RIKEN Nishina Center for Acceletor based Science 1
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1 Rabindanath Tago C. V. Raman 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science
2 Bijay K. Agawal Saha Institute of Nuclea Physics Kolkata, India 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science
3 Outline of talk Intoduction /Motivation Nuclea enegy density functional Pobes fo nuclea symmety enegy Results Conclusions 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 3
4 Giant esonances Neuton ich nuclei Neuton dip line B ava / as A 3 I N N Z Z acz A/3 s A/3 AI... 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 4
5 Neuton sta intenal stuctue 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 5
6 3 4 c M Mc c Μ G P P G d dp 4 c d d M Stuctue Equations Equation of State EOS fo Asymmetic nuclea matte ,,...,, L K E E I E I E MeV K 6 MeV,.6 fm 3 E - MeV? L 3 MeV 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 6
7 Poton faction at β equilibium x β c3 x / 3 4 x Neuton sta popeties Coe-cust tansition popeties Cooling Composition Mass-adius elation ship Knowledge of ρ and Lρ is indispensable!! 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 7
8 Status of L 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 8
9 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 9 3 Slope paamete,,, Symmetyenegy L L d d L E E I I E I Definitions
10 Nuclea enegy density functional. Non-Relativistic mean field model. Relativistic mean field model 3. Density dependant meson exchange model 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science
11 Non-Relativistic mean field model : Skyme type kin 3 eff kin m t x x p n 4 3 t3 x3 x3 p n 4 eff 8 8 t x t x t x t x p n kineticeneg y density, numbe density m nucleon mass, t i x i i,,and 3 detemined fom finite nuclei popeties. 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science
12 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science , ~ 4 ~ 4 ~ 4 ~ m g M m g M m g M m g M m g M m g m m M k m g M k m g g M g i p n lin lin kin Relativistic mean field model
13 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 3, ] exp[, fo i i f i d x i c i d x i b i a x i f sat x x a sat g g x i f sat i g i g Density dependant meson exchange model DDME
14 Density dependence of symmety enegy can not be measued diectly!! 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 4
15 Pobes fo the nuclea symmety enegy Supa satuation densities Supenovae, Nucleosynthesis, Rel. HIC, Neuton Stas Isospin Tansfe Popeties, Multi-fagmentation ρ = ρ stuctue and low enegy excitations of asymmetic nuclei, skin thickness, Isovecto giant esonances 6-Ma-4 Nuclea Stuctue: Neuton-skin, Giant esonance RIKEN Nishina Cente fo Acceleto based Science 5
16 Neuton skin thickness Giant dipole esonance ipigmy dipole esonance iidipole polaizability Giant quadupole esonance Nuclea binding enegies 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 6
17 Covaiance Analysis Conside a model descibed by coupling constants: P,P,...,P N At the optimum paamete set P P min Reasonable domain of paamete satisfy: P easonable domain P P P P P 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 7 P
18 c AB AB AB A ij B pi A Μ c AB = : Fully coelated c AB = : Uncoelated o Statistically independent ij pj B A M ij pi ij pi A A pi pj pi P A Μ P ij pj A 6 Mach 4 8 RIKEN Nishina Cente fo Acceleto based Science
19 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 9
20 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science
21 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science Neuton skin thickness n p q d d R q q q p n skin, 3 3 / /
22 L= 75±5MeV M. Centelles et.al PRL,5 9 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science
23 Fist PREX data PRL 8, 5 R skin fm PREX II DATA awaited!! 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 3
24 Pigmy Dipole Resonance PDR PDR A. Cabon et.al PRC 8,43 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 4
25 Pigmy Dipole Resonance PDR Skymee RMF EWSR E E ES E de L L=64.8 ± 5.7 MeV A. Cabon et.al PRC 8,43 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 5
26 L and R skin fom Diapole polaizability Reinhad et.al, PRC 8, 533 R High esolution p,p measuement of D. Tamii et. al PRL 7 R skin L 44MeV fm 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 6
27 L and R skin fom Diapole polaizability R skin =.68 ±. fm L= 47 ± MeV Piekaewicz, B.K. Agawal, et.al PRC R 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 7
28 8 Pb neuton skin fm neuton skin fm Using α D =. ±.6 fm 3 in 8 Pb and = 3± MeV Neuton skin =.65 ±.43 fm L= 43 ± 6 MeV Agawal, et. al PRC 88, A. Tamii et. al, PRL 7, 65 Lattime et. al, Annu.Rev. Nucl.Pat.Sci., 6,485 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 8
29 L and R skin fom Giant Quadupole Resonances SAMi-m SAMi-j 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 9
30 R skin =.4 ±.3 fm L = 37 ± 8 MeV Xavi, Maco, Agawal et.al PRC 87, Ma-4 RIKEN Nishina Cente fo Acceleto based Science 3
31 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 3 ] 9 3 [ 3, / 3 A A A s A sym A A a L A effectivenucleon density A... /3 /3 3 A Z c a AI A s / A s A-a v a B s Aima et, al. PRC 85,
32 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 3 models mean field.8fm.55,, -3 3 A p n p n A Z N Z N X X 3 X d X A ] [ 3 3 /3 A A s A
33 R skin =.88 ±.4 fm L = 64 ±5 MeV Agawal,De and Samadda PRL 9, 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 33
34 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 34 I II / 3 k k C C * 5/ 3 / 3 3 III m m C C C C C k k k R skin =.9 ±.6 fm L = 56 ± MeV B. K. Agawal, et. al PRC 87, 536 R 3
35 L = 66 ±7 MeV ian Liu, et. Al Phys. Rev. C 88, Ma-4 RIKEN Nishina Cente fo Acceleto based Science 35
36 Ou esults L = 47± 9 MeV R skin =.7±. fm 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 36
37 Lage no of the nuclea enegy density functional ae employed to undestand the density dependence of the nuclea symmety enegy aound the satuation density. Neuton-skin in 8 Pb nucleus and the symmety enegy slope paamete Lρ ae extacted using expeimental data on giant esonances and the nuclea masses. Ou esults: R skin =.7 ±. fm Lρ = 47± 9MeV Moe accuate data fo the dipole polaizability and the neuton-skin thickness in 8 Pb needed to constaint in a naow window the value of the symmety enegy slope paamete. 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 37
38 S. K. Samadda SINP.N.De SINP P. -G. Reinhad Inst. Theoetical Phys. Gemany. Piecaewicz Floida State Univesity, USA W. Nazaewicz ORNL, USA G. Colo INFN, Italy X. Roca-Maza INFN, Italy D. Vetena Phys. Dept. Coatia N. Paa Phys. Dept. Coatia M. Benna INFN, Italy Li-Gang Cao IMP China 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 38
39 6-Ma-4 RIKEN Nishina Cente fo Acceleto based Science 39
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