rabindranath tagor c. v. raman - rikenseminar/ribf-npseminar/np... · rabindranath tagor c. v....
Post on 21-Sep-2020
12 Views
Preview:
TRANSCRIPT
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
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 3
Outline of talk
Introduction /Motivation Nuclear energy density functional Probes for nuclear symmetry energy Results Conclusions
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 4
ZNZNI
AIAsJJAZca/AsaAvaB
...2)3/1(3/1232
Giant resonances Neutron rich nuclei Neutron drip line
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 5
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 !!
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 7
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
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 8
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 9
)(
)(
3)(
parameter Slope
)0,()1,(
),(
2
1)(
energySymmetry
0
0
0
2
2
LL
JJ
d
dJL
EE
I
IEJ
I
Definitions
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 10
Nuclear energy density functional
1. Non-Relativistic mean field model
2. Relativistic mean field model
3. Density dependant meson exchange model
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 11
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
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 12
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
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 13
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
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 14
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
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 16
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
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 19
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 20
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 21
Neutron skin thickness
npq
rdr
rdrrr
rrR
q
q
q
pnskin
,
)(
)(
3
32
2
2/12
2/12
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 22
M. Centelles et.al PRL 102,122502 (2009)
L= 75±25MeV
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 23
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
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 24
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)
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 25
L=64.8 ± 15.7 MeV
Skyrmee
RMF
High resolution (p,p’) measurement of D.
Tamii et. al PRL 107 (2011)
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 26
MeV1441
fm0.156 R 0.0250.021-skin
L
Reinhard et.al, PRC 81, 051303 (R) 2010
L and Rskin from Diapole polarizability
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 27
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
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 28
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)
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 29
SAMi-m
SAMi-j
L and Rskin from Giant Quadrupole Resonances
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 30
Rskin = 0.14 ± 0.03 fm L = 37 ± 18 MeV
Xavi , Marco, Agrawal et.al PRC 87, 034301 (2013)
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 31
])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
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 32
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
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 33
Agrawal ,De and Samaddar PRL 109,2012
Rskin= 0.188 ± 0.014 fm L = 64 ±5 MeV
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 34
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)
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 35
Jian Liu, et. Al Phys. Rev. C 88, 024324 (2013)
L = 66 ±7 MeV
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 36
Our results
L = 47± 9 MeV Rskin
= 0.17± 0.02 fm
26-Mar-14 RIKEN Nishina Center for Acceletor based Science 37
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 38
26-Mar-14 RIKEN Nishina Center for Acceletor
based Science 39
top related