the impact of isospin dynamics on nuclear strength...
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![Page 1: The impact of isospin dynamics on nuclear strength functionstid.uio.no/workshop2015/talks/Oslo2015_Litvinova.pdfConclusions • Effects of isospin dynamics are studied within self-consistent](https://reader036.vdocuments.mx/reader036/viewer/2022070207/60f7ff6632931a46bd397b9d/html5/thumbnails/1.jpg)
Elena Litvinova
The impact of isospin dynamics on nuclear strength
functions
Western Michigan University
5th Workshop on Nuclear Level Density and Gamma Strength, Oslo, May 18 - 22, 2015
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Outline
• Nuclear field theory in relativistic framework: Quantum Hadrodynamics and emergent phenomena
• Approach: Covariant Density Functional Theory + correlations (quantum field theory); non-perturbative treatment Current developments: pion degrees of freedom
• Isovector excitations: Gamow-Teller resonance, spin dipole resonance, higher multipoles. Precritical phenomenon in neutron-rich nuclei. Quest for pion condensation revisited.
• Pion exchange beyond Fock approximation
• ‘Isovector’ phonons and their coupling to single-particle motion
• *Higher-order correlations in nuclear response
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ρ
ω
Emerging collective phonons: ~1-10 MeV
Nucleon separation energies: ~1-10 MeV
mπ ~140 MeV, mρ ~770 MeV, mω ~783 MeV
Strong coupling: non-perturbative techniques
Short range: Mean-field approximation
Long range: Time blocking
Covariant nuclear field theory: Nucleons, mesons, phonons
+ superfluidity!
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Systematic expansion in the covariant nuclear field theory
New order parameter: phonon coupling vertex
Finite size & angular Momentum couplings => Hierarchy: Mean field -> line corrections -> vertex corrections
Emergent collective degrees of freedom: phonons
QHD
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Quasiparticle-vibration coupling: Pairing correlations of the superfluid type + coupling to phonons
Sexp Sth (nlj) ν
0.54 0.58 3p3/2
0.35 0.31 2f7/2
0.49 0.58 1h11/2
0.32 0.43 3s1/2
0.45 0.53 2d3/2
0.60 0.40 1g7/2
0.43 0.32 2d5/2
Spectroscopic factors in 120Sn: E.L., PRC 85, 021303(R) (2012):
A. Afanasjev and E. Litvinova, arXiv:14094855 Spin-orbit splittings: Tensor force or meson-nucleon dynamics? Energy splittings between dominant states which are used to adjust the mean-field tensor interaction. Here no tensor. Good agreement in the middle of the shell The discrepancies at large isospin asymmetries may point out to the missing isospin vibrations.
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Response function in the neutral channel
response
interaction
Subtraction to avoid double counting
Static: RQRPA
Dynamic: particle- vibration coupling in time blocking approximation
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Spin-isospin response function
response
interaction Subtraction to avoid double counting
Dynamic: particle- vibration coupling in time blocking approximation
Static: RRPA
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Gamow-Teller Resonance with finite momentum transfer
Fig. & calculation from T. Marketin (U Zagreb)
ΔL = 0 ΔT = 1 ΔS = 1
Finite q: a correction for Isovector spin monopole resonance (IVSMR) – overtone of GTR
pn-RRPA pn-RTBA
GT-+IVSM
„Microscopic“ quenching of B(GT): (i) relativistic effects, , (ii) (ii) ph+phonon configurations, (iii) finite momentum transfer
Isovector Spin Monopole
Resonance RRPA RTBA
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Spin-isospin response: Gamow-Teller Resonance in 28-Si
„Proton-neutron“ relativistic time blocking approximation (pn-RTBA): ρ, π, phonons
ΔL = 0 ΔT = 1 ΔS = 1
r 0
-‐1800 -‐1600 -‐1400 -‐1200 -‐10000,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7F ermi s eacontribution
SGT [M
eV -‐1]
E [MeV ]
D ira c s eacontribution
5 10 15 20 25 30 35 400
1
2
3
4
510
12
14
G T _
28S i
E [MeV ]
pn-‐R R P A pn-‐R T B A
G T _
28S i
„Microscopic“ quenching of B(GT): (i) relativistic effects, , (ii) ph+phonon configurations,
10 20 30 40 50 60 70 80 900
2
4
6
8
10
12
Σ B(G
T)
ω [MeV ]
pn-‐R R P A pn-‐R T B A
(E win = 90 MeV )
28S iG T _
70% 100%
Ikeda Sum rule (model independent):
S- - S+ = 3(N – Z),
S± = ∑ B(GT ±) (?)
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ΔL = 0 ΔT = 1 ΔS = 1
28Si: N=Z
? ?
Problem: finite basis
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GTR in 78-Ni: G-matrix+QRPA, RRPA and RTBA
G-matrix+QRPA based on Skyrme DFT with m* = 1 (D.-L. Fang & A. Fässler & B.A. Brown) RTBA: Relativistic RPA + phonon coupling (T. Marketin & E.L.) E.L., B.A. Brown, D.-L. Fang, T. Marketin, R.G.T. Zegers, PLB 730, 307 (2014)
ΔL = 0 ΔT = 1 ΔS = 1
Beta-decay window
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Spin-dipole resonance: beta-decay, electron capture
ΔL = 1 ΔT = 1 λ = 0,1,2 ΔS = 1
T. Marketin, E.L., D. Vretenar, P. Ring, PLB 706, 477 (2012).
RQRPA
RQTBA
Sum rule:
Skin thickness:
S-
S+
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ΔL = 1 ΔT = 1 λ = 0,1,2 ΔS = 1
RQRPA
RQTBA
Recently measures in RIKEN
Neutron-rich nuclei: softening of the pion mode
2- states are found at very low energy. In some nuclei – similar situation with 0- states. Precritical phenomenon?
2-
2-
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Isovector part of the interaction: diagrammatic expansion
+
ρ-meson pion
Landau-Migdal contact term (g’-term)
IV interaction:
Free-space pseudovector coupling
RMF- Renormalized
Fixed strength
Infinite sum:
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Low-lying states in ΔT=1 channel and nucleonic self-energy
In spectra of medium-mass nuclei we see low-lying collective states with natural and unnatural parities: 2+, 2-, 3+, 3-,… Their contribution to the nucleonic self-energy is expected to affect single-particle states:
(N,Z) (N+1,Z-1)
Forward
Backward
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Single-particle states in 56-Ni (preliminary)
57Ni
55Ni
57Cu
55Co
Truncation scheme Phonon basis: T=0 phonons: 2+, 3-, 4+, 5-, 6+ T=1 phonons: 2±, 3±, 4±, 5±, 6±
Approximation: No backward going terms
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Single-particle states in 208-Pb (preliminary)
Truncation scheme Phonon basis: T=0 phonons: 2+, 3-, 4+, 5-, 6+ T=1 phonons: 2±, 3±, 4±
Approximation: No backward going terms
209Bi
207Tl
209Pb
207Pb
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Fragmentation of states in odd and even systems (schematic)
Spectroscopic factors Sk(ν)
Ener
gy
Dominant level
Single-particle structure
No correlations Correlations
Response
No correlations Correlations
Strong fragmentation
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E.L. PRC 91, 034332 (2015)
Multiphonon RQTBA: toward a unified description of high-frequency oscillations and low-energy spectroscopy
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E.L. PRC 91, 034332 (2015)
Convergence
Amplitude Φ(ω) in a coupled form (spherical basis):
n=1 (1p1h)
n=2 (2p2h)
n=3 (3p3h)
Fragmentation:
…
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Conclusions
• Effects of isospin dynamics are studied within self-consistent covariant framework. Pion exchange is included with a free-space coupling constant. Thereby, ab-initio component in introduced in the approach.
• Gamow-Teller resonance and other spin-isospin excitations are studied. Considerable softening of the pion mode is found in (some) neutron-rich nuclei.
• Pion exchange is included into the nucleonic self-energy non-perturbatively beyond Fock approximation in the spirit of quasiparticle-phonon coupling model.
• The effects of the corresponding new terms in the self-energy on single-particle states (excited states of odd-even nuclei) are found noticeable.
• The influence of the ‘isovector’ phonons on strength functions is expected (work in progress).
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Many thanks for collaboration:
Peter Ring (Technische Universität München) Victor Tselyaev (St. Petersburg State University) Tomislav Marketin (U Zagreb) A.V Afanasjev (MisSU) B.A. Brown (NSCL), D.-L. Fang (NSCL) R.G.T. Zegers (NSCL) Vladimir Zelevinsky (NSCL) Eugeny Kolomeitsev (UMB Slovakia)
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Nuclear theory group at Western
Dr. Caroline Robin
Postdoc: Graduate Students:
Irina Egorova Herlik Wibowo
This work was supported by NSCL @ Michigan State University and by US-NSF Grants PHY-1204486 and PHY-1404343
Hasna Alali
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Ground state: Covariant EDFT
E[R] σ ω ρ
p h
P‘ h‘
V = δ2E[R] δR2
Self- consistency
1p1h excitations: RQRPA
2p2h excitations: Particle-Vibration Coupling P‘ h‘
p h
P‘ h‘
p p h
P‘ h‘
3p3h excitations: iterative PVC
h
p
h P‘ h‘
p h
P‘ h‘
p h
P‘ h‘
np-nh
Outlook
DD-MEδ CEDFT: Ab initio Brückner +
4 adjustable parameters PRC 84, 054309 (2011)
Toward „ab initio“
Time- dependent CEDFT ???
Generalized CEDFT ???
Dat
a =>
Con
stra
ints
fr
om R
IB f
acili
ties
Data => Constraints
from RIB facilities
Applications 3 4 5 6 7 8 9 10
0
10
20
30
40
50
60
BnTh
140Sn
S [ e
2 fm 2 /
MeV
]
RQRPA RQTBA
0 5 10 15 20 25 300
200
400
600
800
1000
1200
1400
140Sn
RQRPA RQTBA
3 4 5 6 7 8 9 100
10
20
30
40
50
60
BnTh
138Sn
RQRPA RQTBA
S [ e
2 fm 2 /
MeV
]
0 5 10 15 20 25 300
200
400
600
800
1000
1200
1400
138Sn
cros
s se
ction
[mb]
cros
s se
ction
[mb]
cros
s se
ction
[mb]
RQRPA RQTBA
3 4 5 6 7 8 9 100
10
20
30
40
50
60
BnTh
RQRPA RQTBA
136Sn
S [ e
2 fm 2 /
MeV
]
E [MeV]0 5 10 15 20 25 30
0
200
400
600
800
1000
1200
1400
136Sn
E [MeV]
RQRPA RQTBA
5 10 15 20 25 300
200
400
600
800
1000
1200
1400
1600
1800 WS-RPA (LM) WS-RPA-PC
E1 208Pb
σ [m
b]
E [MeV]
5 10 15 20 25 300
200
400
600
800
1800
2000
2200
2400
2600
E1208Pb
RH-RRPA (NL3) RH-RRPA-PC
E [MeV]5 10 15 20 250
500
1000
1500
2000
2500
3000
3500
Γ = 2.4 MeV
Γ = 1.7 MeV
RH-RRPA RH-RRPA-PC
E0 208Pb
R [e
2 fm4 /M
eV] I
SGM
R
E [MeV]5 10 15 20 25
0
200
400
600
800
1000
Γ = 3.1 MeV
Γ = 2.6 MeV
E0 132Sn
RH-RRPA RH-RRPA-PC
E [MeV]
0 5 10 15 20
-0.04
0.00
0.04
E = 10.94 MeV (RQRPA)
neutrons protons
r 2 ρ [M
eV -1
]
r [fm]
0 5 10 15 20
-0.1
0.0
0.1
E = 7.18 MeV (RQRPA)r 2 ρ
[MeV
-1]
neutrons protons
4 6 8 100
10
20
30
40
50
E1 140Sn
S [e
2 fm 2 /
MeV
]
E [MeV]
RQRPA RQTBA
0 5 10 15 20-0.08
-0.04
0.00
0.04
0.08
140Sn
r2 ρ [f
m-1]
E = 4.65 MeV (RQTBA)
0 5 10 15 20
E = 5.18 MeV (RQTBA)
neutrons protons
0 5 10 15 20
-0.04
-0.02
0.00
0.02
0.04
E = 6.39 MeV (RQTBA)
r2 ρ [f
m-1]
0 5 10 15 20
E = 7.27 MeV (RQTBA)
0 5 10 15 20
-0.02
0.00
0.02
E = 8.46 MeV (RQTBA)
r2 ρ [f
m-1]
r [fm]0 5 10 15 20
E = 9.94 MeV (RQTBA)
r [fm]
Consistent input for r-process
nucleosynthesis
Nuclear matter, Neutron stars, …
Pion dynamics