Rabindranath Tagor C. V. Raman - Rikenseminar/RIBF-NPseminar/NP... · Rabindranath Tagor C. V....

26-Mar-14 RIKEN Nishina Center for Acceletor based Science 1

Rabindranath Tagor C. V. Raman

26-Mar-14 RIKEN Nishina Center for Acceletor based Science

2

Bijay K. Agrawal Saha Institute of Nuclear Physics

Kolkata, India


Outline of talk

Introduction /Motivation Nuclear energy density functional Probes for nuclear symmetry energy Results Conclusions


ZNZNI

AIAsJJAZca/AsaAvaB

...2)3/1(3/1232

Giant resonances Neutron rich nuclei Neutron drip line


Neutron star internal structure

13 21

411

2222 rc

M

Mccr

Μ GPrPG

dr

dP

2

24c

rdr

d

M

Structure Equations

Equation of State (EOS) for Asymmetric nuclear matter

...)0(

03

0)0()(

...32

1)0,()0,(

...)()0,(),(

2

0

00

2

LJJ

KEE

IJEIE

MeV220K

MeV16)0,(

fm16.0

0

30

E

?MeV120-20)(L

MeV32)(

0

0

J

26-Mar-14 RIKEN Nishina Center for Acceletor based Science

6

Knowledge of J(ρ0) and L(ρ0) is indispensable !!


Proton fraction at β equilibrium xβ

)()21(4)3( 3/12 Jxxc

Neutron star properties

Core-crust transition properties Cooling Composition Mass-radius relation ship

Status of L



)(

)(

3)(

parameter Slope

)0,()1,(

),(

2

1)(

energySymmetry

0

0

0

2

2

LL

JJ

d

dJL

EE

I

IEJ

I

Definitions


Nuclear energy density functional

1. Non-Relativistic mean field model

2. Relativistic mean field model

3. Density dependant meson exchange model


Non-Relativistic mean field model : Skyrme type

.properties nuclei finite from determined 3)and0,1,2(ixt

, mass nucleon m

density number density,energkinetic

)()12()12(8

1)2()2(

8

1

))(12()2(24

1

))(12()2(4

1

2

ii

11222211

223

2333

220

2000

2

30

y

xtxtxtxt

xxt

xxt

m

npeff

np

np

kin

effkin


22222

2

22222

2

1

222222

2

2221

22

420

22

42

2

432322

21

,

~

4

~

4

~

242

~

2

1

24

1

2

1

246

.2

1)(

mgM

mgM

mgM

mgM

mgM

m

gm

mM

kmg

M

km

ggMgi

pnJ

Jlin

linkin

Relativistic mean field model


1)1(

2)(1

2)(1)(

,

)]1(exp[)()(

,ifor )()()(

if

idx

ic

idx

ib

iaxif

sat

x

xasatgg

xifsatigig

Density dependant meson exchange model DDME


Density dependence of symmetry energy

J can not be measured directly !!

Supra saturation densities Supernovae,

Nucleosynthesis, Rel. HIC, Neutron Stars

Isospin Transfer Properties,

Multi-fragmentation

Nuclear Structure:

Neutron-skin, Giant resonance 26-Mar-14 RIKEN Nishina Center for Acceletor based Science 15

ρ = ρ0

structure and low energy excitations of asymmetric nuclei, skin thickness, Isovector giant resonances

Probes for the nuclear symmetry energy

Neutron skin thickness

Giant dipole resonance i)Pigmy dipole resonance ii)Dipole polarizability

Giant quadrupole resonance

Nuclear binding energies


Covariance Analysis

Consider a model described by coupling constants: (P1,P2,....,PN)

At the optimum parameter set P0 2min0

2 )( P

Reasonable domain of parameter satisfy:

1)()( 022 PP

1)( 02 P

)( 02 P

0P26-Mar-14 RIKEN Nishina Center for Acceletor based Science 17

reasonable domain

P

)(2 P

0

0

2

12

1

22

)(

)(

P

pi

Ppjpiij

pjij

ij

pi

pjij

ij

pi

AB

pi

AA

M

AAA

BABA

BA

BAc

Μ

Μ

|cAB|= 1 : Fully correlated

cAB= 0 : Uncorrelated or Statistically independent

26 March 2014 18 RIKEN Nishina Center for Acceletor based Science


Neutron skin thickness

npq

rdr

rdrrr

rrR

q

q

q

pnskin

,

)(

)(

3

32

2

2/12

2/12


M. Centelles et.al PRL 102,122502 (2009)

L= 75±25MeV


fm33.0 16.018.0

skinR

First PREX data PRL 108, 112502 (2012)

PREX II DATA awaited!!

A. Carbon et.al PRC 81,041301 (2010)

Pigmy Dipole Resonance (PDR)

PDR


2

1

)(

E

E

dEEESEWSR

3.13.32)(

7.158.64)(

0

0

J

L

A. Carbon et.al PRC 81,041301 (2010)

Pigmy Dipole Resonance (PDR)


L=64.8 ± 15.7 MeV

Skyrmee

RMF

High resolution (p,p’) measurement of D.

Tamii et. al PRL 107 (2011)


MeV1441

fm0.156 R 0.0250.021-skin

L

Reinhard et.al, PRC 81, 051303 (R) 2010

L and Rskin from Diapole polarizability


Rskin= 0.168 ±0.022 fm L= 47 ±12 MeV

Piekarewicz , B.K. Agrawal, et.al PRC (R) 2012

L and Rskin from Diapole polarizability


neutron skin (fm) neutron skin (fm)

208Pb

Using αD = 20.1 ±0.6 fm3 † in 208Pb and J= 31± 2 MeV††

Neutron skin = 0.165 ± 0.043 fm L= 43 ± 26 MeV

Agrawal, et. al PRC 88, 024316 (2013) † . A. Tamii et. al, PRL 107, 062502 (2011) †† Lattimer et. al, Annu.Rev. Nucl.Part.Sci., 62,485(2012)


SAMi-m

SAMi-j

L and Rskin from Giant Quadrupole Resonances


Rskin = 0.14 ± 0.03 fm L = 37 ± 18 MeV

Xavi , Marco, Agrawal et.al PRC 87, 034301 (2013)


])1(2

931)[()()(

))(()()(

)(3,))(()(

20

3/10

0

00

0

0

AAAs

Asym

JJAJJ

JJAa

JLJJ

A

densitynucleoneffectiveA

...3/1

223/132

A

Zc

aAIAs

JJ/As

A-av

aB

08.191.58

31.010.32

sJ

JArima et, al. PRC 85,2012


modelsfieldmean(r)

fm008.0155.0

,)(

,

3-0

3

)()(

)()(

0

0

0

A

pn

pn

A

rr

rr

ZNZN

rX

X

21 )()()(320

rXrrrdXA

])1([)(3 2

233/1

0 AAs AJJ


Agrawal ,De and Samaddar PRL 109,2012

Rskin= 0.188 ± 0.014 fm L = 64 ±5 MeV


I))(()(0

0

JJ

II)))()((

)()(

0

0

0

3/2

k

k

CJ

CJ

*

3/510

13/2

13

III))()((

)()()(

0

00

m

mC

CCJ

CCJ

k

k

k

Rskin= 0.190 ± 0.016 fm L = 56 ±12 MeV

B. K. Agrawal, et. al PRC 87, 051306 (R) (2013)


Jian Liu, et. Al Phys. Rev. C 88, 024324 (2013)

L = 66 ±7 MeV


Our results

L = 47± 9 MeV Rskin

= 0.17± 0.02 fm


Large no of the nuclear energy density functional are employed to understand the density dependence of the nuclear symmetry energy around the saturation density. Neutron-skin in 208Pb nucleus and the symmetry energy slope parameter L(ρ0) are extracted using experimental data on giant resonances and the nuclear masses.

Our results: Rskin = 0.17 ± 0.02 fm L(ρ0) = 47± 9MeV

More accurate data for the dipole polarizability and the neutron-skin thickness in 208Pb needed to constraint in a narrow window the value of the symmetry energy slope parameter.

S. K. Samaddar (SINP) J.N.De (SINP) P. -G. Reinhard (Inst. Theoretical Phys. Germany) J. Piecarewicz (Florida State University, USA) W. Nazarewicz (ORNL, USA) G. Colo (INFN, Italy) X. Roca-Maza (INFN, Italy) D. Vretenar (Phys. Dept. Croatia) N. Paar (Phys. Dept. Croatia) M. Brenna (INFN, Italy) Li-Gang Cao (IMP China)


26-Mar-14 RIKEN Nishina Center for Acceletor

based Science 39

Rabindranath Tagor C. V. Raman - Rikenseminar/RIBF-NPseminar/NP... · Rabindranath Tagor C. V....

Documents

Transcript of Rabindranath Tagor C. V. Raman - Rikenseminar/RIBF-NPseminar/NP... · Rabindranath Tagor C. V....