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Nature of Mixed-Symmetry 2 + States in 94 Mo from High-Resolution Electron and Proton Scattering

Nature of Mixed-Symmetry 2 + States in 94 Mo from High-Resolution Electron and Proton Scattering and Line Shape of the First Excited 1/2 + State in 9 Be. Oleksiy Burda , 19.11.2007. Motivation. Experiments. Results and microscopic interpretations. Summary.

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Nature of Mixed-Symmetry 2 + States in 94 Mo from High-Resolution Electron and Proton Scattering

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  1. Nature of Mixed-Symmetry 2+ States in 94Mofrom High-Resolution Electron and Proton Scattering and Line Shape of the First Excited 1/2+ State in 9Be Oleksiy Burda, 19.11.2007

  2. Motivation • Experiments • Results and microscopic interpretations • Summary

  3. Pairing of nucleons to s- / d- bosons F-spin: p boson: Fz = 1/2 n boson: Fz = -1/2 Np + Nn |Np – Nn| ≥ F ≥ Np, Nn: Fmax = 2 2   F = Fmax: fully symmetric states (FSS) isoscalar   F < Fmax: mixed-symmetry states (MSS) isovector + + |21  Qs | 01 Q-phonon scheme: Qs = Qp+ Qn N N + + |2ms  Qms| 01 Qms = Qp– Qn 2 Np 2 Nn Interacting Boson Model - 2

  4. F = Fmax (FSS) F = Fmax – 1 (MSS) QsQms + + Strong E2 transitions 0ms,…,4ms for decay of symmetric Q-phonon Qms QsQs + Weak E2 transitions 2ms for decay of ms Q-phonon + + + 02,22,41 Qs Strong M1 transitions + for decay of ms states to symmetric states 21 + Test case 94Mo 01 N. Pietralla et al., Phys. Rev. Lett. 83, 1303 (1999); Phys. Rev. Lett. 84, 3775 (2000) C. Fransen et al., Phys. Lett. B 508, 219 (2001); Phys. Rev. C 67, 024307 (2003) Signatures of MSS

  5. Why (e,e´) and (p,p´)? • Study of one- and two-phonon 2+ FSS and MSS with (e,e´) and (p,p´) sensitive to one-phonon components of the wave functions test of fundamental phonon character isoscalar / isovector decomposition purity of two-phonon states

  6. (e,e´): • S-DALINAC, TU Darmstadt (p,p´): iThemba LABS Ee = 70 MeV Ep = 200 MeV Qe = 93° – 165° Qp = 4.5° – 26° DE = 30 keV (FWHM) DE = 35 keV (FWHM) Experiments • High resolution required to resolve all 2+ states below 4 MeV • Lateral dispersion matching technique

  7. Data: Strong Transitions

  8. Data: Weak Transitions

  9. Theoretical Calculation • Quasiparticle Phonon Model (QPM) • full (up to 3 phonons) • pure one- or two-phonon states • Shell Model (SM) • 88Sr core / Vlow-k • IBM-2 •  transition densities from SM • U(5) limit to describe dominant transitions • Cross Section • DWBA / Love-Franey effective • projectile-target interaction for (p,p´)

  10. One-Phonon FSS and MSS • one-phonon character confirmed

  11. Wave Functions of One-Phonon FSS and MSS • FSS isoscalar • MSS isovector

  12. Two-Phonon FSS and MSS • pure two-phonon state • two-step contributions ? • ~10% one-phonon • admixtures in MSS

  13. Coupled-Channel Analysis • pure two-phonon FSS confirmed • admixture to two-phonon MSS confirmed

  14. + • Study of one- and two-phonon FSS and MSS 2 states in 94Mo • with high-resolution (e,e´) and (p,p´) experiments + + dominant one-phonon character of 21 and 23 states Summary • Combined analysis with microscopic models reveals:  isovector character of one-phonon MSS within the valence shell  quantitatively consistent conclusions after inclusion of two-step processes in (p,p´) cross sections  two-phonon FSS quite pure  dominant two-phonon character of two-phonon MSS

  15. Mo94: Theoretical Predictions

  16. Mo94: Radial Transition Charge Densities

  17. Possible Role of 9Be in the Production of 12C • In n-rich environment (core-collapse supernovae) this reaction path • may provide an alternative route for building up the heavy elements • and triggering the r process

  18. Jp = 1/2+ State at Threshold

  19. Lintott Spectrometer

  20. 10 cm Focal Plane Detector System • Si microstrip detector system: • 4 modules, each 96 strips with • pitch of 650 mm • Count rate up to 100 kHz • Energy resolution 1.5x10-4

  21. Data

  22. – For T9 = 0.1 – 3 K this resonance determines exclusively 4He(a,g)8Be(n,g)9Be chain – Determined reaction rate differs up to 20% from adopted values Comparison: 9Be(g,n) and 9Be(e,e´) • Final values: Ex = 1.748(6) MeV and G = 274(8) keV of Jp = 1/2+ resonance

  23. Form Factor of the Jp = 1/2+ State • NCSM: correct q dependence but difference • in magnitude compared to the data (C. Forssén) • B(C1) ≠ B(E1) at photon point k = q •  violation of Siegert theorem ?

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