Low-energy dipole response: the plot thickens?

—— Advances in Nuclear Many-Body Theory, Primosten, Croatia, June 2011 ——

Panagiota Papakonstantinou

Institute of Nuclear Physics, T.U.Darmstadt, Germany

Herzlichen Gluckwunsch!

1

Electric dipole strength vs. collectivity

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 2

Energy/MeV

Strength

5 10 15

?

E1 strength below / around threshold

There tends to be more of it in neutron-rich isotopes

... though the variation with N is not always monotonic!

Microscopic models predict the existence of a neutron-skin mode

... though that alone cannot explain the observed systematics

Incoherent concentration of strength is still possible

2

Case studies and moral stories

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 3

Isoscalar-dipole response of N=Z nuclei

• On “isospin-forbidden” E1 transitions

Isoscalar vs electromagnetic response

• along Ca isotopes, etc

Dipole collectivity atlow energies does notrequire a neutron (or

proton...) skin

E1 strength is notnecessarily a good absolutemeasure of collectivity (i.e.,

the coherence of avibrational state)

3

Isoscalar vs Eλ strength

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 4

Consider perfectly isoscalar mode of multipolarity λ > 1:

δρp(r) = δρn(r) =1

2[δρp(r) + δρn(r)] =

1

2δρIS(r)

Isoscalar strength: ∫δρIS(r)r

λ+2dr

Eλ strength: ∫δρp(r)r

λ+2dr =1

2

∫δρIS(r)r

λ+2dr

A large/small B(Eλ) value implies large/small isoscalar strength too

4

Isoscalar vs E1 strength

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 5

Consider perfectly isoscalar mode of multipolarity λ = 1:

δρp(r) = δρn(r) =1

2[δρp(r) + δρn(r)] =

1

2δρIS(r)

Isoscalar strength: ∫δρIS(r)r

5dr

E1 strength vanishes:∫

δρp(r)r3dr =

1

2

∫δρIS(r)r

3dr = 0

due to translational invariance,

but the transition is no less collective for this reason, in the IS channel

5

Pygmy Dipole Strength in Ca isotopes

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 6

J.Chambers et al., PRC50(1994)R2671

2 4 6 8 10Ex [MeV]

0

10

20 48Ca

0

10

20

B(E1)[10-3 e2 fm2 ]

44Ca

0

10

20 40Ca

T.Hartmann et al., PRL93(2004)192501

40Ca

44Ca

48Ca

0.0

0.2

0.4

0.6

0.8

E1

-EW

SR

(%)

QRPA

ETFFS

Experiment

6

Dipole response of Ca isotopes with Skyrme

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 7

Terasaki&Engel, PRC74

SGII

7

Pygmy Dipole Strength in Ca isotopes

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 8

Gogny D1S UCOM(SRG)S,δ3N

0

2

4

6

40Ca

dB(E1)/dE [e2fm2/MeV]

0

2

4

6

40Ca

0

2

4

6

44Ca

0

2

4

6

44Ca

0

2

4

6

0 10 20 30 40 50

E [MeV]

48Ca

0

2

4

6

0 10 20 30 40 50

E [MeV]

48Ca48Ca

8

Pygmy Dipole Strength in Ca isotopes

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 9

Gogny D1S UCOM(SRG)S,δ3N

0

500

1000

1500

2000

2500

3000

3500

0

2

4

6

40Ca

BISD [fm6], left axis dB(E1)/dE [e2fm2/MeV], right axis

0

500

1000

1500

2000

2500

3000

3500

0

2

4

6

40Ca

0

500

1000

1500

2000

2500

3000

3500

0

2

4

6

44Ca

0

500

1000

1500

2000

2500

3000

3500

0

2

4

6

44Ca

0

500

1000

1500

2000

2500

3000

3500

0 10 20 30 40 50

0

2

4

6

E [MeV]

48Ca

0

500

1000

1500

2000

2500

3000

3500

0 10 20 30 40 50

0

2

4

6

E [MeV]

48Ca

9

A collective dipole excitation hidden in the attic

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 10

“Isospin-forbidden” E1 transitions explained

N=Z nuclei undergo collective, isoscalar 1~ω dipole transitions.

E1 strength: isospin mixing

PP,Ponomarev,Roth,Wambach, Eur.Phys.J.A47(2011)14

2 4 6 8 10Ex [MeV]

0

10

20 48Ca

0

10

20

B(E1)[10-3 e2 fm2 ]

44Ca

0

10

20 40Ca

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 2 4 6 8r2 δ

ρ [fm

-1]

r [fm]

16Oprotons

Gogny D1SUCOM(SRG)S,δ3N

Brink-Boeker B1experiment

Prediction: up to 100Sn10−4 of the TRK...

T.Hartmann et al., PRL93(2004)192501

(γ, γ′)

...but 4% of the isoscalar EWSR!

T.Poelhakken et al., PLB278(1992)423

10

Electroexcitation form factor

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 11

0 0.1 0.2 0.3 0.4

q2 (fm

-2)

10-4

10-3

10-2

[dσ/

dΩ /

dσ/d

ΩM

ott]1/

2

D1SUCOM(SRG)S,δ3N

exp. dens.

0 0.1 0.2 0.3 0.4 0.5

9.8 MeVno Coul.eff. charges35 MeV

0 0.1 0.2 0.3 0.4

D1SUCOM(SRG)S,δ3N

exp. data

D1S

(e,e’), θ = 90o

(a) 16

O (b) 40

Ca (c) 40

Ca

minimum at low qreproduced!

11

Reality check

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 12

What models predict a strong IS-LED mode?

()Valence shell model

()Valence RPA

()QPM

Almost self-consistent CRPA (Skyrme)

Self-consistent RPA with finite-range forces

“Self-consistent” Second RPA

Self-consistent Vlasov equations

()ETFFS

()Self-consistent RPA with Skyrme interactions

?? Self-consistent Relativistic RPA

-nothing in the literature-

V.Yu.Ponomarev, priv. comm.

PP et al., 2011

PP

M.Urban, priv.comm.

Tertychny et al., 2006

Terasaki&Engel, 2006

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0

2 0

4 0

6 0

8 0

1 0 01

3 6C a

3 8C a

4 0C a

0

0 . 5

1

1 . 5

2

4 2C a

0

2 0

4 0

6 0

8 0

1 0 0

4 4C a

4 6C a

4 8C a

0

0 . 5

1

1 . 5

2

5 0C a

0

1 0 0

2 0 0

3 0 0

5 2C a

5 4C a

5 6C a

0

0 . 5

1

1 . 5

2

5 8C a

0

1 0 0

2 0 0

3 0 0

SIS (e2fm6/MeV)

6 0C a

6 2C a

6 4C a

0

0 . 5

1

1 . 5

2

SIV (e2fm2/MeV)

6 6C a

0

1 0 0

2 0 0

3 0 0

E ( M e V )

6 8C a

1 0 2 0 3 0 4 0

7 0C a

0 1 0 2 0 3 0 4 0

7 2C a

x 0 . 1

0 1 0 2 0 3 0 4 0 5 0

0

0 . 5

1

1 . 5

2

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x 0 . 1

0

1 0 0

2 0 0

3 0 0

0 1 0 2 0 3 0 4 0 5 0

7 6C a

x 0 . 1

E(MeV)0 40

12

Low-Energy Isoscalar Dipole Strength

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 13

(α, α′γ)

Harakeh and van der Woude, ”Giant Resonances”

4% – 14% ISD EWSR at low energies!

T.Poelhakken et al., PLB278(1992)423

M.Harakeh et al., PLB62 (1976)155

Isospin-forbiddenE1 transitions in

N=Z nuclei

13

Dipole response of N=Z nuclei

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 14

0

50

100

150

200

Gogny D1S UCOM(SRG)S,δ3N

16O

BISD [fm6], left axis

dB(E1)/dE [e2fm2/MeV], right axis

0

0.4

0.8

1.2

1.616O

0

500

1000

1500 40Ca

0

2

4

640Ca

0

1000

2000

3000

400056Ni

0

2

4

6

856Ni

0

4000

8000

12000

0 10 20 30 40 50

E [MeV]

100Sn

0 10 20 30 40 50 0

4

8

12100Sn

Strong ISD state atlow energy with

very little E1strength!

14

IS-LED vs compression mode

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 2 4 6 8 10

r2 δρ [f

m-1

]

r [fm]

40CaD1S

9.82 MeV

0 2 4 6 8 10

r [fm]

35.0 MeV

protonsneutrons

9.82 MeV35.0 MeV

Transition density:node @ surface

... but no compression

??

from Bastrukov et al., PLB664(2008)

15

Pygmy Dipole Strength in Ca isotopes

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 16

J.Chambers et al., PRC50(1994)R2671

T.Hartmann et al., PRL93(2004)192501

40Ca

44Ca

48Ca

0.0

0.2

0.4

0.6

0.8

E1

-EW

SR

(%)

QRPA

ETFFS

Experiment

16

Pygmy Dipole Strength in Ca isotopes

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 17

Gogny D1S UCOM(SRG)S,δ3N

0

2

4

6

40Ca

dB(E1)/dE [e2fm2/MeV]

0

2

4

6

40Ca

0

2

4

6

44Ca

0

2

4

6

44Ca

0

2

4

6

0 10 20 30 40 50

E [MeV]

48Ca

0

2

4

6

0 10 20 30 40 50

E [MeV]

48Ca48Ca

17

Pygmy Dipole Strength in Ca isotopes

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 18

Gogny D1S UCOM(SRG)S,δ3N

0

500

1000

1500

2000

2500

3000

3500

0

2

4

6

40Ca

BISD [fm6], left axis dB(E1)/dE [e2fm2/MeV], right axis

0

500

1000

1500

2000

2500

3000

3500

0

2

4

6

40Ca

0

500

1000

1500

2000

2500

3000

3500

0

2

4

6

44Ca

0

500

1000

1500

2000

2500

3000

3500

0

2

4

6

44Ca

0

500

1000

1500

2000

2500

3000

3500

0 10 20 30 40 50

0

2

4

6

E [MeV]

48Ca

0

500

1000

1500

2000

2500

3000

3500

0 10 20 30 40 50

0

2

4

6

E [MeV]

48Ca

18

Transition densities in 40Ca, 48Ca

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 19

-0.2

-0.1

0

0.1

0.2

0 2 4 6 8 10

δρ (

r) r

2 40Ca

Gogny D1S

protonsneutrons

-0.2

-0.1

0

0.1

0.2

0 2 4 6 8 10

40Ca

UCOM(SRG)S,δ3N

-0.2

-0.1

0

0.1

0.2

0 2 4 6 8 10

δρ (

r) r

2

r [fm]

48Ca

-0.2

-0.1

0

0.1

0.2

0 2 4 6 8 10

r [fm]

48Ca48Ca

19

Electroexcitation in 48Ca?

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 20

0 0.1 0.2 0.3 0.4 0.5

q2 (fm

-2)

10-4

10-3

10-2

10-1[d

σ/dΩ

/ dσ

/dΩ

Mot

t]1/2

gognyav18

0 0.1 0.2 0.3 0.4 0.510-4

10-3

10-2

10-1

40Ca(e,e’), θ=90

o 48Ca(e,e’), θ=90

o

Excitation of low-lying 1- state in (e,e’) reaction

20

Summary

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 21

Low-energy dipole response

• Revisiting isospin-“forbidden” transitions: Dipole collectivity does not re-quire a neutron or proton skin

• A predominantly “isoscalar” vibrational mode can acquire increased E1strength simply as a consequence of neutron-proton asymmetry, but doesnot necessarily become more coherent

Increased E1 strength (e.g., along an isotopic chain) may indicate astructural change for a coherent mode, but not necessarily enhancedcoherence

The low-energy collective state in Ca isotopes:

• Two very different predictions were presented for 48Ca: IS-LED-type andneutron-skin type

• An IS probe could locate it; electron scattering could distinguish between thetwo types of vibration ... and tell us which models are wrong!

• Other similar cases may exist among stable nuclei...

...

are there two different

modes, maybe?

See also: M.Urban, arXiv:1103.0861

21

Stay tuned!

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 22

Many thanks to ...

R. Roth and the TNP++ group, V.Yu.Ponomarev, J.Wambach, P. vonNeumann-Cosel, ... (Institut fur Kernphysik, TU Darmstadt, Ger-many), A. Richter, (TUD,ECT*), H.Hergert (MSU) ...

Thank you!

22

IS-LED : energy and strength

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 23

6

8

10

12

14

16

18

20

20 40 60 80 100

E(1

- 1) [M

eV]

A

(a)

41 A-1/3Brink-Boeker B1

UCOMvar

SRGS,δ3N

UCOM(SRG)S,δ3N

Gogny D1Sexperiment

0 2 4 6 8

10 12 14

% IS

D E

WS

R (b)

0.0001

0.001

0.01

0.1

1

B(E

1) [e

2 fm2 ] (c)

0.001

0.01

0.1

1

20 40 60 80 100

% T

RK

A

(d)

23

Transition density

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 24

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 2 4 6 8

r2 δρ

[fm-1

]

r [fm]

16Oprotons

Gogny D1SUCOM(SRG)S,δ3N

Brink-Boeker B1experiment

Experimental transitiondensity with node

reproduced!

exp: MIT Bates; Buti et al, PRC33(1986)755

24

Transition density

Primosten, Croatia, June 9, 2011 - P.Ring’s Fest – 25

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 2 4 6 8 10

r2 δρ [f

m-1

]

r [fm]

100Sn

Gogny D1S

9.67 MeV

0 2 4 6 8 10

r [fm]

100Sn

UCOM(SRG)S,δ3N

10.67 MeV

0 2 4 6 8 10

r [fm]

40Ca

UCOM(SRG)S,δ3N

11.50 MeV

protonsneutrons

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 2 4 6 8 10

r2 δρ [f

m-1

]

r [fm]

40CaD1S

9.82 MeV

0 2 4 6 8 10

r [fm]

35.0 MeV

protonsneutrons

E1 strength solely due toCoulomb interaction

role of symmetry energy?

25