Spectroscopy at the Particle Threshold
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Transcript of Spectroscopy at the Particle Threshold
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Spectroscopy at the Particle Threshold
H. Lenske
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Agenda:
• Pairing in the continuum• Nuclear Polarizability and Spectral Functions• Continuum spectroscopy and Fano-Resonances• Summary
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Pairing in the Continuum:Quasiparticle Resonances
Extended HFB Theory as Coupled Channels Problem: The Gorkov-
Equations
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(q) 2q n j
n j
Mean-Field Hamiltonian (q p,n):
H U( )2m2j 1 (r) | v (r) |4
jn
qjn
qjnq
qSEq
rvrujr
V
)()(
412)(
:n)p,(qDensity & Field-Pairing
*)()(
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jmsrvjmsru qj
qj )(|)(~ ; )(|)(~ )()(
EH
H)(
Spectrum of the Gorkov Equation:
Extended HFB Theory: Pairing Self-Energies
• Energy Shifts and Widths• Spectral Functions for particles and holes
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Pairing in Infinite Nuclear Matter
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3
0
3(1 ( ))(
( ) ( , ) u(q;k ) v(q;k ) ~ N(k ) (k , k ) ( ) I ,2
1 ( ) N(k ) (k , k ) I ,( )
( ) ~ e ( ) eF
F SE F F F F SE F F F F
F F SE F F FF
G kG k
F F F
d qk V k q V k k
G k V kG k
k k
)F
Free Space SE (S=0,T=1) Interaction:(Bonn-B Potential)
Pairing is a LOW DENSITY Phenomenon
Pairing in Infinite Nuclear Matter
Pairing Gap Anomal Density
Pairing Correlations in Nuclear Matter
Pairing Gap and Anomal Density in Symmetric Nuclear Matter
Pairing-Field in a Nucleus
RA RA
Neutron Spectrum :
11Li : Continuum HFB Spectral Functions
Dissolution of Shell Structures!
g.s. Densities
g.s. Densities r2 :
2)( |),(|4
12)( revdejrq
qj
jq
jmsrvnpqfor qj
q )(|)(:, )()(
11Li : Continuum HFB g.s.
Densities
Neutron Spectral Functions in 9Li(3/2-): Continuum Admixtures into
the g.s.
Continuum Admixtures!
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Pairing in the Continuum
S. Orrigo, H.L., PLB 677 (2009)
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Pairing Resonances in Dripline Nuclei 9Li+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., REX-ISOLDE Collaboration, 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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New experimental results (Dec. 2013): 10Li continuum spectroscopy at TRIUMF
S. Orrigo, M. Cavallo, F. Capppuzzello et al.
1 3 3 5,2 2 2 2
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Spectral Structures by Dynamical Polarization
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(kF) a(w, p) dw
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Nuclear Dynamics…
cJ
Eth [MeV] Eexp [MeV]
2+ 3.220 3.368
1- 6.423 5.960
0+ 6.513 6.179
2- 6.446 6.263
3- 7.372 7.371
4- (9.270)
1+ 7.122
3+ 7.159
0- 7.374
QRPA Response in 10Be
DCP Neutron Spectral Distributions in 11Be
[0+ × 1/2+]: 0.79[2+ × 5/2+]: 0.18
[0+ × 1/2-]: 0.58[2+ × 3/2-]: 0.28
Spectral Distributions in Carbon Isotopes …normalized to sum rule
E1 Dipole E2 Quadrupole
Polarizability of C-Isotopes:HFB+QRPA results
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1
0
( ) 0
( ) ( )
nn aS E a T
SPS
Multipole polarizabilties coefficients by sum rules:
Longitudinal Momentum Distributions: 17,19C → 16,18C + n
Carbon Target, Elab 900 AMeV•Binding: Correlation Dynamics•17C(5/2+,g.s.)• Sn(the.)=715keV
• C2S(g.s.) = 0.41G(the.): 132 MeV/cG(exp.): 143 ± 5 MeV/cs(-1n,the.): 124 mbs(-1n,exp.): 129± 22 mb
•Binding: Correlation Dynamics•19C(1/2+,g.s.)• Sn(the.)=263keV
• C2S(g.s.) = 0.40G(the.): 69 MeV/cG(exp.): 68 ± 3 MeV/cs(-1n,the.): 192 mbs(-1n,exp.): 233± 51 mb
17C
19C
Hole Spectru
m
Particle Spectru
m
Dynamical Core Polarization:• HFB g.s.:
„3-body renormalized“ G-Matrix
• ph-Interactions:Fermi Liquid Theory
Fano Resonances
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Interactions of Closed and Open Channels:
Fano Resonances
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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
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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), Y‘‘(3770)…
• Baryons: Confined qqq-configurations embedded into the continuum of meson-nucleon scattering states, e.g. (1232), N*(1440), L(1405)…
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Visualizing Quantum Interference in Microscopic Systems:
Asymmetric Fano-Line Shapes of Resonances ( ) (c)d
E i i k ki k
a d b Y
Historically:The famous Silverman-Lassettre data
He(e,e‘)He*(1P) @ 500eV
Note: q must be negative – q=-1.84
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Fano-Resonances in Nuclei
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11 13
22 23
31 32 33
00
b
s
x
H VH H V
V V H
13 '
23 '
' ' 31 32 '
' 0 s.p. motion w.r.t. the g.s.
' 0
( E ) ' ' ' ' 0C
bn n J j c
c
sj J j c
c
j J j c nn
z n V j c z
z n V j c z
z j c V n z d j c V z
Hamiltonian and Wave function
The coupled equations (core nucleus integrated out):
Multi-channel Fano wave function:
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Extension to Several Open Channels
• n=2 open channels• n=2 energetically degenerate solutions with
outgoing flux
2 21 2 ; E E i
i
V W G G G G
( )arctan( )
( ')( ) ''
EE E G E
P EG E dEE E
G
G
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1 21 1 ' 1 '
1 z( , ') sin ( ') cos'
sin ; ( , ') ; c ( , ')E E
PE E E EE E
a b z E E z E E
G G
G G G
1 22 2 ' 2 '0 ; ( ') ; c ( ')E Ea b E E E E G G
G G
Solution 1: fully mixed
Solution 2: continuum mixed
Resonance superimposed on a smoothly varying background!
„Dark States“
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Multi-channel Coupling
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Resonance Scenarios in Nuclear Physics
The Fano-Wave Function:
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, ,*
,
| |1| | | | sin cot| |E E
E E
TM T T
V T
Y
2 2
2
,
2
,*
| cot |= ~1 cot
| | q=
| |
1 ~ | |
s
E
sE
E
q M
TT
TV
s s
s
Reaction Matrix Elements and Formation Cross Section
The (single channel) Fano-Formula:
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Correlation Dynamics in an Open Quantum System: d-wave Fano-Resonances in 15C
G~60…140keV
Sonja Orrigo, H.L., Phys.Lett. B633 (2006)
Xu Cao, H. L., PRL, submitted
DD-Dynamics at Threshold Channel Coupling and the Line Shape of Y(3770)
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0 0D D threshold 3729.7 MeV
D D threshold 3739.2 MeV
3.65
(2s / 3686)
X(3900) ??
q=-2.1±0.6
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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)