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P.Guazzoni Dipartimento di Fisica dell’Università degli Studi and

Homologous States in 139,140 Pr via the 142,143 Nd (p,α) 139,140 Pr Reactions. P.Guazzoni Dipartimento di Fisica dell’Università degli Studi and L.Zetta Istituto Nazionale di Fisica Nucleare, I-20122 Milano, Italy T. Faesterman Physik Department TUM - D­85748 Garching, Germany

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P.Guazzoni Dipartimento di Fisica dell’Università degli Studi and

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  1. Homologous States in 139,140Pr via the 142,143Nd (p,α)139,140Pr Reactions P.GuazzoniDipartimento di Fisica dell’Università degli Studi and L.Zetta Istituto Nazionale di Fisica Nucleare, I-20122 Milano, Italy T. FaestermanPhysik Department TUM - D­85748 Garching, Germany R.Hertenberger Fakultät für Physik der LMU-D­85748 Garching, Germany H-F.WirthFakultät für Physik der LMU-D­85748 Garching, Germany M.JaskolaSoltan Institute for Nuclear Studies - 00-681 Warsaw, Poland B.F.BaymanSchool of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA P.Guazzoni - SPIN 2010, Juelich

  2. What ? High Resolution Measurement of Three Nucleon Transfer Reactions with Polarized Protons Where ? Data Taking: Maier Leibnitz Laboratorium - Garching Tandem Accelerator, Polarized Source, Q3D, Focal Plane Detector P.Guazzoni - SPIN 2010, Juelich

  3. Why (p,a) ? (HI,xnγ) studies bring information on the structure of nuclei at high spin. On the other hand one nucleon transfer-reactions almost exclusively populate the single-particle component of the final states, while two- or three-nucleon transfer reactions better evidence at low excitation energy the correlation associated with the pairing interaction. The two kind of reactions [(HI,xnγ) & few nucleon transfer] complement each other non only in their degree of selecting particular states in the residual nucleus, but also in their spin and energy ranges. High resolution few nucleon transfer reactions with light projectiles remain a very important source of detailed knowledge for the nuclear structure of nuclei close to the stability valley. P.Guazzoni - SPIN 2010, Juelich

  4. Why (p,a) ? 142Nd (p,a) 139Pr The dependence of s(q)and Ay (q) of the emitted particles on the transferred total angular momentum J is of the greatest importance for identifying the spin and parity of the levels excited in a nuclear reaction. In particular for (p,a) reactions, as a general rule, the mean behavior of Ayis strictly Jp dependent. Hypothetical level at Ex=1500 keV positive parity states negative parity states P.Guazzoni - SPIN 2010, Juelich

  5. (p,a) and (p,a) reactions on even-even target nuclei (p,a) and (p,a) reactions on odd mass target nuclei Several l and j transferred; necessity of incoherent sum of different contributions even-even and odd mass target nuclei Only one transferred orbital and total angular momentum Great advantage if only one l and j dominate a given transition amplitude Good spectroscopic information from the analysis of the experimental data P.Guazzoni - SPIN 2010, Juelich

  6. When only one l and j dominate a given transition amplitude for (p,a) reactions on odd mass target nuclei? at higher excitation energies, multiplets of states are found, whose configuration results from a process in which the unpaired nucleon is not involved This behavior can be systematically observed for a number of transitions induced on near magic target nuclei having one unpaired nucleon outside a completely filled magic shell The dominant contribution to the a-spectrum results from a process in which the incident proton picks up a proton and a pair of neutrons from the nuclear core, while the valence nucleon outside the core acts as spectator at lower excitation energies, weakly excited states are found, populated by a process involving the unpaired nucleon two parts in the a-spectrum : P.Guazzoni - SPIN 2010, Juelich

  7. HOMOLOGY Start-up 209Bi(p,a)206Pb 208Pb(p,a)205Tl spectator proton 1h9/2 Ep = 24 MeV θc.m. = 60 ◦ Milano AVF Cyclotron The two spectra have almost the same shape, but are shifted by the energy given by the gap between unpaired proton and the closed shell G.S. Qval 10.391 MeV Qval 6.936 MeV 3.25 MeV G.S. ΔQval 3.455 P.Guazzoni - SPIN 2010, Juelich

  8. 123Sb (p,) 120Sn Qval = 6.745 MeV ~ 3.6 MeV 122Sn(p,) 119In Qval = 2.623 MeV Qval = 4.122 MeV Homology region spectator proton 1g7/2 P.Guazzoni - SPIN 2010, Juelich

  9. What isHOMOLOGY? Homology is the occurrence of corresponding states in neighboring systems, which implies the persistence of preferred structures that survive after the addition of one particle that behaves as a spectator in the studied process. P.Guazzoni - SPIN 2010, Juelich

  10. HOMOLOGOUS STATES The one-proton-hole-two-neutron-hole states excited in (p,a) reactions on magic target nuclei, with a magic neutron and/or proton shell- we denote as parent states. In near magic target nuclei, with one more nucleon outside the magic shell-the spectator nucleon- the weak coupling of a parent state with the spectator nucleon originates a multiplet of states, daughter states, with spin J |Jp-Jc| J  (Jp+Jc) Jp= spin of the spectator Jc= spin of the core. We denote the daughter states and the corresponding parent state as HOMOLOGOUS STATES states with a close structural relationship P.Guazzoni - SPIN 2010, Juelich

  11. closed shell N=50 the pair 91Zr, 90Zr 91Zr (p,a) 88Y 90Zr (p,a) 87Y spectator: shell 2d5/2 closed shell N=82 the pair 143Nd, 142Nd 143Nd (p,)140Pr 142Nd (p,)139Pr spectator: shell 2f7/2 Experiments The concept of homologous states has been investigated in high resolution experiments Maier Leibnitz Beschleuniger Laboratorium - Garching Tandem Accelerator, Polarized Source, Q3D, Focal Plane Detector spectator nucleon : neutron P.Guazzoni - SPIN 2010, Juelich

  12. 91Zr (p,a) 88Y 90Zr (p,a) 87Y P.Guazzoni - SPIN 2010, Juelich

  13. closed shell Z=50 the pairs 123Sb, 122Sn 121Sb , 120Sn 123Sb(p,)122Sn 122Sn(p,)119In spectator: shell 1g7/2 121Sb(p,)120Sn 120Sn(p,)117In spectator: shell 1d5/2 closed shells Z=82, N=126 the pair 209Bi, 208Pb 209Bi(p,a)206Pb 208Pb(p,a)205Tl spectator: shell 1h9/2 closed shell Z=20 the pair 44Ca, 45Sc 45Sc(p,)44Ca 44Ca(p,)41K spectator: shell 1f7/2 Z=38 Subshell the pair 89Y, 88Sr 89Y(p,)86Sr 88Sr(p,)85Rb spectator: shell 2p1/2 spectator nucleon : proton P.Guazzoni - SPIN 2010, Juelich

  14. Parent Daughters 209Bi(p,a)206P 208Pb(p,a)205Tl P.Guazzoni - SPIN 2010, Juelich

  15. 209Bi(p,a)206P & 208Pb(p,a)205Tl 205Tl Parent 206Pb Daughters P.Guazzoni - SPIN 2010, Juelich

  16. 123Sb(p,)120Sn daughter & 122Sn(p,)119In parent P.Guazzoni - SPIN 2010, Juelich

  17. HOMOLOGOUS STATES: Methodology Angular distributions of s(q) and Ay(q) very similar in shape for all the multiplet and parent states 1 scaled by (2Ji+1)/Si(2Ji+1) Parent state s(q) and Ay(q) magnitude same as s(q) and Ay(q) SUM of all the corresponding daughter states cumulative cross section and asymmetry 2 ratio between daughter (J) s(q) and parent state s(q) PROPORTIONAL to (2J+1) 3 In case of weak coupling between the parent state and the spectator nucleon, it is expected for the excited multiplets of daughter states that: P.Guazzoni - SPIN 2010, Juelich

  18. 1 Angular distributions of s(q)and Ay(q)very similar in shape for all the multiplet states and the parent state scaled by (2Ji+1)/Si(2Ji+1) 208Pb(p,a)205Tl 209Bi(p,a)206Pb 0,225 0,275 Parent (solid line) 205Tl 0.204 MeV 3/2+ Daughters (dots) 206Pb Quartet 3— 4— 5— 6— 0,325 0,175 P.Guazzoni - SPIN 2010, Juelich

  19. s(q) and Ay(q)for the parent state is the same as the SUM of the s(q)’s and Ay(q)’sof all the corresponding daughter states of the multiplet 2 found missed 208Pb(p,a)205Tl 4-,5- == G.S. 209Bi(p,a)206Pb 3-,4-, == 5-,6- 0.204 MeV cumulative angular distributions for s(q)and Ay(q) 2-,3-,4-, == 5-,6-,7- 0.619 MeV 2-,3-,4-, 5-, 1- 6-,7-,8- 0.924 MeV 2-,3-,5-, 6-, 0-,1-, 7-,8-, 9- 4- of the DAUGHTER STATES 1.430 MeV 1+,2+ 3+,4+, 5+, 6+,7+,8+, 9+,10+ 1.484 MeV P.Guazzoni - SPIN 2010, Juelich

  20. The ratio between the daughter (Ji) s(q) and parent state s(q) is PROPORTIONAL to (2 Ji +1). 3 Parent 9/2+ 122Sn(p,a)119In 123Sb(p,a)120Sn Parent 1/2- Dots: daughter states Dashed: (2 Ji +1) lines Parent 3/2- Parent 5/2- sdaughter(120Sn,Ji ) = sparent(119In) * (2 Ji+1)/S(2 Ji+1) {sdaughter(120Sn,Ji )/ sparent(119In) } *S(2 Ji+1) = (2 Ji+1) P.Guazzoni - SPIN 2010, Juelich

  21. True Not Homologous States False Homologous States CLUSTER DWBA CALCULATIONS A generally accepted rule for (p,a) reactions is that a’s feeding states with the same Jphave nearly the same shape for angular distributions of cross sections and asymmetries. P.Guazzoni - SPIN 2010, Juelich

  22. 91Zr(p,a)88Y -- 2- states 90Zr(p,a)87Y parent Homologous 87Y G.S. 1/2— DWBA - configuration of the possible parent state Homologous 87Y 0.794 5/2— Homologous 87Y 0.982 3/2— DWBA - incoherent sum of different l,j ang. distr. for 88Y states Not Homologous • • • • • • • • Not Homologous 88Y - experimental values P.Guazzoni - SPIN 2010, Juelich

  23. The achieved results clearly indicate: COMMON CONFIGURATIONS for HOMOLOGOUS STATES SHELL MODEL CALCULATIONS FOR THE HOMOLOGOUS STATES A  208 A  90 A  40 This similarity is more evident in case of purest states as, for example, the 206Pb multiplet of daughter states, homologous to the 1.484 MeV, 11/2–, 205Tl parent state. P.Guazzoni - SPIN 2010, Juelich

  24. 208Pb(p,a)205Tl 209Bi(p,a)206Pb EXPERIMENTAL AND SHELL MODEL ENERGY SPECTRUM spectator nucleon: proton 1h9/2 P.Guazzoni - SPIN 2010, Juelich

  25. P.Guazzoni - SPIN 2010, Juelich

  26. 45Sc(p,a)42Ca daughter reaction spectator nucleon: proton 1f7/2 44Ca(p,a)41K parent reaction Multiplet corresponding to 41K G.S. 3/2+ Parent State Expected 2 –,3 –,4 –,5– |Jp-Jc| J  (Jp+Jc) Jp=2 –,3 –,4 –,5– s(q)values for all the daughter states Jp=2–s(q) parent scaled by0.1562 not seen Jp=3–s(q) parent scaled by0.2187 @ 4.117 MeV Jp=4–s(q) parent scaled by0.2812 @ 3.954 MeV Jp=5–s(q) parent scaled by0.3437 @ 4.100 MeV P.Guazzoni - SPIN 2010, Juelich

  27. SHELL MODEL CALCULATIONS 45Sc(p,a)42Ca 44Ca(p,a)41K Code Antoine by E. Caurier Interaction used: sdfp.sm for both 41K and 42Ca {Nummela et al. Phys Rev C63 (2001) 044316} 41K GS 9/2+ 3/2+Dominant configuration:(d3/2-1)(f7/2 2) 42Ca 3–, 4–, 5–Dominant configuration:(f7/21 d3/2-1)(f7/2 2) 42Ca 2– Different structure: several configurations contribute to the state wave function Homologous structure P.Guazzoni - SPIN 2010, Juelich

  28. 87,8 Parent Hom. 64,7 Hom. 74,1 Hom. 68,9 29,4 Not 18,6 Multiplet of Daughter States corresponding to 41K G.S. 3/2+ Parent State P.Guazzoni - SPIN 2010, Juelich

  29. 123Sb(p,α)120Sn Fully microscopic calculations: the proton and two neutrons are picked up from individual shell-model states, and then their overlap with respect to the transferred three-particle cluster is calculated MICROSCOPIC DWBA CALCULATIONS 123Sb G.S. is taken to be a 1g7/2 proton outside filled proton shells. 22 valence neutrons move in the 1g7/2 –2d5/2 – 2d3/2 –3s1/2 – 1h11/2 shells interacting via a neutron-neutron pairing force which spreads the neutrons over the valence cells with a total neutron angular momentum of zero The pickup reaction to 120Sn G.S. involves the transfer of a 1g7/2 proton and a neutron pair coupled to zero angular-momentum The pickup reaction to 120Sn multiplet homologous to 119In G.S. removes a 1g9/2 proton and a neutron pair coupled to zero angular-momentum, while the 1g7/2 proton remains spectator P.Guazzoni - SPIN 2010, Juelich

  30. 120Sn G.S. 123Sb(p,a)120Sn Cumulative angular distributions of Multiplet homologous to 119In G.S. 9/2+ 119In 0.311 1/2- 1/2– 119In 0.604 3/2- 3/2– 119In 1.044 5/2- 5/2– MICROSCOPIC DWBA CALCULATIONS Dots : experimental values Solid line : Microscopic DWBA calculations P.Guazzoni - SPIN 2010, Juelich

  31. N=82 closed shell 142Nd(p,)139Pr & 143Nd(p,)140Pr Ep=23.5 MeV spectator nucleon: neutron 2f7/2 142Nd(p,α)139PrGS 9/2+ Qval = 3.734 MeV 143Nd(p,α)140PrGS 9/2+ Qval = 5.552MeV Observed levels 46 Confirmed assignments 9 Removed ambiguities 5 Changed assignments 7 New levels 7 New assignments 11 Observed levels 82 New levels 50 New Jπassignments 18 (17 to new levels) P.Guazzoni - SPIN 2010, Juelich

  32. P.S. P.S. P.S. Homology 143Nd(p,α)140Pr Spin up θlab= 20○ 142Nd(p,α)139Pr Spin up θlab= 20○ ΔQ = 1.818 MeV 142Nd(p,α)139PrGS 9/2+ Qval = 3.734 MeV 143Nd(p,α)140PrGS 9/2+ Qval = 5.552MeV P.Guazzoni - SPIN 2010, Juelich

  33. 142Nd(p,α)139Pr P.Guazzoni - SPIN 2010, Juelich

  34. HOMOLOGOUS STATES: Experiment 143Nd(p,α)140Pr – observed daughter states 139Pr 0.114 MeV 7/2+ Parent State 6 daughter states of 8 Energy coeff. Jπ not seen 0.0156 → 0- 1.939 MeV 0.0469 → 1- 1.870 MeV 0.0781 → 2- 1.984 MeV 0.1094 → 3- 2.020 MeV 0.1406 → 4- 1.718 MeV 0.1719 → 5- not seen 0.2031 → 6- 1.672 MeV 0.2344 → 7- 139Pr G.S. 5/2+ Parent State 5 daughter states of 6 Energy coeff. Jπ not seen 0.0625 → 1- 1.652 MeV 0.1042 → 2- 1.484 MeV 0.1458 → 3- 1.565 MeV 0.1875 → 4- 1.684 MeV 0.2292 → 5- 1.586 MeV 0.2708 → 6- 139Pr 0.828 MeV 9/2+ Parent State 7 daughter states of 8 Energy coeff. Jπ Energy coeff. Jπ not seen 0.0375 → 1- 3.084 MeV 0.0625 → 2- 2.333 MeV 0.0875 → 3- 2.829 MeV 0.1125 → 4- 2.349 MeV 0.1375 → 5- 2.221 MeV 0.1625 → 6- 2.415 MeV 0.1875 → 7- 2.632 MeV 0.2125 → 8- P.Guazzoni - SPIN 2010, Juelich

  35. 143Nd(p,α)140Pr – cumulative angular distributions 5/2+ 7/2+ 9/2+ P.Guazzoni - SPIN 2010, Juelich

  36. 143Nd(p,α)140Pr daughter state angular distributions dots Parent State 139Pr G.S. 5/2+ (solid lines) Scaled by the proper (2J+1) factor P.Guazzoni - SPIN 2010, Juelich

  37. 143Nd(p,α)140Pr daughter state angular distributions dots Parent State 139Pr 0.114 MeV 7/2+ (solid lines) Scaled by the proper (2J+1) factor P.Guazzoni - SPIN 2010, Juelich

  38. 143Nd(p,α)140Pr daughter state angular distributions dots Parent State 139Pr 0.828 MeV 9/2+ (solid lines) Scaled by the proper (2J+1) factor P.Guazzoni - SPIN 2010, Juelich

  39. The ratio between the daughter (Ji) s(q) and parent state s(q) is PROPORTIONAL to (2 Ji +1) sdaughter(140Pr,Ji ) = sparent(139Pr) * (2 Ji+1)/S(2 Ji+1) Parent 5/2+ 142Nd(p,a)139Pr 143Nd(p,a)140Pr Dots: daughter states Dashed: (2 Ji +1) lines Parent 7/2+ Parent 9/2+ P.Guazzoni - SPIN 2010, Juelich

  40. CONCLUSIONS •Shell Model calculations: strongly support the homologous state experimental results indicate the correctness of the approach also for closed subshells •Applicability limits for the theory are the shell model limitations •DWBA microscopic calculations also support the validity of the spectator role of the unpaired proton weakly coupled to the parent core-state. CONSEQUENTLY •Homology concept is an useful spectroscopic tool for nuclei in the regions nearby closed shells, because the concept of the spectator nucleon allows a unambiguous attribution of spin and parity to several states at relatively high excitation energies. P.Guazzoni - SPIN 2010, Juelich

  41. That’s all Thanks! P.Guazzoni - SPIN 2010, Juelich

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