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Spectroscopy at the Particle Threshold

Spectroscopy at the Particle Threshold. H. Lenske. Agenda: Pairing in the continuum Nuclear Polarizability and Spectral Functions Continuum spectroscopy and Fano -Resonances Summary. Pairing in the Continuum : Quasiparticle Resonances.

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Spectroscopy at the Particle Threshold

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  1. Spectroscopy at theParticleThreshold H. Lenske

  2. Agenda: • Pairing in thecontinuum • NuclearPolarizabilityandSpectralFunctions • ContinuumspectroscopyandFano-Resonances • Summary

  3. Pairing in theContinuum:Quasiparticle Resonances

  4. Extended HFB TheoryasCoupled Channels Problem: The Gorkov-Equations

  5. Spectrum of theGorkovEquation:

  6. Extended HFB Theory: Pairing Self-Energies • EnergyShiftsandWidths • SpectralFunctionsforparticlesandholes

  7. Pairing in Infinite Nuclear Matter

  8. Pairing in Infinite Nuclear Matter Free Space SE (S=0,T=1) Interaction: (Bonn-B Potential) Pairing is a LOW DENSITYPhenomenon

  9. Pairing Gap Dand Anomal Densityk in SymmetricNuclear Matter Pairing Correlations in Nuclear Matter Pairing Gap D Anomal Densityk

  10. Pairing-Field in a Nucleus RA RA

  11. 11Li : ContinuumHFB SpectralFunctions Neutron Spectrum :  Dissolution of Shell Structures!

  12. 11Li : Continuum HFB g.s. Densities g.s. Densities g.s. Densities r2 :

  13. Neutron SpectralFunctions in 9Li(3/2-): ContinuumAdmixturesintotheg.s. ContinuumAdmixtures!

  14. Pairing in the Continuum S. Orrigo, H.L., PLB 677 (2009)

  15. Pairing Resonances in DriplineNuclei 9Li+n 10Li S. Orrigo, H.L., PLB 677 (2009) & ISOLDE newsletter Spring 2010, p.5

  16. ContinuumSpectroscopy at REX-ISOLDE: 10Li=9Li+n d(9Li,10Li)p@2.36AMeV S. Orrigo, H.L., PLB 677 (2009) & ISOLDE newsletter Spring 2010, p.5 Data: H. Jeppesen et al., REX-ISOLDE Collaboration, NPA 738 (2004) 511 & NPA 748 (2005) 374.

  17. New experimental results (Dec. 2013): 10Li continuumspectroscopy at TRIUMF S. Orrigo, M. Cavallo, F. Capppuzzello et al.

  18. SpectralStructuresbyDynamicalPolarization

  19. BeyondtheMean-Field: Short-range Correlations in Nuclear Matter Momentum Distribution n(p) = N(kF) a(w, p) dw PLB483 (2000) 324NPA723 (2003) 544 NPA (2005)in print

  20. Nuclear Dynamics…

  21. QRPA Response in 10Be

  22. DCP Neutron SpectralDistributions in 11Be [0+ × 1/2-]: 0.58 [2+ × 3/2-]: 0.28 [0+ × 1/2+]: 0.79 [2+ × 5/2+]: 0.18

  23. SpectralDistributionsin Carbon Isotopes …normalizedtosumrule E1 Dipole E2 Quadrupole

  24. Polarizability of C-Isotopes: HFB+QRPA results Multipole polarizabiltiescoefficientsbysumrules:

  25. Longitudinal MomentumDistributions: 17,19C →16,18C + n Carbon Target, Elab 900 AMeV • Binding: Correlation Dynamics • 17C(5/2+,g.s.) • Sn(the.)=715keV • C2S(g.s.) = 0.41 • G(the.): 132 MeV/c • G(exp.): 143 ± 5 MeV/c • s(-1n,the.): 124 mb • s(-1n,exp.): 129± 22 mb 17C • Binding: Correlation Dynamics • 19C(1/2+,g.s.) • Sn(the.)=263keV • C2S(g.s.) = 0.40 • G(the.): 69 MeV/c • G(exp.): 68 ± 3 MeV/c • s(-1n,the.): 192 mb • s(-1n,exp.): 233± 51 mb 19C

  26. Dynamical Core Polarization: • HFB g.s.: • „3-body renormalized“ G-Matrix • ph-Interactions: • Fermi Liquid Theory Hole Spectrum FanoResonances ParticleSpectrum DCP Calculations (HFB+QRPA Core excitations) DCP Calculations (HFB+QRPA Core excitations) DCP Calculations (HFB+QRPA Core excitations) DCP Calculations (HFB+QRPA Core excitations)

  27. Interactions of Closedand Open Channels:Fano Resonances

  28. The SpectralSituation encountered in Atoms, Molecules, Nuclei, andHadrons • A closedchannel E* isembeddedinto a continuumof open channels • E* interacts via V(r)with open channelsgivenbyscatteringstates • E* Interacts via V(r)withclosedchannels, e.g. of (simple) boundstates •  Bound State Embedded intotheContinuum - BSEC

  29. Examples: • Atoms: self-ionizingstates of multi-electronconfiguration • Nuclei: Multi-particle-hole statesabovethreshold • Mesons: Confinedqq-configurationsembeddedintothecontinuum of meson-meson scatteringstates, e.g. D(1232), r(770), Y‘‘(3770)… • Baryons: Confinedqqq-configurationsembeddedintothecontinuum of meson-nucleonscatteringstates, e.g. D(1232), N*(1440), L(1405)…

  30. Visualizing Quantum Interferencein MicroscopicSystems: AsymmetricFano-Line Shapes of Resonances

  31. Historically: The famousSilverman-Lassettredata He(e,e‘)He*(1P) @ 500eV Note: q must be negative – q=-1.84

  32. Fano-Resonances in Nuclei

  33. Hamiltonianand Wave function The coupledequations (corenucleusintegrated out): Multi-channelFanowavefunction:

  34. Extension toSeveral Open Channels • n=2 open channels • n=2 energeticallydegeneratesolutionswithoutgoingflux

  35. Solution 1: fullymixed Solution 2: continuummixed „Dark States“  Resonancesuperimposed on a smoothlyvaryingbackground!

  36. Multi-channelCoupling

  37. Resonance Scenarios in Nuclear Physics • The Fano-Wave Function:

  38. Reaction Matrix Elements and Formation Cross Section The (singlechannel) Fano-Formula:

  39. Correlation Dynamics in an Open Quantum System: d-waveFano-Resonances in 15C G~60…140keV Sonja Orrigo, H.L., Phys.Lett. B633 (2006)

  40. DD-Dynamics atThreshold Channel Coupling and the Line Shape of Y(3770) q=-2.1±0.6 X(3900) ?? 3.65 Xu Cao, H. L., PRL, submitted

  41. Summary • Dynamics attheparticlethreshold • Pairing at thedripline/in thecontinuum • Nuclearpolarizabilities • Fanoresonances in atomicnuclei • Tools forcontinuumspectroscopy • Universality of quantuminterference …withcontributionsby Sonja Orrigo (Valencia) andXuCao (Giessen/Lanzhou)

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