1. Bound States Embedded in the Continuum in Nuclear and Hadronic Systems H. Lenske Institut für Theoretische Physik, U. Giessen and GSI Darmstadt 1

2. Agenda: Interference in open quantum systems Continuum spectroscopy in nuclei Charmonium line shapes Universality of the Fano-mechanism Summary 2

3. Formation of Line Shapes by Quantum Interference 3 closed channel |1) is embedded into a continuum of open channels |k) |1) decays by interactions with the „simple“ scattering states |k) Bound State Embedded into the Continuum – BSEC

4. Historically: The famous Silverman-Lassettre data He(e,e‘)He*( 1 P) @ 500eV Measured : 1959@Ohio State U., published: S. M. Silverman, E. N. Lassettre, J. Chem. Phys. 40 (1964) 1265. 4 Fano-Resonance: Defining features:  r <<E r ; line shape parameter q (above: q=-1.84) O. K. Rice, J. Chem. Phys. 1, 375 (1933), U. Fano, Phys. Rev. 24,1866 (1961)

5. Science 340,716 (2013) Manipulating Quantum Interference by Laser-Modelling of Fano-Line Shapes 5

6. Fano-Resonances in Nuclei 6

7. 7 Introducing Bound States Embedded in the Continuum BSEC into nuclear physics: n.b.: BSEC  BIC in Atomic/Laser/Molecular Physics

8. Hamiltonian and Wave Function The wave function: 8

9. BSEC excitation by an external probe 9 …e.g. by scattering of a real or a virtual photon on an atom or a nucleus: A*

10. Reaction Matrix Elements and Production Cross Section The Fano-Cross Section Formula: 10

11. Populating the Continuum in Nuclear Physics 11

12. The Nucleus as an Open Quantum System: Fano-Resonances in 15 C  ~60…140keV (!) 12 Sonja Orrigo, H.L., Phys.Lett. B633 (2006) Relevant core states:

13. BIC at the Neutron Dripline 13

14. Pairing Theory as Coupled Channels Problem: The Gorkov-Equations 14

15. Pairing in the Continuum S. Orrigo, H.L., PLB 677 (2009) 15

16. Pairing Resonances in Dripline Nuclei 9 Li+n 10 Li S. Orrigo, H.L., PLB 677 (2009) & ISOLDE Newsletter Spring 2010, p.5 16

17. Continuum Spectroscopy at REX-ISOLDE: 10 Li= 9 Li+n d( 9 Li, 10 Li)p@2.36AMeV Data: H. Jeppesen et al., NPA 738 (2004) 511 & NPA 748 (2005) 374. S. Orrigo, H.L., PLB 677 (2009) & ISOLDE newsletter Spring 2010, p.5 17

18. 18 10 Li(3/2 - ) 10 Li(1/2 - ) 10 Li(5/2+) Continuum Spectroscopy and Core Polarization in 10 Li: Fano Resonances at the Threshold Sonja Orrigo, H.L., 2015

19. 19 New experimental results: High Resolution 10 Li continuum spectroscopy at TRIUMF S. Orrigo, M. Cavallo, F. Cappuzzello et al.

20. Fano-Resonances in Hadrons: Charmonium Spectroscopy 20

21. Confined cc-States: Charmonium Spectrum in the Quark Model J. Lopez, H.L., 2014 21 Unified description of D-mesons and Charmonium Spectra, wave functions, form factors…

22. Xu Cao, H. L., arXiv:1410.1375, and to be published DD-Dynamics at Threshold Channel Coupling and the Line Shape of  3 D 1 (3770) 22 3.65 X(3900) ?? q=-2.1 ±0.6

23. Line Shape of Reaction Form Factor and Physics Content q=-0.2q=-1q=-10 Dominance of hadronic production balanced quarkonic and hadronic production Dominance of quarkonic production Line shape controlled by quarkonic content Line shape depends on production reaction Spectral distribution of the SAME final state depend on initial state 23

24. Production of  ‘‘ (3770) and the DD Spectral Distributions Dependence on Exit Channel (Data: BES Collaboration) Derived Parameters: 24 Xu Cao, H.L., 2015

25. 25 Exploratory Study: Charmonium Production in Antiproton-Proton Annihilation R. Shyam, H.L., Phys. Rev. D 90 (2014) 014017, and to be published

26. Summary Dynamics close to the particle threshold Fano resonances in atoms and moleculs Fano resonances in nuclei: continuum dynamics@driplines Fano resonances in hadrons: charmonium spectroscopy Universality and physics content of line shape dynamics …credits to Xu Cao, Juan Lopez, Sonja Orrigo, and Radhey Shyam 26