1

Bound States Embedded in the Continuum

in

Nuclear and Hadronic Systems

H. Lenske

Institut für Theoretische Physik, U. Giessen

and

GSI Darmstadt

2

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)

5Science 340,716 (2013)

Manipulating Quantum Interference by Laser-Modelling of

Fano-Line Shapes

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Fano-Resonances in Nuclei

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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*

10

, ,*

,

| |1| | | | sin cot

| |E E c cE E

TM T T

V T

22

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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Populating the Continuum in Nuclear Physics

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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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BIC at the Neutron Dripline

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Pairing Theory as Coupled Channels Problem: The Gorkov-Equations

jmsrvjmsru qj

qj )(|)(~ ; )(|)(~ )()(

EH

H

)(

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Pairing in the Continuum

S. Orrigo, H.L., PLB 677 (2009)

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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)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

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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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Fano-Resonances in Hadrons:Charmonium Spectroscopy

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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