1. Spectroscopy at the Particle Threshold H. Lenske 1

2. Agenda: Pairing in the continuum Nuclear Polarizability and Spectral Functions Continuum spectroscopy and Fano-Resonances Summary 2

3. Pairing in the Continuum: Quasiparticle Resonances 3

4. Extended HFB Theory as Coupled Channels Problem: The Gorkov-Equations

5. Spectrum of the Gorkov Equation:

6. Extended HFB Theory: Pairing Self-Energies Energy Shifts and Widths Spectral Functions for particles and holes

7. 7 Pairing in Infinite Nuclear Matter

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

9. Pairing Gap  Anomal Density  Pairing Correlations in Nuclear Matter Pairing Gap  and Anomal Density  in Symmetric Nuclear Matter

10. Pairing-Field in a Nucleus RARA RARA

11. Neutron Spectrum : 11 Li : Continuum HFB Spectral Functions  Dissolution of Shell Structures!

12. g.s. Densities g.s. Densities  r 2 : 11 Li : Continuum HFB g.s. Densities

13. Neutron Spectral Functions in 9 Li(3/2-): Continuum Admixtures into the g.s. Continuum Admixtures!

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

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

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

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

18. Spectral Structures by Dynamical Polarization 18

19. Beyond the Mean-Field: Short-range Correlations in Nuclear Matter PLB483 (2000) 324 NPA723 (2003) 544 NPA (2005)in print Momentum Distribution n(p) = N(k F )  a(  p) d 

20. 20 Nuclear Dynamics…

21. E th [MeV]E exp [MeV] 2+2+ 3.2203.368 1-1- 6.4235.960 0+0+ 6.5136.179 2-2- 6.4466.263 3-3- 7.3727.371 4-(9.270) 1+1+ 7.122 3+3+ 7.159 0-0- 7.374 QRPA Response in 10 Be

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

23. Spectral Distributions in Carbon Isotopes …normalized to sum rule E1 Dipole E2 Quadrupole

24. Polarizability of C-Isotopes: HFB+QRPA results Multipole polarizabilties coefficients by sum rules:

25. Longitudinal Momentum Distributions: 17,19 C → 16,18 C + n Carbon Target, E l ab  900 AMeV Binding: Correlation Dynamics 17 C(5/2+,g.s.) S n (the.)=715keV C 2 S(g.s.) = 0.41  (the.): 132 MeV/c  (exp.): 143 ± 5 MeV/c  (-1n,the.): 124 mb  (-1n,exp.): 129± 22 mb Binding: Correlation Dynamics 19 C(1/2+,g.s.) S n (the.)=263keV C 2 S(g.s.) = 0.40  (the.): 69 MeV/c  (exp.): 68 ± 3 MeV/c  (-1n,the.): 192 mb  (-1n,exp.): 233± 51 mb 17 C 19 C

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

27. Interactions of Closed and Open Channels: Fano Resonances 27

28. The Spectral Situation encountered in Atoms, Molecules, Nuclei, and Hadrons A closed channel E* is embedded into a continuum of open channels E* interacts via V (r) with open channels given by scattering states E* Interacts via V (r) with closed channels, e.g. of (simple) bound states  Bound State Embedded into the Continuum - BSEC 28

29. Examples: Atoms: self-ionizing states of multi-electron configuration Nuclei: Multi-particle-hole states above threshold Mesons: Confined qq-configurations embedded into the continuum of meson-meson scattering states, e.g.  (1232),  (770),  ‘‘(3770)… Baryons: Confined qqq-configurations embedded into the continuum of meson-nucleon scattering states, e.g.  (1232), N*(1440),  (1405)… 29

30. Visualizing Quantum Interference in Microscopic Systems: Asymmetric Fano-Line Shapes of Resonances 30

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

32. Fano-Resonances in Nuclei 32

33. Hamiltonian and Wave function The coupled equations (core nucleus integrated out): Multi-channel Fano wave function: 33

34. 34 Extension to Several Open Channels n=2 open channels n=2 energetically degenerate solutions with outgoing flux

35. 35 Solution 1: fully mixed Solution 2: continuum mixed  Resonance superimposed on a smoothly varying background! „Dark States“

36. 36 Multi-channel Coupling

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

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

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

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

41. Summary Dynamics at the particle threshold Pairing at the dripline/in the continuum Nuclear polarizabilities Fano resonances in atomic nuclei Tools for continuum spectroscopy Universality of quantum interference …with contributions by Sonja Orrigo (Valencia) and Xu Cao (Giessen/Lanzhou) 41