Z=40 Z=54  E/E < 2% Z/  Z ~ 60 for Z=20  E/E < 2% Z/  Z ~ 60 for Z=20 Energy [arb. units]

63. Total kinetic energy loss distributions in 40 Ca+ 208 Pb E lab =235 MeV θ lab =84 o TKEL corresponding to the two-touching sphere configuration (maximal amount of energy that can be lost in binary collisions)

64. 40 S β decay NSCL-MSU (1) GANIL (2) PRISMA/CLARA 40 S N.Marginean, Trento Workshop, 2006 X.Liang, PRC74(2006)014311 Collectivity above N=20 shell closure D. Sohler et al. PRC 66(2002)054302 J.A.Wigner et al., PRC 64(2001)064318 36 S (230MeV) + 208 Pb 40 Ar(205MeV) + 170 Er S

65. 82 Ge 80 Zn reliable production cross sections for exotic nuclei like the N=50 82 Ge or 80 Zn are mandatory when one project γ-spectroscopy experiments Cross sections measurements 82 Se+ 238 U E lab =500 MeV 74 Ni

66. GRAZING code possibility to explore multiple particle transfers in the pick-up and stripping of both neutrons and protons

67. Z,A yields - time-of-flight spectrometer data (LNL) Total cross sections – data compared with Complex WKB calculations S.Szilner et al, Phys.Rev.C71(2005)044610 N/Z of the compound pure proton stripping pure neutron pick-up

68. D.G.Fleming et al, PR165(1968)1153 for 1p and 2s1d shells upper bound that can be expected in comparing (p,t) and (p, 3 He) reactions in the limit of pure S=0 transfer for (p, 3 He) due to the additional S=1 spin transfer in (p, 3 He), the cross section ratio should be modified

69. Pairing vibration model

70. The understanding of low energy heavy ion reactions requires a careful and consistent experimental and theoretical work - elastic scattering (nuclear potential) - inelastic scattering (phonon form factor) - one particle transfer (single particle form factors) - two particle transfer (nucleon-nucleon correlations) - multiple particle transfer (multipair transfer,... towards DIC) mandatory a complete set of observables A, Z, TKEL, dσ/dΩ, σ tot

71. sub-barrier transfer cross section measurements are important to compare with fusion cross sections in a similar energy and angular momentum range A.M.Stefanini et al., PRC76,014610(2007) Sub-barrier fusion of 40 Ca+ 94 Zr Sub-barrier fusion of 40 Ca+ 94 Zr Interplay of phonon and transfer couplings Sub-barrier fusion of 40 Ca+ 94 Zr Sub-barrier fusion of 40 Ca+ 94 Zr Interplay of phonon and transfer couplings

72. G.Pollarolo, Phys.Rev.Lett.100,252701(2008) Quasielastic barrier distributions : role of particle transfer channels

73. Pairing vibrations : (p,t) reactions J.B.Ball et al., PRL29(1972)1014

74. In ( 3 He,p) reactions p-n pairs may be transferred either with S=0,T=1 or with S=1,T=0. In (α,d) reactions only S=1,T=0 is possible. Selection rules for (one step) two nucleon transfer reactions

75. A.O.Macchiavelli et al.,Phys.Lett.B480(2000)1 May T=0 collective effects show up as a vibrational phonon ? pairing strenght weak collective correlations strong collective correlations, possibility to develop a permanent deformation in gauge space Experimental excitation spectrum for addition phonons around 56 Ni

76. E.Maglione et al., PLB162(1985)59 Two nucleon transfer : simultaneous vs successive contributions