PYGMY DIPOLE RESONANCE IN A SCHEMATIC MODEL

PYGMY DIPOLE RESONANCE IN A SCHEMATIC MODEL

Andreea CroitoruUniversity of Bucharest

ROMANIA

Braşov 2014

Virgil Băran• University of Bucharest, Romania

Daniel Dumitru• University of Bucharest, Romania

Maria Colonna• Laboratori Nazionali del Sud, Catania, Italy

Massimo de Torro• Laboratori Nazionali del Sud, Catania, Italy

Virgil Băran• University of Bucharest, Romania

For further information please see Prof. Virgil Băran’s presentation on Thursday

What…?

• GDR• PDR

Why…?

How…?

• Brink’s model• Beyond Brink’s

model

How good…?• Testing

predictions

What…?

• GDR• PDR

Why…?

How…?


model


predictions

Collective motions in nuclei

GDR

A Van der Wounde - "Electric and magnetic giant resonances in nuclei", pg 99

Giant Dipole Resonance in Nuclear Systems

])[(

4)(

22222

22

EEE

E

A

NZ

mc

eE

GDRabs

Photoreaction cross-section for Au (A=197)

MeVAEGDR3

1

80

protonsneutrons

R. A. Broglia , P. F. Bortignon, A. Bracco - Prog. Part. Nucl. Phys. (1992) 28,517

413. (1950) 5 h.Naturforsc Z. Jensen, J. ,Steinwedel A.

1046. (1948) 74 Rev. Phys.Teller, E.Goldhaber, M.

Macroscopic pictures for the Giant Dipole Resonance

What happens below 10 MeV?

Andreas Zilgres - "The Pygmy Dipole Resonance-history and overview"

What…?

• GDR• PDR

Why…?

How…?


model


predictions

Motivation • Information about the shapes of nuclei and excited states

• Information about the symmetry energy and EOS

• Influence in nucleosynthesis processes

• Relation with the neutron skin thickness

What…?

• GDR• PDR

Why…?

How…?


model


predictions

A schematic model for GDR

,221 1

22

A

i

A

ii

iSM r

K

m

pH

DCMpnSM HHHHH int_int_

N

ji

N

iiji

ji rrK

Nm

pp

1, 1,

22

)(22

1

2

)(

2

1

Z

ji

Z

iiji

ji rrK

Zm

pp

1, 1,

22

)(22

1

2

)(

2

1

22

22

1CMCM R

KAP

mA

22

22X

A

KNZP

mNZ

A

For

We can split

G-T macroscopic picture for GDR

therefore int int (R ) (X)n p CM

Proton sphere

Neutron sphere

pR

nR

XA

NZD

moment dipole The

np RRX


pnX

,22

1 2202 X

MP

MH D

DD

3/13/10 8040 AExperimentMeVA

PROBLEMThe GDR described by

has

…but there is a problem

A

i

A

ii

iSM r

m

m

pH

1 1

220

2

22

Beyond Brink

22

20

2

2

)(

2

1X

Mm

MP

MH

DD

DD

1?

2D D

2 1/3 1/30 2

79.27 80DM A MeV Experiment Am

What if

We still can separate


2 3

2 20

0

5(b )

: (b ) 32 , 1.2 ,

940MeV

sym potD

sym pot

M Am mr

with MeV r fm

m

Where the coupling parameter is related to the (potential) symmetry energy

PROBLEM

SOLVED

From a “Giant” to a “Pygmy”

A

i

A

ii

iSM r

m

m

pH

1 1

220

2

22

, ,c e cN N N N Z

_ int _ int _ intc en n p CM c yH H H H H H

Considering three subsystems: neutron core,proton core, neutron in excess

we can still separate

into

But there are two problems…

A schematic model for PDR

xc

Y

2 220

2 2c c

c cc

P MH X

M

Core Hamiltonian:

2 20 2

2 2y y

yy

P MH Y

M

Pygmy Hamiltonian:

…first problem

PROBLEM

EPDR <10MeV

EGDR >15MeV

0 Both modes have energy !

…and second problem

PROBLEM

Experiment

~ 0.04

Dc

ey NA

ZN

Overestimation of exp. data for Nc=Z!

Better…

But Ne=?

Dc

ey NA

ZN

Solving the overestimation of EWSR: Vlasov approach

5

33 3/2 2

0 0

5

3

54 ( )

3

n

p

R

e n n p np

R

N d r R R

obtained using Vlasov approach.

V. Baran et al, PRC (2013)

V. Baran et al

88, 044610

2012 85, 05160PRC 1 R

A

i

A

ii

iSM r

m

m

pH

1 1

220

2

22

,resV

?2

1

2

13

22

21 ycycres DDDDV

But what if

with

~ ; 1231

Solving the energy problem: Generalization of D-D residual

interaction

c c c ec y c

c

Z N Z ND D D X Y

A A

YCXYM

M

PX

M

M

PH cy

y

y

ycc

c

c

ccollective 222

0

2222

0

2

)(22

)(22

Core neutrons and protons sphere

Excess neutrons

Neutron sphere

Proton sphere

Core neutron sphere

Coupled modes

cX

pc nc

Yncpc,

22

21

3ycycMMC

The quest for normal modes

2 21 1

2 22 2

( ( ) )

( ( ) X )

yc

cc

MX R X Y

CM

X R YC

BEHOLD :YCXY

M

M

PX

M

M

PH cy

y

y

ycc

c

c

ccollective 222

0

2222

0

2

)(22

)(22

22

22

2

222

121

1

21

2222X

M

M

PX

M

M

PH collective

122

221

22

22

21

23222

2220

2,

2,

20

22,1

)))((1(

4)(2

1

2

C

MMR yc

ycycyc

yc

A

ZNmM

A

ZNmM

ey

c

cc

What…?

• GDR• PDR

Why…?

How…?


model


predictions

12

321res

2.0 ; 62

1

2

1V

e

ycyycc

N

DDDDDD

Ni68

AGREEMENT WITH EGDR_exp=17.1 MeV, EPDR_exp=9.55 MeV (Rossi et al PRL(2013)242503)AGREEMENT WITH f2_exp=0.028 (Rossi et al PRL(2013)242503)

PREDICTS TWO NORMAL MODESX1: Xc and Y in phaseX2: Xc and Y out of phase

22

21

3ycycMMC

cX

pc nc

Yncpc,

n

ne

Y

cX

Y

cX

1X

nncpc

ne

2Xn ncpc

ne

phase ofout Yand XC phase in Yand XC

The structure of the normal modes from Vlasov simulation (see V. Băran)

So…

• The EWSR exhausted by the pygmy mode overestimates the experimental data if Nc=Z

• But…For a more accurate picture we need microscopic self-consistent models

• A better result is obtained for a more stable core Nc>Z

• The HOSM+Vres is a useful tool in offering a microscopic description of the PDR and the GDR (centroid energy, sum rule) and a picture of nucleon vibrations in the PDR

Thank you !

CRITICAL QUESTIONS

A

ii

A

i

iSM r

K

m

pH

1

2

1

2

22

MODELSHELL OSCILLATOR HARMONIC

N

iin

Z

iip r

NRr

ZR

11

1;

1

CM Neutrons and Protons

NZCMnpCM PPPRNRZA

R

;1

N

iiN

Z

iiZ pPpP

11

;;

momenta Neutrons and Protons

NZnp P

NP

ZA

NZPRRX

11;

freedom of degrees Collective

MomentaConjugate and sCoordinate CollectiveNew

eccecc

cecc

cccc

Ne

NZc

ceynp

cc

cn

cc

c

NZnc

ne

pnp

Nc

Zcc

cccnpc

PN

PPAA

ANPRR

ZN

ZR

ZN

NY

PN

PZA

NZPR

N

NR

N

NRRRX

PN

PZA

ZNPRRX

1)(

1;

11;

11;

xc

Y

excess in neutrons

ofCM theand core ofCM thebetween distance theY

neutrons core

and protons core ofCM thebetween distance the

CX

excess in neutrons ofnumber theN

neutrons core ofnumber theN

e

c

freedom of degrees Collective

ycec

cc

cc DDYA

NZX

A

ZNX

A

NZD

DyDc

cey

c

ceyyy

ysmyi

yiyy

fNA

ZN

A

NZ

mc

e

NA

ZNDHD

c

e

DHDc

eDiE

c

edEE

20,,0

2

0,,02

140

4)(

2222

222

22

0

%1512

%5.193268

132

ye

ye

fNiN

fSnN

%5.55

%51068

132

ye

ye

fNiN

fSnN

1482 (1982) 49 PRL Bertsch,G.F. Gai, M.Alhassid, Y.

Molecular sum-rule for Pygmy Dipole Resonance

Applying the Thomas-Reiche-Kuhn sum rule 1

224m

c

eD

we obtain Dc

ey NA

ZN

XA

NZD 0|]],[,[|0

2

1,,,1 ySMyy DHDmwith and

A schematic model for PDR

A GENERALIZATION OF THE DIPOLE-DIPOLE RESIDUAL INTERACTION

ycyycc DDDDDD

321res 2

1

2

1V

ationdiagonaliza perform

modes two theof coupling the:an Hamiltoni theofpart collective The

~ ; 1231

energysymmetry theof dependenceDensity

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PYGMY DIPOLE RESONANCE IN A SCHEMATIC MODEL