Many-body correlations in the structure of heavy nuclei
Recent developments on relativistic models
Elena Litvinova
Western Michigan University
Interfacing Structure and Reaction Dynamics, Trento, September 1-4,
Outline
• Nuclear field theory in relativistic framework (10 yrs):
Quantum Hadrodynamics and emergent collective phenomena
• Approach: Covariant Density Functional Theory
+ beyond mean-field correlations (Nuclear Field Theory);
non-perturbative techniques
Current developments:
1) pion degrees of freedom
2) high-order correlations in nuclear response
• Isovector excitations: Gamow-Teller resonance, spin dipole resonance,
higher multipoles.
Precritical phenomenon in exotic nuclei: soft pionic modes (0-,1+,2-,…)
• Pion exchange beyond Fock approximation:
‘Isovector’ phonons and their coupling to single-particle motion
• *Higher-order correlations in nuclear response: extensions of NFT
Building blocks of nuclear structure models
 Degrees of freedom
Separation of the scales
at ~1-50 MeV excitation energies:
single-particle & collective (vibrational, rotational)
NO complete separation of the scales!
-Coupling between single-particle and collective:
-Coupling to continuum
as nuclei are open quantum systems
 Symmetries -> Eqs. of motion
Galilean inv. -> Schrödinger Eq.
Lorentz inv. -> Dirac Eq.
 Interaction VNN : 3 basic concepts
Ab initio: from vacuum VNN -> in-medium VNN
Configuration interaction: matrix elements for
in-medium VNN
Density functional: an ansatz for in-medium VNN
+ correlations = Nuclear Field Theory
Here based on QHD

ρ
mπ ~140 MeV
mρ ~770 MeV
m ~783 MeV
Nuclear models
Figure from: G.F. Bertsch, J. Phys.: Conf. Ser. 78, 012005 (2007)
Relativistic nuclear field theory: CDFT + CI + ab initio
Systematic expansion in the covariant nuclear field theory
≈
Quantum Hadrodynamics
(„QCD motivated“)
Relativistic Mean Field (Walecka, Serot et al.)
Covariant DFT (P. Ring et al.)
Emergent collective degrees
of freedom: ‘phonons‘
New order parameter:
phonon coupling vertex
Finite size & angular
Momentum couplings =>
Hierarchy:
Mean field -> line corrections
-> vertex
corrections
Nuclear Field Theory
CopenhagenMilano,
St.PetersburgJuelich, …
Recent developments: relativistic formulation; pairing correlations; two-phonon coupling;
spin-isospin channel; high-order correlations
Covariant density functional theory
Walecka model
+ later modifications
(P. Ring et al.)
Lorentz
symmetry
Pion π:
No contribution
to RMF; included
in dynamics
nucleons
interaction
mesons
(as classical fields)
Relativistic mean field
Nucleons
{
Mesons
no sea
RHB
Hamiltonian
RMF
selfenergy
Dirac
Hamiltonian
Eigenstates
Uncorrelated ground state as the zero approximation:
Relativistic Mean Field (RMF)
Continuum
Fermi
sea
-S-V
0
r
FE
Dirac
sea
-S+V
2mN*
„No sea“ approximation
2mN
Small perturbation =>
Coherent oscillations of the mean nuclear potential
Continuum
Fermi
sea
-S-V
0
r
FE
…
Dirac
sea
Vibrational modes
(phonons Jπ)
-S+V
2mN*
2+
34+
56+
„No sea“ approximation
p
P‘
h
h‘
2mN
First step beyond relativistic mean field:
quasiparticles coupled to vibrations
Additional “potential”
= “self-energy” =
= “mass operator”
with energy dependence
k1
e
Σ =
Vibration
μ
k2
k
nucleon
coupling
“Fish” diagram
One-body propagator G: Dyson equation
k
k‘
G
p
h
Time arrow
=
k
=
k‘
+
G0 +
k
k1
e
Σ
G0 Ʃe
k2
k‘
G
Energy dependence
Pairing correlations:
Doubled quasiparticle space:
Fragmentation of states in odd and even systems (schematic)
Single-particle structure
No correlations
Correlations
Energy
Dominant level
Strong
fragmentation
Spectroscopic factors Sk(ν)
Response
No correlations
Correlations
Quasiparticle-vibration coupling:
Pairing correlations of the superfluid type + coupling to phonons
E.L., PRC 85, 021303(R) (2012)
Spectroscopic factors in
120Sn
(nlj) ν
Sth
Sexp
2d5/2
0.32
0.43
1g7/2
0.40
0.60
2d3/2
0.53
0.45
3s1/2
0.43
0.32
1h11/2
0.58
0.49
2f7/2
0.31
0.35
3p3/2
0.58
0.54
Spectroscopic factors in
E.L., PRC 85, 021303(R)(2012)
:
132Sn:
(nlj) ν
Sth *
Sexp **
2f7/2
0.89
0.86±0.16
3p3/2
0.91
0.92±0.18
1h9/2
0.88
3p1/2
0.91
1.1±0.3
2f5/2
0.89
1.1±0.2
*E. L., A.V. Afanasjev,
PRC 84, 014305 (2011)
**K.L. Jones et al.,
Nature 465, 454 (2010)
Nuclear shapes and Qα values at Z>90 (Skyrme SLy4)
S. Ćwiok, P.-H. Heenen, W. Nazarewicz, Nature 285 (2005) 705
RMF+QVC: Dominant neutron states in Z = 120
Interplay of pairing and particle-vibration coupling
Comparable
Spectroscopic
strengths
0.28
0.30
PC+QVC:
Formation of
the „shell
gap“ !
RMF+BCS
…+QVC
RMF+BCS
Delocalization of the shell closures
…+QVC
Shell evolution in superheavy Z = 120 isotopes:
Quasiparticle-vibration coupling (QVC) in a relativistic framework
1. Relativistic Mean Field: spherical minima
2. π: collapse of pairing, clear shell gap
3. ν: survival of pairing coexisting with the shell gap
4. Very soft nuclei: large amount of low-lying collective
vibrational modes (~100 phonons below 15 MeV)
Vibration corrections
to binding energy (RQRPA)
Vibration corrections
to -decay Q-values
Q [MeV]
13
RMF
RMF+QVC
Z = 120
12
11
296
298
300
302
304
A
Vibrational corrections:
1.
Impact on the shell gaps
2. Smearing out the shell
effects
Shell stabilization & vibration stabilization/destabilization (?)
E.L., PRC 85, 021303(R) (2012)
Vertex corrections, excited states: nuclear response function
QRPA
Extension
Bethe-Salpeter
Equation (BSE):
E.L., V. Tselyaev,
PRC 75, 054318 (2007)
=
:
δΣRMF
V =
δρ
R(ω) = A(ω) + A(ω) [V + W(ω)] R(ω)
Selfconsistency
W(ω) = Φ(ω) - Φ(0)
δ
i
δG
i
δ
δG
×
G
= i
=
δΣe
δG
=
=
Ue
δΣe
=i
δG
Consistency
on 2p2h-level
Time blocking
3p3h
Problem:
NpNh
‘Melting‘
diagrams
Approx.
schemes
Unphysical result:
negative
cross sections
Time
Solution:
Timeprojection
operator:
R
Partially
fixed
V.I. Tselyaev,
Yad. Fiz. 50,1252 (1989)
Allowed terms: 1p1h, 2p2h
Time blocking approximation =
= „one-fish“ approximation!
Blocked terms: 3p3h, 4p4h,…
Separation of the integrations in the BSE kernel
R has a simple-pole structure (spectral representation)
»» Strength function is positive definite!
Response function in the neutral channel
response
interaction
Subtraction
to avoid double
counting
Static:
RQRPA
Dynamic:
particlevibration
coupling
in time blocking
approximation
Dipole strength in neutron-rich nuclei
within Relativistic Quasiparticle Time Blocking Approximation (RQTBA)
Neutron-rich Sn
Test case: E1 (IVGDR) stable nuclei
S [e fm / MeV]
8
132
Sn
2
4
2
6
2
-
(a)
1
0
0
5
10
15
20
25
30
35
Experiment*
RQTBA**
RQTBA with
detector response
(A. Klimkiewicz)
S [e fm / MeV]
8
130
Sn
2
4
2
6
2
-
1
0
(b)
0
5
10
15
20
25
30
35
E [MeV]
E. L., P. Ring, and V. Tselyaev,
Phys. Rev. C 78, 014312
(2008)
* P. Adrich, A. Klimkiewicz, M. Fallot et al.,
PRL 95, 132501 (2005)
**E. L., P. Ring, V. Tselyaev, K. Langanke
PRC 79, 054312 (2009)
200
10
15
E [MeV]
20
25
0
10
E5 [MeV]
25
15
E [MeV]
30
20
25
5
10
15
20
E [MeV]
25
8
9
10
0
5
10
E
[MeV]
Pb
400
0.04
0
-1
200
500
0
5
10
15
5
6
7
8
9
10
0
10
15
20
10
15
15
10
0.02
20
5
10
15
Sn
600
400
0
0
3
4
5
6
7
8
9
10
0
5
10
E [MeV]
15
10
15
25
30
0.08
140
0.04
15
200
20
neutrons
protons
Sn
0.00
E = 4.65 MeV
(RQTBA)
-0.04
-0.08
0
0
20
25
15
30
20
25
5
10
15
20
25
30
E [MeV]
E [MeV]
20 0
5
20 0
5
10
15
5
10
15
E = 5.18 MeV
(RQTBA)
20 0
5
10
15
20
0.04
E = 7.27 MeV
(RQTBA)
E. L., H.P. Loens, K. Langanke, et al.
Nucl. Phys. A 823, 26 (2009).
5
20
E [MeV]
600
400
5
10
E
[MeV]
E = 6.39 MeV
(RQTBA)
-0.04
cross section [mb]
136
800
Th
200
Sn
E = 5.18 MeV
(RQTBA)
20 0
0
25
0.00
E [MeV]-0.02
30
1000
Sn
132
 = 3.1 MeV
10
25
RQRPA
RQTBA
200
5
20
1200
136
Bn
10
RH-RRPA
RH-RRPA-PC
0.04
0
5
1400
RQRPA
RQTBA
30
800
E = 4.65 MeV
(RQTBA)
-0.04
-0.08
0
4
400
0.00
 = 2.4 MeV
5
0
5
1800
neutrons
protons
2
1000
30
0
3
E = 10.94 MeV 208
20
(RQRPA) E1
Pb
2000
 = 2.6 MeV
Sn
Sn
200
(NL3)
40
RH-RRPA-PC
2400
138
600
400
50
2200
E0
Sn
Th
60
20
neutrons
RH-RRPA
protons
208
800
600
140
15
0.00
208
 =0.081.7 MeV
10
2600
30
-1
E0
600
1500
5
800
138
Bn
10
E = 7.18 MeV
(RQRPA)
-0.1
25
RQRPA
RQTBA
cross section [mb]
2
2
20
20
1000
40
30
15
1200
-1
5
20
7
1400
10
neutrons
protons
r [fm]
RH-RRPA
800
2
0
15
1000
0
2000
-1
200
0
10
8
E [MeV]
0
4
 = 3.1 MeV
200
5
6
1000
r  [fm ]
400
 = 2.4 MeV
200
3500
r  [fm ]
0
1200
0.02
0.00
-0.02
E = 6.39 MeV
(RQTBA)
-0.04
E = 7.27 MeV
(RQTBA)
20
0
5
10
15
20 0
5
20 0
5
10
15
20
0.02
-1
600
4
0.0
E1 -0.04 Pb
400
2
200
500
Sn
600
1400
Th
E [MeV]
2500
Sn
400
1000
1600
800
136
Bn
3 4 5 6 730008 9 10 0RH-RRPA-PC
5 10 15 20 25 30
132
 = 2.6 MeV
0
0.1
0
0.00
2
E0
600
6
2
0
800
Pb
5
RQRPA
RQTBA
r  [fm ]
10
4
50
2
20
3
60
10
r  [fm ]
15
0
20
RQRPA
RQTBA
0.04
WS-RPA (LM)
136 WS-RPA-PC
1800
1000
R [e fm /MeV] ISGMR
2
10
RH-RRPA
RH-RRPA-PC
800
208
 = 1.7 MeV
400
1500
2
2
 [mb]
600
2000
5
1800
5 10 15 20 25 30
1200
Sn
30
E = 10.94 MeV 208
20
(RQRPA) E1 Pb
2000
r [fm]
RH-RRPA
RH-RRPA-PC
800
E0
2500
4
R [e fm /MeV] ISGMR
3000
2
2200
1000
1000
S [ e fm / MeV ]
-1
r  [MeV ]
2400
Sn
30
1400
RQRPA
RQTBA
50
208
0
3500
3 4 5 6 7 8 9 10 0
60
20
0.00
E1 -0.04 Pb
0
neutrons
200
E = 8.46 MeV
(RQTBA)
-0.02
0
5
10
r [fm]
15
E = 9.94 MeV
(RQTBA)
10
r [fm]
15
0.02
-1
15
Sn
400
200
RH-RRPA
(NL3)
protons
40
RH-RRPA-PC
400
Th
0
RQRPA
RQTBA
0.00
2
10
Bn
Sn
600
20
10
140
800
Sn
r  [fm ]
5
2600
138
600
Th
cross2 section
[mb]
-1
r  [MeV ]
2
0
Sn
0
1000
140
30
Input for
r-process nucleosynthesis:
(n,γ) cross sections
and reaction rates
800
138
Bn
10
r  [fm ]
-1
r  [MeV ]
-0.1
0.04
WS-RPA (LM)
WS-RPA-PC
1200
20
E = 7.18 MeV
(RQRPA)
1800
1400
30
E1
40
140
S [ e fm / MeV ]
10
neutrons
protons
 [mb]
8
E [MeV]
2
6
0.0
RQRPA
RQTBA
1200
1000
40
2
4
S [ e fm / MeV ]
2
0
0.1
1600
RQRPA
RQTBA
50
10
2
5 10 15 20 25 30
1400
2
60
20
RQRPA
RQTBA
1200
40
50
0
3 4 5 6 7 8 9 10 0
30
2
400
Th
0
2
2
600
1400
RQRPA
RQTBA
50
S [ e fm / MeV ]
Bn
10
RQRPA
RQTBA
Sn
Sn
2
S [e fm / MeV]
40
140
140
800
Sn
S [ e fm / MeV ]
E1
2
S [ e fm / MeV ]
50
20
60
1000
140
30
RQRPA
RQTBA
1200
40
cross section [mb]
1400
RQRPA
RQTBA
50
cross section [mb]
60
cross section [mb]
2
-1
r  [MeV ]
2
2
S [e fm / MeV]
Response of superheavy nuclei:
From giant resonances‘ widths
to transport coefficients
E = 8.46 MeV
(RQTBA)
-0.02
E = 9.94 MeV
(RQTBA)
20
0
5
10
r [fm]
15
10
r [fm]
15
20
Isospin splitting of the pygmy dipole resonance in
J. Endres, E.L., D. Savran et al.,
PRL 105, 212503 (2010)
&
124Sn
E. Lanza, A. Vitturi, E.L., D. Savran,
PRC 89, 041601(R) (2014)
2q+phonon
IS-E1 RQRPA
2q
3-phonon
3-phonon
2q+phonon
Electromagnetic E1
2q+2phonon
configurations
Included
Recently:
E.L. PRC
91, 034332 (2015),
See below)
Spin-isospin response function
response
interaction
Static:
RRPA
Dynamic:
particlevibration
coupling
in time blocking
approximation
Subtraction
to avoid double
counting
Gamow-Teller Resonance with finite momentum transfer
pn-RRPA
pn-RTBA
GT-+IVSM
Fig. & calculation
from T. Marketin
(U Zagreb)
Isovector
Spin Monopole
Resonance
RRPA
RTBA
Finite q:
a correction for
Isovector spin monopole
resonance
(IVSMR) – overtone of GTR
ΔL = 0
ΔT = 1
ΔS = 1
„Microscopic“ quenching of B(GT):
(i) relativistic effects, ,
(ii)
(ii) ph+phonon configurations,
(iii) finite momentum transfer
Spin-dipole resonance: beta-decay, electron capture
T. Marketin, E.L., D. Vretenar, P. Ring,
PLB 706, 477 (2012).
SRRPA
RTBA
S+
W.H. Dickhoff et al., PRC 23, 1154 (1981)
J. Meyer-Ter-Vehn, Phys. Rep. 74, 323 (1981)
A.B. Migdal et al., Phys. Rep. 192, 179 (1990)
Existence of low-lying unnatural parity states
indicates that nuclei may be close to the pion
condensation point. However, it is not clear which
observables are sensitive to this phenomenon.
Only nuclear matter and doubly-magic nuclei were
studied
ΔL = 1
ΔT = 1
ΔS = 1
λ = 0,1,2
Neutron-rich nuclei: softening of the pion modes
Recently measured in RIKEN
RQRPA
RQTBA
2-
In some exotic nuclei
2- states are found at very low
energy.
Similar situation
with 0-, 4-, 6-,… states.
Precritical phenomenon:
Vicinity of the onset of pion condensation
2-
ΔL = 1
ΔT = 1
ΔS = 1
λ = 0,1,2
Isovector part of the interaction: diagrammatic expansion
IV interaction:
pion
ρ-meson
Free-space
pseudovector
coupling
RMFRenormalized
Landau-Migdal
contact term
(g’-term)
+
Fixed strength
Infinite sum:
…
…
Low-lying states in ΔT=1 channel and nucleonic self-energy
(N,Z)
(N+1,Z-1)
In spectra of neighboring odd-odd 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:
Nucleonic self-energy
beyond mean-field:
Forward
Backward
Underlying
Mechanism
for
pn-pairing?
Isoscalar
Isovector
Single-nucleon
Self-energy
Spin dipole resonance in
100Sn
and
RQRPA
RQTBA
• Low-lying states with high transition
probabilities in 132-Sn:
2-, 4-, 6-: collective!
• Strongly coupled to single-particle
and other collective states
• Generic for neutron-rich nuclei?
132Sn
ΔL = 1
ΔT = 1
ΔS = 1
λ = 0,1,2
Low-lying isovector states of unnatural parities: 100-Sn; pn-RRPA
r2τ+[σxY1]0
r2τ-[σxY1]0
0
rτ+[σxY1]2
-
2
r3τ+[σxY3]4
r3τ-[σxY3]4
4
rτ-[σxY1]2
r5τ+[σxY5]6
-
E [MeV]
-
r5τ-[σxY5]6
6
λp-λn ≈ 14 MeV
-
E [MeV]
Single-particle states in 100-Sn
Truncation scheme
Phonon basis: T=0 phonons: 2+, 3-, 4+, 5-, 6+
No backward going terms
T=1 phonons: 2±, 3±, 4±, 5±, 6±
Single-particle states in 132-Sn
Truncation scheme
Phonon basis: T=0 phonons: 2+, 3-, 4+, 5-, 6+
No backward going terms
T=1 phonons: 2±, 3±, 4±, 5±, 6±
Effects of ground state correlations -? TBD
Fine structure of spectra: next-order correlations
from “2q+phonon” to “2 phonons”
P. Schuck, Z. Phys. A 279, 31 (1976)
V.I. Tselyaev, PRC 75, 024306 (2007)
&
Mode Coupling Theory
Time Blocking
Replacement of the uncorrelated
propagator inside the Φ amplitude
by QRPA response
Nuclear response:
R = A + A (V + Φ – Φ0) R
Poles may appear at lower energies:
‘2q+phonon’ response:
Φiji’j’(ω) ~ Σμk αijkμ/(ω - Ei’- Ek - Ωμ)
‘2 phonon’ response:
Φiji’j’(ω) ~ Σμν αiji’j’/(ω - Ων - Ωμ)
Fine features of dipole spectra: two-phonon effects
First two-phonon state 1-1 : [2+ x 3-]
2 phonon
2q+phonon
E(1-1)
B(E1)
120Sn
Pygmy dipole resonance in neutron-rich Ni:
2q+phonon vs 2 phonon
S [arb. units]
Does not exist
2
1
0
E.L., P.Ring, V.Tselyaev, PRL 105, 02252 (2010)
PRC 88, 044320 (2013)
ddE [mb / MeV]
3
68Ni
1-
6
8 10
E [MeV]
12
3
2
1
0
3
70Ni
2
1-
6
1
8 10
E [MeV]
12
0
72Ni
1-
6
8 10
E [MeV]
12
Data: O. Wieland et al., PRL 102, 092502 (2009)
Multiphonon RQTBA: toward a unified description
of high-frequency oscillations and low-energy spectroscopy
Bethe-Salpeter Equation:
“Conventional” NFT:
Extension:
n-th order correlated propagtor:
E.L. PRC 91, 034332 (2015)
Convergence
E.L. PRC 91, 034332 (2015)
Amplitude Φ(ω) in a coupled form
(spherical basis):
Fragmentation:
n=1 (1p1h)
n=2 (2p2h)
n=3 (3p3h)
…
Conclusions
• Correlations beyond mean field are important for the structure of heavy nuclei
and the relativistic NFT offers a powerful framework for introducing them.
However, in its ‘standard’ formulation NFT is often not sufficient.
• Effects of isospin dynamics are introduced within a self-consistent covariant
framework. Pion exchange is included with a free-space coupling constant.
• Gamow-Teller resonance and other spin-isospin excitations are studied.
Considerable softening of the pion modes is found in (some) exotic 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 excited states of even-even nuclei
is expected (work in progress).
• Nuclear response theory is extended for multiphonon couplings toward a unified
description of high-frequency oscillations and low-energy spectroscopy.
Many thanks for collaboration:
Peter Ring (Technische Universität München)
Victor Tselyaev (St. Petersburg State University)
Tomislav Marketin (U Zagreb)
B.A. Brown (NSCL),
D.-L. Fang (NSCL)
R.G.T. Zegers (NSCL)
A. Afanasjev (MisSU)
D. Ackermann (GSI & GANIL)
E. Kolomeitsev (UMB Slovakia)
D. Savran (GSI/EMMI)
V. Zelevinsky (NSCL)
Nuclear theory group at Western
Graduate Students:
Postdoc:
Dr. Caroline Robin
Herlik Wibowo
Irina Egorova
Hasna Alali
This work was supported by NSCL @ Michigan State University
and by US-NSF Grants PHY-1204486 and PHY-1404343
Correlations
in the models based on the density functional:
NpNh: …
p
P‘
h
h‘
P‘
p
P‘
h‘ h
p
h
h‘
2p2h correlations:
p
P‘
p
P‘
p
P‘
h
h‘
h
h‘
h
h‘
1p1h correlations:
p
P‘
h
h‘
V=
δ2E[R]
δR2
Uncorrelated ground state: Density functional theory
E[R]
σ
(J,T)=(0+,0)
ω
(J,T)=(1-,0)
ρ
(J,T)=(1-,1)
(covariant: 7-9
parameters)
Self-consistent
Self-consistent
3p3h correlations: iterative scheme
Mechanism of the RSF formation at low
1. Saturation of RSF with Δ
at Δ = 10 keV for T>0
2. The low-energy RSF is not
a tail of the GDR and not a part of
PDR!
3. The nature of RSF at Eγ-> 0
is continuum transitions
from the thermally unblocked states
4. Spurious translation mode should be
eliminated exactly
Eγ
Low-energy limit of the RSF in even-even Mo isotopes
a = aEGSF => Tmin (RIPL-3)
Tmax
(microscopic)
Exp-1: NLD norm-1,
M. Guttormsen et al., PRC 71, 044307 (2005)
Exp-2: NLD norm-2,
S. Goriely et al., PRC 78, 064307 (2008)
Theory: E. Litvinova, N. Belov,
PRC 88, 031302(R)(2013)
Data: A.C. Larsen, S. Goriely, PRC 014318 (2010)
Low-energy limit of the RSF in
116,122Sn
No upbend?
Larger microscopic level density
parameter a
=> Lower upper limit for the
temperature at Sn
Other effects
(ideally, all to be combined in one approach)
At 3-4 MeV:
•2-phonon state (as above)
Above 4-5 MeV:
•Coupling to vibrations (as above),
•Thermal fluctuations:
M. Gallardo et al., NPA443, 415 (1985)
•More correct for γ-emission:
„final temperature“,
V. Plujko, NPA649, 209c (1999)
Theory: E. Litvinova, N. Belov,
PRC 88, 031302(R)(2013)
Data: H.K. Toft et al., PRC 81, 064311 (2010),
PRC 83, 044320 (2011)
Nucleons, mesons, phonons

Short range:
Mean-field approximation
ρ
mπ ~140 MeV, mρ ~770 MeV, m ~783 MeV
+ superfluidity!
Strong coupling:
non-perturbative techniques
Nucleon separation energies: ~1-10 MeV
Emergent collective phonons: ~1-10 MeV
Long range:
Time blocking
Single-quasiparticle Green‘s function
Doubled quasiparticle space:
Spectroscopic
factors
Energies
One-body Green’s function in N-body system (Lehmann):
Model
dependence
of S!
Excited state (N+1)
Ground state
(N)
Response to an external field: strength function
Nuclear Polarizability:
External
field
Strength function:
Transition density:
Response function:
Nuclear vibrational motion
Gamow-Teller
Monopole
L = 0
Dipole
L = 1
Quadrupole
L = 2
T = 0
S = 0
T = 1
S = 0
T = 0
S = 1
T = 1
S = 1
* M. N. Harakeh and A. van der Woude: Giant Resonances
Spin-orbit splittings: Tensor force or meson-nucleon dynamics?
A. Afanasjev and E. Litvinova, arXiv:14094855
Energy splittings between dominant states which are used to adjust
the mean-field tensor interaction. Here no tensor.
A conventional
description including
isoscalar phonons
is used in the
quasiparticle-vibration
coupling (QVC)
self-energy. The
discrepancies at larger
isospin asymmetries may
point out to the missing
isospin vibrations.
Pion dynamics is to be
included in the QVC
In progress.
Giant Dipole Resonance
within Relativistic Quasiparticle Time Blocking Approximation (RQTBA)*
ΔL = 1
ΔT = 1
ΔS = 0
1p1h
2p2h
*E. L., P. Ring, and V. Tselyaev,
Phys. Rev. C 78, 014312 (2008)
Covariant NFT for nuclear response (RQTBA)
E. Litvinova, P. Ring, V. Tselyaev, PRC 88, 044320 (2013).
PRL 105, 022502 (2010)
Giant resonances (here dipole)
PRC 78, 014312 (2008).
Perspectives: inclusion higher-order correlations
Description of low-energy spectroscopy:
From giant resonances‘ widths
to transport coefficients
J. Endres et al. PRL 105, 212503 (2010), PRC 85, 064331 (2012).
E. Lanza et al., PRC 89, 041601(R) (2014).
R. Massarczyk et al. PRC 86, 014319 (2012).
And other…
B. Ozel-Tashenov, PRC (2014).
Fragmentation of pygmy dipole resonanse
E. L., P. Ring, and V. Tselyaev, Phys. Rev. C 78, 014312 (2008)
Low-lying dipole strength in
Experiment*
Fine structure
116Sn
Gross structure
2+,3-,…
surface
vibrations
Integral
5-8 MeV:
ΣB(E1)↑ [e2 fm2]
QPM up to 3p3h
(V.Yu. Ponomarev)
* K. Govaert et al.,
PRC 57, 2229 (1998)
RQTBA 2p2h
RQRPA 1p1h vs
RQTBA 2p2h
Exp.
0.204(25)
QPM
0.216
RQTBA 0.27
RQTBA dipole transition densities in
68Ni
at 10.3 MeV
Theory:
-0.04000
Neutrons
Protons
-0.03000
-0.02000
-0.01000
E.L., P.Ring, V.Tselyaev,
PRL 105, 02252 (2010)
-0.005000
Experiment:
0.005000
25
0.01000
0,03
0.02000
15
neutrons
protons
0,02
0,01
10
r  [fm -1]
counts
20
2
5
0.03000
0,00
-0,01
= 10.6 MeV
E =E10.3
MeV
-0,02
0
5.0
7.5
10.0
12.5
Energy [MeV]
O.Wieland et al.,
PRL 102, 092502 (2009)
-0,03
Experiment:
Coulomb excitation
of 68Ni at 600 AMeV
-0,04
0
2
4
6
8
r [fm]
10
12
14
0.04000
RQTBA dipole transition densities in
68Ni
at 10.3 MeV
Theory: RQTBA-2
Neutrons
Protons
E.L., P.Ring, V.Tselyaev,
PRL 105, 02252 (2010)
Experiment:
25
0,03
neutrons
protons
0,02
2
r  [fm -1]
0,01
counts
20
15
10
0,00
5
-0,01
= 10.6 MeV
E = E10.3
MeV
-0,02
0
5.0
-0,03
-0,04
0
2
4
6
8
r [fm]
10
12
14
7.5
10.0
12.5
Energy [MeV]
O.Wieland et al.,
PRL 102, 092502 (2009)
Dipole strength in Sn isotopes
E.L. et al, PRC 79, 054312 (2009)
6
7
8
9 10 11 5
10
15
20
25
2
400
200
5
6
7
8
10
15
20
25
800
10
114
114
Sn
8
Sn
600
6
2
400
4
200
2
0
5
6
7
8
9 10 11 5
10
15
20
25
30
15
20
25
cross section [mb]
30
RQRPA
RQTBA
Sn
15
120
Sn
600
400
10
200
5
0
5
6
7
8
9
10 5
10
15
20
25
30
1200
RQRPA
RQTBA
30
RQRPA
RQTBA
1000
800
25
130
130
Sn
20
Sn
600
15
400
10
200
5
0
0
4
120
35
2
12
RQRPA
RQTBA
10
800
40
1000
10 5
1000
2
RQRPA
RQTBA
9
40
30
1200
14
8
RQRPA
RQTBA
4
S [ e fm / MeV ]
16
9 10 11 5
7
0
0
4
6
1200
2
Sn
Sn
0
5
2
106
Sn
0
200
45
S [ e fm / MeV ]
1200
1
2
4
cross section [mb]
RQRPA
RQTBA
2
106
400
50
1400
116
600
4
30
1600
RQRPA
RQTBA
Sn
0
0
5
800
116
20
cross section [mb]
200
22
RQRPA
RQTBA
1000
cross section [mb]
400
3
2
Sn
cross section [mb]
2
1
4
S [ e fm / MeV ]
100
600
RQRPA
RQTBA
2
Sn
2
100
1200
24
S [ e fm / MeV ]
800
0
2
RRPA
RTBA
1000
2
2
S [ e fm / MeV ]
RRPA
RTBA
S [ e fm / MeV ]
26
1200
cross section [mb]
3
0
4
5
6
7
8
E [MeV]
9
10 5
10
15
20
E [MeV]
25
30
Dipole
strength
Sn isotopes
Dipole
strength
in Sninisotopes
E.L. et al, PRC 79, 054312 (2009)
134
Sn
600
15
Bn
10
Exp
Bn
400
Th
5
200
0
0
3
4
5
6
7
8
9 10 0
Sn
400
10
5
200
0
0
5
6
Bn
40
8 Th 9 10 0
Bn
30
5
1200
130
130
800
Sn
20
Sn
600
2
15
400
10
200
5
0
0
3
4 5 6
E [MeV]
7
Bn
Exp
8
9 10 0
Bn
5
6
7
8
RQRPA
RQTBA
10 15 20 25 30
10 15 20 25 30
RQRPA
RQTBA
1000
800
138
30
Sn
20
Bn
138
Sn
600
400
Th
200
0
3
4
5
6
7
8
9 10 0
5
10 15 20 25 30
1400
RQRPA
RQTBA
50
RQRPA
RQTBA
1200
1000
40
136
10
Sn
600
20
Bn
136
800
Sn
30
400
Th
200
0
5
5
1200
40
10
9 10 0
1400
60
RQRPA
RQTBA
1000
25
0
4
0
10 15 20 25 30
1400
RQRPA
RQTBA
35
2
7
Exp
2
4
2
3
S [ e fm / MeV ]
Sn
S [ e fm / MeV ]
15
132
600
2
800
132
20
200
50
2
1000
25
cross section [mb]
2
2
S [ e fm / MeV ]
30
400
Th
60
RQRPA
RQTBA
1200
S [ e fm / MeV ]
RQRPA
RQTBA
Sn
600
20
Bn
140
800
Sn
3
1400
35
140
30
0
10 15 20 25 30
cross section [mb]
40
5
1000
40
10
RQRPA
RQTBA
1200
0
3
4
5
6
7
8
9 10 0
5
10 15 20 25 30
Th
E [MeV]
cross section [mb]
Sn
20
RQRPA
RQTBA
cross section [mb]
800
2
134
1400
50
2
1000
25
2
2
S [ e fm / MeV ]
30
60
RQRPA
RQTBA
1200
S [ e fm / MeV ]
RQRPA
RQTBA
35
E [MeV]
E [MeV]
cross section [mb]
1400
cross section [mb]
40
Spin-isospin response: Gamow-Teller Resonance in 28-Si
„Proton-neutron“ relativistic time blocking approximation (pn-RTBA): ρ, π, phonons
0,7
r
SGT [MeV -1]
0,6
0,5
GT_
0,4
14
Fermi sea
contribution
12
10
5
28
Si
GT_
0,3
3
0,2
2
0,1
1
0,0
0
-1800 -1600 -1400 -1200 -1000 5
Ikeda Sum rule
(model independent):
28
Si
4pn-RRPA
pn-RTBA
ΔL = 0
ΔT = 1
ΔS = 1
10 15 20 25 30 35 40
E [MeV]
E [MeV]
12
10
S- - S+ = 3(N – Z),
S± = ∑ B(GT ±)
„Microscopic“ quenching of B(GT):
(i) relativistic effects, ,
(ii) ph+phonon configurations,
28
GT_
8
B(GT)
0
Dirac sea
contribution
6
Si
pn-RRPA
pn-RTBA
(Ewin = 90 MeV)
70%
4
100%
2
0
10
20
30
40
50
60
70
80
90
(?)
28Si:
N=Z
ΔL = 0
ΔT = 1
ΔS = 1
?
?
Problem: finite basis
Low-lying dipole strength in 136-Ba
R. Massarczyk, R. Schwengner, F. Doenau, E. Litvinova, G. Rusev et al.,
Phys. Rev. C 86, 014319 (2012)
RQTBA systematics for PDR:
A proper definition of Pygmy Dipole Resonance is important!
PDR = all states with the “isoscalar” underlying structure!
8
6
2
120Sn
4
α = (N – Z)/A
(Asymmetry parameter)
132Sn
Mean energies
18
100Sn
78Ni
68Ni
0
0,00
0,02
Sn
16
14
0,04

0,06
0,08
2
 132Sn: 1h11/2 (n)
68Ni  78Ni: 1g9/2 (n)
120Sn
Intruder orbits !
E.L. et al. PRC 79, 054312 (2009)
E [MeV]
2
Strength vs α2
140Sn
Z = 50 (Sn)
Z = 28 (Ni)
Z = 82 (Pb)
2
B(E1) [e fm ]
10
<E>GDR
12
<E>PDR
10
8
6
115
120
125
130
A
135
140
GTR in 78-Ni: G-matrix+QRPA, RRPA and RTBA
Beta-decay window
ΔL = 0
ΔT = 1
ΔS = 1
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)
2
2
S [ e fm / MeV ]
Outlook
1400
RQRPA
RQTBA
50
RQRPA
RQTBA
1200
cross section [mb]
60
1000
40
140
Bn
Sn
600
20
10
140
800
Sn
30
400
Th
200
50
E1
S [e fm / MeV]
40
140
0
RQRPA
RQTBA
Sn
0
3
30
4
5
6
7
8
9 10 0
7
8
9 10 0
10 15 20 25 30
5
10 15 20 25 30
1400
2
60
5
8
2
0
5
1800
10
2
15
0.00
E0
600
5
6
15
20
RQRPA
RQTBA
1200
1000
136
136
800
Sn
30
Bn
10
Sn
600
400
Th
200
0
0
3
4
5
6
7
8
9 10 0
5
10 15 20 25 30
E [MeV]
132
Sn
Nuclear matter,
Neutron stars, …
Applications
1400
RQRPA
RQTBA
2
2
 [mb]
10
r [fm]
800
Pb
 = 1.7 MeV
E [MeV]
600
 = 2.6 MeV
0.08
400
1500
140
400
0.04
200
20
25
30
5
10
15
20
25
30
10
E5 [MeV]
15
20
25
E [MeV]
E [MeV]
E = 4.65 MeV
(RQTBA)
5
10
15
E = 5.18 MeV
(RQTBA)
20 0
5
20 0
5
20 0
5
10
15
20
0.04
-1
15
0
2
25
0.02
0.00
-0.02
E = 6.39 MeV
(RQTBA)
-0.04
0
5
10
15
E = 7.27 MeV
(RQTBA)
10
15
20
0.02
-1
10
20
0.00
2
15
E [MeV]
r  [fm ]
10
-0.08
0
0
5
5
r  [fm ]
0
0
neutrons
protons
0.00
-0.04
200
500
Sn
-1
 = 3.1 MeV
 = 2.4 MeV
2
200
1000
r  [fm ]
400
4
2
5
1800
RH-RRPA
RH-RRPA-PC
800
208
600
0
E = 10.94 MeV 208
20
(RQRPA) E1
Pb
2000
0
RH-RRPA
RH-RRPA-PC
800
E0
2
2200
208
E1 -0.04 Pb
1000
1000
Sn
400
4
60
20
138
600
Th
200
3
(NL3)
40
RH-RRPA-PC
2400
-1
r  [MeV ]
1400
1200
2500
2000
Bn
0
neutrons
RH-RRPA
protons
0.04
WS-RPA (LM)
WS-RPA-PC
1600
3500
3000
Sn
20
10
50
2600
RQRPA
RQTBA
800
138
30
E = 7.18 MeV
(RQRPA)
S [ e fm / MeV ]
-1
r  [MeV ]
neutrons
protons
1200
1000
40
10
E [MeV]
2
6
cross section [mb]
S [ e fm / MeV ]
4
0.0
cross section [mb]
2
50
0
R [e fm /MeV] ISGMR
Consistent input
for r-process
nucleosynthesis
RQRPA
RQTBA
20
10
0.1
-0.1
E = 8.46 MeV
(RQTBA)
-0.02
0
5
10
r [fm]
15
E = 9.94 MeV
(RQTBA)
10
15
20
r [fm]
Timedependent
CEDFT ???
3p3h excitations: iterative PVC
p
P‘
p
P‘
h‘
h
h
h‘
p
P‘
h‘
h
2p2h excitations: Particle-Vibration Coupling
p
p
P‘ p
P‘
h
h‘
h‘
h
h
1p1h excitations: RQRPA
p
SelfP‘
consistency
h
h‘
P‘
h‘
δ2E[R]
V=
δR2
Ground state: Covariant EDFT
DD-MEδ CEDFT:
Ab initio Brückner +
4 adjustable parameters
PRC 84, 054309 (2011)
σ
ω
ρ
Toward „ab initio“
E[R]
Data => Constraints
from RIB facilities
Data => Constraints
from RIB facilities
np-nh
Generalized
CEDFT ???
Pion
dynamics