bound states embedded in the continuum in nuclear and hadronic systems h. lenske institut für...
TRANSCRIPT
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Bound States Embedded in the Continuum
in
Nuclear and Hadronic Systems
H. Lenske
Institut für Theoretische Physik, U. Giessen
and
GSI Darmstadt
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Agenda:
• Interference in open quantum systems
• Continuum spectroscopy in nuclei
• Charmonium line shapes
• Universality of the Fano-mechanism
• Summary
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Formation of Line Shapes by Quantum Interference
• 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
Historically: The famous Silverman-Lassettre data He(e,e‘)He*(1P) @ 500eV
Measured : 1959@Ohio State U., published: S. M. Silverman , E. N. Lassettre, J. Chem. Phys. 40 (1964) 1265.
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Fano-Resonance: Defining features: Gr<<Er; line shape parameter q (above: q=-1.84)
O. K. Rice, J. Chem. Phys. 1, 375 (1933), U. Fano, Phys. Rev. 24,1866 (1961)
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Introducing Bound States Embedded in the Continuum
BSECinto nuclear physics:
n.b.: BSEC BIC in Atomic/Laser/Molecular Physics
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Hamiltonian and Wave Function
The wave function:
0ccc cs
sc ss s
H E VH E
V H E
'
( , ) ( , )C SJ J
J JJ c c s s
c j J s jJ
z E d z E
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BSEC excitation by an external probe
…e.g. by scattering of a real or a virtual photon on an atom or a nucleus:
'
* ( , ) ( , )C SJ J
J JJ c c s s
c j J s jJ
A z E d z E
*eA A NB
A* A*
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, ,*
,
| |1| | | | sin cot
| |E E c cE E
TM T T
V T
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2
,
2
,*
| cot |= ~
1 cot
| | ( )q= ; cot
( ) / 2| |
1 ~ | |
s c
c
Rc
E
sE
E
qM
T m E E
ET
TV
Reaction Matrix Elements and Production Cross Section
The Fano-Cross Section Formula:
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The Nucleus as an Open Quantum System: Fano-Resonances in 15C
G~60…140keV (!)
Sonja Orrigo, H.L.,
Phys.Lett. B633 (2006)
Relevant core states:
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Pairing Theory as Coupled Channels Problem: The Gorkov-Equations
jmsrvjmsru qj
qj )(|)(~ ; )(|)(~ )()(
EH
H
)(
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Pairing Resonances in Dripline Nuclei9Li+n 10Li
S. Orrigo, H.L., PLB 677 (2009) & ISOLDE Newsletter Spring 2010, p.5
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Continuum Spectroscopy at REX-ISOLDE: 10Li=9Li+n d(9Li,10Li)[email protected]
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
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10Li(3/2-) 10Li(1/2-)
10Li(5/2+)
Continuum Spectroscopy and Core Polarization in 10Li:Fano Resonances at the Threshold
Sonja Orrigo, H.L., 2015
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New experimental results: High Resolution 10Li continuum spectroscopy at
TRIUMF
S. Orrigo, M. Cavallo, F. Cappuzzello et al.
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Confined cc-States: Charmonium Spectrum in the Quark Model
0
4( ) ( , )
3Breit s
hyperfineV r V r V rr
J. Lopez, H.L., 2014
• Unified description of D-mesons and Charmonium• Spectra, wave functions, form factors…
Xu Cao, H. L., arXiv:1410.1375, and to be published
DD-Dynamics at Threshold Channel Coupling and the Line Shape of Y3D1
(3770)
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0 0D D threshold
3729.7 MeV
D D threshold
3739.2 MeV
3.65
312 S(3686)
X(3900) ??
q=-2.1±0.6
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Line Shape of Reaction Form Factor and Physics Content
cc
DD
| T | Quarkonic hard q= ~ ~ e e , pp ,...
| T | Hadronic soft
q=-0.2 q=-1 q=-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
cc
cc
cc
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Production of y‘‘(3770) and the DD Spectral DistributionsDependence on Exit Channel
(Data: BES Collaboration)
Derived Parameters:
Xu Cao, H.L., 2015
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Exploratory Study:Charmonium Production in Antiproton-Proton Annihilation
R. Shyam, H.L., Phys. Rev. D 90 (2014) 014017, and to be published
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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