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