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
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
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!
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
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.
Response function in the neutral channel
response
interaction
Subtraction to avoid double counting
Static: RQRPA
Dynamic: particle- vibration coupling in time blocking approximation
Spin-isospin response function
response
interaction Subtraction to avoid double counting
Dynamic: particle- vibration coupling in time blocking approximation
Static: RRPA
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
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 ±) (?)
ΔL = 0 ΔT = 1 ΔS = 1
28Si: N=Z
? ?
Problem: finite basis
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
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+
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-
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:
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
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
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
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
E.L. PRC 91, 034332 (2015)
Multiphonon RQTBA: toward a unified description of high-frequency oscillations and low-energy spectroscopy
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:
…
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).
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)
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
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