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Nucleon-nucleon correlations probed via heavy ion transfer reactions

Nucleon-nucleon correlations probed via heavy ion transfer reactions. L.Corradi Laboratori Nazionali di Legnaro – INFN, Italy. outline. Hystorical background - (p,t) reactions and the pairing vibration model (years 70’s) - (C,O) reactions and simultaneous vs sequential transfer (80’s)

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Nucleon-nucleon correlations probed via heavy ion transfer reactions

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

  2. outline 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. 90Zr(p,t)88Zr normalization factor (zero range approx.) isospin coefficient enhancement factor spectroscopic amplitude transition amplitude The enhancement factor εhas 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 εfrom unity. J.Ball et al., PRC4(1971)196

  4. Scheme levels from the harmonic pairing model

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

  6. 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 W.Mayer et al.,PRC26(1982)500

  7. Two nucleon transfer : simultaneous vs successive contributions

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

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

  10. Distinguishing between gs. and 2qp band in 1 and 2 nucleon transfer F = P2n / (P1n)2 X.T.Liu et al., PRC43(1991)R1

  11. Transfer reactions (multinucleon) among heavy ions The quasi-elastic regime is governed by - form factors < f I Vint I i > (structure) - optimum Q-values (dynamics) ‘ a’ degrees of freedom single particle states surface vibrations pair modes a A A’ 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

  15. The semiclassical theory

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

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

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

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

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

  21. THE PRISMA SPECTROMETER + CLARA GAMMA ARRAY

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

  23. PRISMA spectrometer – trajectory reconstruction ΔE-E Mass A/q q

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

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

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

  31. Population of states close to the pairing vibrational region 2240 1874 3308 3842

  32. identified and known 208Pb(90Zr,92Zr)206Pb E=560 MeV identified but in overlap with other known existing ? 0+ [4283] strong in (t,p) 0+ [3992] strong in (t,p) 0+ [3589] strong in (t,p) non tab 492 934 (4000) non tab 2+ [3500] L=2 (t,p) 1225 1463 439 2+ [3058] L=2 (t,p) 0+ [2903] weak in (t,p) new (120) 1742 (n,n’) 2+ [2820] L=2 (t,p) 837 990 (1000) (n,n’) 972 2+ [2067] L=2 (t,p) 1970 2+ [1848] L=2 (t,p) 1132 (245) 912 (1100) wide peak at 893 2+ [934] L=2 (t,p) 1848 (50) 934 (4000) 0+ [g.s.]

  33. Sub-barrier transfer reactions

  34. Q-value window absorptive potential form factor At energies lower than the Coulomb barrier : - 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. data are very scarse or almost non existing

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

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

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

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

  39. 94Zr+40Ca, Elab=330 MeV, θlab=20o, inverse kinematics

  40. Mass distributions for pure neutron pick-up channels

  41. TKEL distributions for pure neutron pick-up channels Qgs

  42. Mass vs Q-value matrix for (-1p) channels channels (El=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. 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) 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

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

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

  48. GRAZING code

  49. Multinucleon transfer reactions with radioactive beams 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) 140Sn 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

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