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L.Zetta Dipartimento di Fisica dell’Università and

Study of Corresponding H omologous States in 41 K and 42 Ca via (p,  ) reactions. L.Zetta Dipartimento di Fisica dell’Università and P.G. Istituto Nazionale di Fisica Nucleare, I-20122 Milano, Italy F.Della Vedova S.Lenzi Dipartimento di Fisica dell’Università and

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L.Zetta Dipartimento di Fisica dell’Università and

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  1. Study of Corresponding Homologous States in 41K and 42Ca via (p,) reactions L.Zetta Dipartimento di Fisica dell’Università and P.G. Istituto Nazionale di Fisica Nucleare, I-20122 Milano, Italy F.Della Vedova S.Lenzi Dipartimento di Fisica dell’Università and A.Vitturi IstitutoNazionale di Fisica Nucleare, I-35131 Padova, Italy G.Graw R.Hertenberger Sektion Physik der Universität München, H-F.Wirth Am Coulombwall 1, D­85748 Garching, Germany M.Jaskola Soltan Institute for Nuclear Studies, Warsaw, Poland Data Taking: Maier Leibnitz Laboratorium - Garching Tandem Accelerator, Polarized Source, Q3D, Focal Plane Detector P.Guazzoni - spin2004, October 10_16 2004

  2. 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 is strictly Jp dependent -----> 44Ca(p,a)41K Hypothetical level at Ex=1500 keV positive parity states negative parity states P.Guazzoni - spin2004, October 10_16 2004

  3. (p,a) and (p,a) reactions on odd mass target nuclei; several l and j transferred; necessity of incoherent sum of different contributions (p,a) and (p,a) reactions studied for even-even target nuclei Great advantage if only one l and j dominate a given transition amplitude Only one transferred orbital and total angular momentum Good spectroscopic information from the analysis of the experimental data Good spectroscopic information from the analysis of the experimental data P.Guazzoni - spin2004, October 10_16 2004

  4. two parts in the a-spectrum : When only one l and j dominate a given transition amplitude for (p,a) reactions on odd mass target nuclei? 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 lower excitation energies higher excitation energies multiplets of states are found, whose configuration results from a process in which the unpaired nucleon is not involved weakly excited states are found, populated by a process involving the unpaired nucleon P.Guazzoni - spin2004, October 10_16 2004

  5. 45Sc(p,) 42Ca Qval = 2.3415 MeV 45Sc(p, a)42Ca 44Ca(p,) 41K Qval = -1.0462 MeV Qval = 3.3877 MeV higher excitation energies lower excitation energies ~ 3.4 MeV P.Guazzoni - spin2004, October 10_16 2004

  6. 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 - spin2004, October 10_16 2004

  7. 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)magnitude same as s(q)SUM of all the corresponding daughter states 2 cumulative cross section 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 - spin2004, October 10_16 2004

  8. 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 Parent 205Tl 0.204 MeV 3/2+ Daughters 206Pb Quartet 3— 4— 5— 6— P.Guazzoni - spin2004, October 10_16 2004

  9. s(q) for the parent state is the same as the SUM of the s(q)’s of all the corresponding daughter states of the multiplet 2 found missed 208Pb(p,a)205Tl 4-,5- == 209Bi(p,a)206Pb G.S. 3-,4-, == 5-,6- 0.204 MeV cumulative angular distributions 2-,3-,4-, == 5-,6-,7- 0.619 MeV 2-,3-,4-, 5-, 1- 6-,7-,8- 0.924 MeV DAUGHTER STATES 2-,3-,5-, 6-, 0-,1-, 7-,8-, 9- 4- 1.430 MeV 1+,2+ 3+,4+, 5+, 6+,7+,8+, 9+,10+ 1.484 MeV P.Guazzoni - spin2004, October 10_16 2004

  10. The ratio between the daughter (Ji) s(q) and parent state s(q) is PROPORTIONAL to (2 Ji +1). 3 208Pb(p,a)205Tl 209Bi(p,a)206Pb sdaughter(206Pb,Ji ) = sparent(205Tl) * (2 Ji+1)/S(2 Ji+1) P.Guazzoni - spin2004, October 10_16 2004

  11. 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 the pair 209Bi, 208Pb ----> closed shells Z=82, N=126 209Bi(p,a)206Pb 208Pb(p,a)205Tl spectator nucleon: proton 1h9/2 the pair 91,90Zr ----> closed shells Z=82, N=126 91Zr(p,a)88Y 90Zr(p,a)87Y spectator nucleon: neutron 2d5/2 Studied nuclei (already published): P.Guazzoni - spin2004, October 10_16 2004

  12. Studied nuclei (to be published): the pair 123Sb, 122Sn ----> closed shell Z=50 122Sn(p,)119In 123Sb(p,)122Sn spectator nucleon: proton 1g7/2 Measured Reactions: Z=38 Subshell spectator nucleon: proton 2p1/2 89Y(p,)86Sr & 88Sr (p,)85Rb N=82 closed shell spectator nucleon: neutron 2f7/2 143Nd (p,)140Pr & 142Nd (p,)139Pr P.Guazzoni - spin2004, October 10_16 2004

  13. Recent Results 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 Jp=3–s(q) parent scaled by0.2187 Jp=4–s(q) parent scaled by0.2812 Jp=5–s(q) parent scaled by0.3437 P.Guazzoni - spin2004, October 10_16 2004

  14. 44Ca(p,a)41K parent reaction sint=159.11 mb (10°-65°) sint=140.48 mb (10°-65°) sint= 64.92 mb (10°-65°) sint= 22.93 mb (10°-65°) sint= 32.78 mb (10°-65°) sint= 47.82 mb (10°-65°) Solid line: DWBA Dots: exp P.Guazzoni - spin2004, October 10_16 2004

  15. 45Sc(p,a)42Ca daughter reaction Multiplet corresponding to 41K G.S. 3/2+ sint=159.11 mb (10°-65°) sint= 47.82 mb (10°-65°) sint=113.55 mb (10°-65°) sint= 17.17 mb (10°-65°) Expected Jp=2 –,3 –,4 –,5– Solid line: parent state, exp Dots: daughter states, exp 2–: NOT SEEN WHY? P.Guazzoni - spin2004, October 10_16 2004

  16. 45Sc(p,a)42Ca daughter reaction Parent level: 41K ½+ 0.980 MeV Parent level: 41K ½+ 1.593 MeV Expected Jp=3 –,4– some levels of multiplets corresponding to Solid line: parent state, exp Dots: daughter states, exp 3– nth=0.437 4– nth=0.563 P.Guazzoni - spin2004, October 10_16 2004

  17. Not Homologous States  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. True False P.Guazzoni - spin2004, October 10_16 2004

  18. 91Zr(p,a)88Y daughters 90Zr(p,a)87Y parent Homologous 87Y G.S. 1/2— DWBA - configuration of the parent state Homologous 87Y 0.794 5/2— Homologous 87Y 0.982 3/2— DWBA - incoherent sum of different l,j ang. distr. Not Homologous • • • • • • • • 88Y - experimental values Not Homologous P.Guazzoni - spin2004, October 10_16 2004

  19. Work in progress A  40 Done The achieved results clearly indicate: COMMON CONFIGURATIONS for HOMOLOGOUS STATES  A  208 A  90 SHELL MODEL CALCULATIONS FOR THE HOMOLOGOUS STATES 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 - spin2004, October 10_16 2004

  20. SHELL MODEL CALCULATIONS 208Pb(p,a)205Tl 209Bi(p,a)206Pb P.Guazzoni - spin2004, October 10_16 2004

  21. 208Pb(p,a)205Tl 209Bi(p,a)206Pb EXPERIMENTAL AND SHELL MODEL ENERGY SPECTRUM P.Guazzoni - spin2004, October 10_16 2004

  22. SHELL MODEL CALCULATIONS 45Sc(p,a)42Ca Code Antoine by E. Caurier 44Ca(p,a)41K 41K GS 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 Interaction used: sdfp.sm for both 41K and 42Ca {Nummela et al. Phys Rev C63 (2001) 044316} P.Guazzoni - spin2004, October 10_16 2004

  23. Multiplet of Daughter States corresponding to 41K G.S. 3/2+ Parent State P.Guazzoni - spin2004, October 10_16 2004

  24. 123Sb(p,)122Sn 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 - spin2004, October 10_16 2004

  25. 120Sn G.S. 123Sb(p,a)120Sn MICROSCOPIC DWBA CALCULATIONS Cumulative angular distributions of Multiplet homologous to 119In G.S. 9/2+ 119In 0.311 1/2– 119In 0.604 3/2– 119In 1.044 5/2– Dots : experimental values Solid : Microscopic DWBA calculations P.Guazzoni - spin2004, October 10_16 2004

  26. CONCLUSIONS •Shell Model calculations strongly support the Homologous state experimental results •Shell Model calculations seem to indicate the correctness of the approach also for closed subshells, to be verified experimentally •Applicability limits for the theory are the shell model limitations P.Guazzoni - spin2004, October 10_16 2004 Spin2002. BNL, September 9-14,2002

  27. CONCLUSIONS • DWBA microscopic calculations also support the validity of the spectator role of the unpaired proton weakly coupled to the parent core-state. • Homology concept useful spectroscopic tool for regions nearby closed shells • The use of the concept of the spectator nucleon allows a unambiguous attribution of spin and parity to several states at relatively high excitation energies. P.Guazzoni - spin2004, October 10_16 2004

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