Density dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei

Size: px
Start display at page:

Download "Density dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei"

Transcription

1 Density dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei X. Viñas a M. Centelles a M. Warda a,b X. Roca-Maza a,c a Departament d Estructura i Constituents de la Matèria and Institut de Ciències del Cosmos, Universitat de Barcelona, Barcelona, Spain b Katedra Fizyki Teoretycznej, Uniwersytet Marii Curie-Sklodowskiej, Poland c INFN sezione di Milano. Via Celoria 16, Milano, Italy M. Centelles, X. Roca-Maza, X. Viñas and M. Warda, Phys. Rev. Lett (2009) M. Warda, X. Viñas, X. Roca-Maza and M. Centelles, Phys. Rev. C (2009) M. Warda, X. Viñas, X. Roca-Maza and M. Centelles, Phys. Rev. C (2010)

2 Why is important the nuclear symmetry energy? The nuclear symmetry energy is a fundamental quantity in Nuclear Physics and Astrophysics because it governs, at the same time, important properties of very small entities like the atomic nucleus ( R m ) and very large objects as neutron stars ( R 10 4 m ) Nuclear Physics: Neutron skin thickness in finite nuclei, stable nuclei, Heavy-Ion collisions, Giant Resonances... High-Energy Physics: Test of the Standard Model through atomic parity non-conservation observables. Astrophysics: Supernova explosion, Neutron emission and cooling of protoneutron stars, Mass-Radius relations in neutron stars, Composition of the crust of neutron stars...

3 Equation of State in asymmetric matter e(ρ, δ) = e(ρ, 0) + c sym (ρ)δ 2 + O(δ 4 ) ( δ = ρ ) n ρ p ρ Around the saturation density we can write e(ρ, 0) a v K v ɛ 2 and c sym (ρ) J Lɛ+ 1 ( 2 K symɛ 2 ɛ = ρ ) 0 ρ 3ρ 0 ρ fm 3, a v 16MeV, K v 230MeV, J 32MeV However, the values of L = 3ρ c sym (ρ)/ ρ ρ0 and K sym = 9ρ 2 2 c sym (ρ)/ ρ 2 ρ0 which govern the density dependence of c sym near ρ 0 are less certain and predictions vary largely among nuclear theories.

4 Experimental constraints Recent reseach in heavy-ion collisions at intermediate energy is consistent with c sym (ρ) = c sym (ρ 0 ).(ρ/ρ 0 ) γ at ρ < ρ 0. Isospin difussion γ = (L = 88 ± 25 MeV). Isoscaling γ = 0.69 (L 65 MeV) Inferred from nucleon emision ratios γ = 0.5(L 55 MeV). The GDR of 208 Pb analyzed with Skyrme forces suggests a constraint c sym (0.1 fm 3 )= MeV (γ ). The study of the PDR in 68 Ni and 132 Sn predicts L=49-80 MeV. The Thomas-Fermi model of Myers and Swiatecki fitted very precisely to binding energies of 1654 nuclei predicts an EOS that yields γ = 0.51 NEUTRON SKIN THICKNESS?

5 Neutron skin thickness

6 What is experimentally know about neutron skin thickness in nuclei? The neutron skin thickness is defined as S = r 2 n 1/2 r 2 p 1/2, where r 2 n 1/2 and r 2 p 1/2 are the rms radii of the neutron and proton distributions respectively. r 2 p 1/2 is known very accurately from elastic electron scattering measurements (e.g. r ch ( 208 Pb) = ± fm [Angeli (2004)]). r 2 n 1/2 has been obtained with hadronic probes such as: (a) Proton-nucleus elastic scattering (5.522fm < r n ( 208 Pb) < fm [Clark (2003)]). (b) Inelastic scattering excitation of the giant dipole and spin-dipole resonances (r n ( 208 Pb) = 5.67 ± 0.07 fm [Krasznahorkay (1990)]). (c) Antiprotonic atoms: Data from antiprotonic X rays and radiochemical analysis of the yields after the antiproton annihilation (r n ( 208 Pb) = 5.66 ± 0.02 fm) [Trzcińska (2001)].

7 0.2 S (fm) I S = (0.9 ± 0.15)I + ( 0.03 ± 0.02) fm A. Trzcińska et al, Phys. Rev. Lett. 87, (2001) CAN S OF 26 STABLE NUCLEI, FROM 40 Ca TO 238 U, ESTIMATED USING ANTIPROTONIC ATOMS DATA HELP IN CONSTRAINING THE SLOPE AND CURVATURE OF c sym?

8 Symmetry energy and neutron skin thickness in the Liquid Drop Model Symmetry Energy where a sym (A) = J, x A = 9J 1 + x A 4Q A 1/3 E sym (A) = a sym (A)(I + x A I C ) 2 A I = (N Z)/A, I C = e 2 Z/(20JR), R = r 0 A 1/3. Neutron skin thickness S = [ 3/5 t e 2 Z/(70J) + 5 ] 2R (b2 n bp) 2 where t = 3r 0 2 J/Q 1 + x A (I I C )

9 Neutron skin thickness t = 2r 0 3J [J a sym(a)] A 1/3 (I I C )

10 Table: Value of a sym (A) and density ρ that fulfils c sym (ρ) = a sym (A) for A = 208, 116 and 40 in MF models. J and a sym are in MeV and ρ is in fm 3. A = 208 A = 116 A = 40 Model J a sym ρ a sym ρ a sym ρ NL NL-SH FSUGold TF-MS SLy SkX SkM* SIII SGII

11 The c sym (ρ)-a sym (A) correlation There is a genuine relation between the symmetry energy coefficients of the EOS and of nuclei: c sym (ρ) equals a sym (A) of heavy nuclei like 208 Pb at a density ρ = 0.1 ± 0.01 fm 3. A similar situation occurs down to medium mass numbers, at lower densities. We find that this density can be very well simulated by ρ ρ A = ρ 0 ρ 0 /(1 + ca 1/3 ), where c is fixed by the condition ρ 208 = 0.1 fm 3. Using the equality c sym (ρ) = a sym (A) and the LDM, the neutron skin thickness can be finally written as: 3 2r 0 L ( t = 1 ɛ K sym )ɛa 1/3( ) I I C 5 3 J 2L

12 Neutron skin thickness t = 3 2r 0 L ( 1 ɛ K sym )ɛa 1/3( ) I I C 5 3 J 2L

13 Fitting procedure and results We optimize 3 2r 0 L ( t = 1 ɛ K sym )ɛa 1/3( ) I I C 5 3 J 2L using c sym = 31.6( ρ ρ 0 ) γ MeV, ɛ = 1 3(1 + ca 1/3 ), ρ 0 = 0.16fm 3 and taking as experimental baseline the neutron skins measured in 26 antiprotonic atoms. We predict (b n b p ): L = 75 ± 25 MeV

14 S (fm) experiment linear average of experiment Our fit Fe Ca Ni Fe Cd 28 Ni 56 Fe Co Zr Sn Ni Sn Te Te Cd 50 Sn Te 90 Th Te Te Zr Ca Sn I = (N Ζ) / Α Bi Pb S = (0.9 ± 0.15)I + ( 0.03 ± 0.02) fm A. Trzcińska et al, Phys. Rev. Lett. 87, (2001) U

15 Influence of the surface width (b n b p ) S = [ 3/5 t e 2 Z/(70J) + 5 ] 2R (b2 n bp 2 ) b n and b p are obtained at the ETF level.

16 Surface contribution to the neutron skin thickness R (b2 n bp) 2 = σ sw I = (0.3 J Q + c)i

17 Fit and results c = 0.07 c = EXP 0.9 I R np (fm) I J Q =

18 Neutron skin thickness R np (fm) in 208 Pb NL3Λ ν1 NL3Λ ν2 TM1 NL3 NL-SH FSUGold NL3Λ ν3 NL1 SkM* SkX SLy4 SkP T6 SGII D1S SIII 0.1 SVI J / Q NL3Λ ν1 NL3Λ ν2 FSUGold NL3Λ ν3 NL3 TM1 SkM* SkX SLy4 SkP T6 SGII D1S SIII SVI NL1 NL-SH L (MeV) NL3Λ ν1 SVI TM1 NL3 NL-SH NL3Λ ν2 FSUGold SLy4 NL3Λ ν3 SkX SkM* SGII SkP T6 D1S SIII NL J / Q L (MeV) L = MeV

19 Constraints on the slope of the symmetry energy

20 Summary and Conclusions We have described a generic relation between the symmetry energy in finite nuclei and in nuclear matter at subsaturation. We take advantage of this relation to explore constraints on c sym (ρ) from neutron skins measured in antiprotonic atoms. These constraints points towards a soft symmetry energy. We discuss the L values constrained by neutron skins in comparison with most recent observations from reactions and giant resonances. We learn that in spite of present error bars in the data of antiprotonic atoms, the size of the final uncertainties in L is comparable to the other analyses. The generic relation between the symmetry energy in finite nuclei and in nuclear matter at subsaturation plausibly encompasses other prime correlations of nuclear observables with the density content of the symmetry energy as e.g. the constrains of c sym (0.1) from the GDR of 208 Pb (L. Trippa et al. Phys. Rev. C77, (R) (2008)).

21 Thank you for your attention

22 Extra material

23 Some technical details The surface stiffness coeficient Q and the surface widths b n and b p are obtained from self-consistent calculations of the neutron and proton density profiles in asymmetric semi-infinite nuclear matter. To this end one has to minimize the total energy per unit area with the constraint of conservation of the number of protons and neutrons with respect to arbitrary variations of the densities. E const S = [ ε(z) µn ρ n (z) µ p ρ p (z) ] dz, where ε(z) is the nuclear energy density functional. In the non-relativistic framework the densities ρ n and ρ p obey the coupled local Euler-Lagrange equations: δε(z) δρ n µ n = 0, δε(z) δρ p µ p = 0. The relative neutron excess δ = (ρ n ρ p )/(ρ n + ρ p ) is a function of the z-coordinate. When z, the densities ρ n and ρ p approach the values of asymmetric uniform nuclear matter in equilibrium with a bulk neutron excess δ 0.

24 From the calculated density profiles one computes: z oq = zρ q(z)dz ρ q(z)dz, From the relation b 2 q = (z z 0q) 2 ρ q(z)dz. ρ q(z)dz t = z 0n z 0p = 3r 0 2 J Q δ 0, one can evaluate Q from the slope of t at δ 0 = 0. The distance t and the surface widths b n and b p in finite nuclei with neutron excess I = (N Z)/A are obtained using δ 0 given by: I + 3 c 1 Z 2 8 Q δ 0 = A 5/ J 4 Q A 1/3

Density dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei

Density dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei Density dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei X. Roca-Maza a,c X. Viñas a M. Centelles a M. Warda a,b a Departament d Estructura i Constituents

More information

Density dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei

Density dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei Density dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei X. Roca-Maza a,b X. Viñas b M. Centelles b M. Warda b,c a INFN sezione di Milano. Via Celoria 16,

More information

Isospin asymmetry in stable and exotic nuclei

Isospin asymmetry in stable and exotic nuclei Isospin asymmetry in stable and exotic nuclei Xavier Roca Maza 6 May 2010 Advisors: Xavier Viñas i Gausí and Mario Centelles i Aixalà Motivation: Nuclear Chart Relative Neutron excess I (N Z )/(N + Z )

More information

arxiv: v1 [nucl-th] 26 Jun 2011

arxiv: v1 [nucl-th] 26 Jun 2011 Study of the neutron skin thickness of 208 Pb in mean field models X. Roca-Maza 1,2, M. Centelles 1, X. Viñas 1 and M. Warda 1, 1 Departament d Estructura i Constituents de la Matèria and Institut de Ciències

More information

Pygmy dipole resonances in stable and unstable nuclei

Pygmy dipole resonances in stable and unstable nuclei Pygmy dipole resonances in stable and unstable nuclei Xavier Roca-Maza INFN, Sezione di Milano, Via Celoria 16, I-2133, Milano (Italy) Collaborators: Giacomo Pozzi, Marco Brenna, Kazhuito Mizuyama and

More information

Dipole Polarizability and Parity Violating Asymmetry in 208 Pb

Dipole Polarizability and Parity Violating Asymmetry in 208 Pb Dipole Polarizability and Parity Violating Asymmetry in 208 Pb Xavier Roca-Maza INFN, Sezione di Milano, Via Celoria 16, I-20133, Milano (Italy) 2nd European Nuclear Physics Conference EuNPC 2012, 16-21

More information

The pygmy dipole strength, the neutron skin thickness and the symmetry energy

The pygmy dipole strength, the neutron skin thickness and the symmetry energy The pygmy dipole strength, the neutron skin thickness and the symmetry energy Xavier Roca-Maza INFN, Sezione di Milano, Via Celoria 16, I-2133, Milano (Italy) Giacomo Pozzi Marco Brenna Kazhuito Mizuyama

More information

The Nuclear Equation of State

The Nuclear Equation of State The Nuclear Equation of State Theoretical models for nuclear structure studies Xavier Roca-Maza Università degli Studi di Milano e INFN, sezione di Milano Terzo Incontro Nazionale di Fisica Nucleare LNF,

More information

The dipole strength: microscopic properties and correlations with the symmetry energy and the neutron skin thickness

The dipole strength: microscopic properties and correlations with the symmetry energy and the neutron skin thickness The dipole strength: microscopic properties and correlations with the symmetry energy and the neutron skin thickness Xavier Roca-Maza INFN, Sezione di Milano, Via Celoria 16, I-2133, Milano (Italy) Giacomo

More information

Nuclear symmetry energy and neutron skin thickness

Nuclear symmetry energy and neutron skin thickness Nuclear symmetry energy and neutron skin thickness M. Warda arxiv:1202.4612v1 [nucl-th] 21 Feb 2012 Katedra Fizyki Teoretycznej, Uniwersytet Marii Curie Sk lodowskiej, ul. Radziszewskiego 10, 20-031 Lublin,

More information

Covariance analysis for Nuclear Energy Density Functionals

Covariance analysis for Nuclear Energy Density Functionals Covariance analysis for Nuclear Energy Density Functionals Xavier Roca-Maza Università degli Studi di Milano and INFN Information and statistics in nuclear experiment and theory ISNET-3 16 20 November

More information

Dipole Polarizability and the neutron skin thickness

Dipole Polarizability and the neutron skin thickness Dipole Polarizability and the neutron skin thickness Xavier Roca-Maza Università degli Studi di Milano and INFN MITP Scientific Program Neutron Skins of Nuclei May 17th-27th 2016. 1 Table of contents:

More information

arxiv: v1 [nucl-th] 14 Feb 2012

arxiv: v1 [nucl-th] 14 Feb 2012 The pygmy dipole strength, the neutron radius of 8 Pb and the symmetry energy arxiv:1.38v1 [nucl-th] 14 Feb 1 X. Roca-Maza 1,, M. Brenna 1,3, M. Centelles, G. Colò 1,3, K. Mizuyama 1, G. Pozzi 3, X. Viñas

More information

Dipole Polarizability and the neutron skin thickness

Dipole Polarizability and the neutron skin thickness Dipole Polarizability and the neutron skin thickness Xavier Roca-Maza Università degli Studi di Milano and INFN Joint LIA COLL-AGAIN, COPIGAL, and POLITA Workshop, April 26th-29th 2016. 1 Table of contents:

More information

Dipole Polarizability and Parity Violating Asymmetry in 208 Pb

Dipole Polarizability and Parity Violating Asymmetry in 208 Pb Dipole Polarizability and Parity Violating Asymmetry in 208 Pb Xavier Roca-Maza INFN, Sezione di Milano, Via Celoria 16, I-20133, Milano (Italy) Nuclear Structure and Dynamics II. July 9th to 13th 2012.

More information

Parity-Violating Asymmetry for 208 Pb

Parity-Violating Asymmetry for 208 Pb Parity-Violating Asymmetry for 208 Pb Matteo Vorabbi Dipartimento di Fisica - Università di Pavia INFN - Sezione di Pavia Rome - 2015 January 15 Matteo Vorabbi (Università di Pavia) Parity-Violating Asymmetry

More information

Neutron Rich Nuclei in Heaven and Earth

Neutron Rich Nuclei in Heaven and Earth First Prev Next Last Go Back Neutron Rich Nuclei in Heaven and Earth Jorge Piekarewicz with Bonnie Todd-Rutel Tallahassee, Florida, USA Page 1 of 15 Cassiopeia A: Chandra 08/23/04 Workshop on Nuclear Incompressibility

More information

Nuclear Matter Incompressibility and Giant Monopole Resonances

Nuclear Matter Incompressibility and Giant Monopole Resonances Nuclear Matter Incompressibility and Giant Monopole Resonances C.A. Bertulani Department of Physics and Astronomy Texas A&M University-Commerce Collaborator: Paolo Avogadro 27th Texas Symposium on Relativistic

More information

Neutron Skins with α-clusters

Neutron Skins with α-clusters Neutron Skins with α-clusters GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt Nuclear Astrophysics Virtual Institute Hirschegg 2015 Nuclear Structure and Reactions: Weak, Strange and Exotic International

More information

The Nuclear Symmetry Energy: constraints from. Giant Resonances. Xavier Roca-Maza

The Nuclear Symmetry Energy: constraints from. Giant Resonances. Xavier Roca-Maza The Nuclear Symmetry Energy: constraints from Giant Resonances Xavier Roca-Maza Dipartimento di Fisica, Università degli Studi di Milano and INFN, Sezione di Milano Trobada de Nadal 2012 Table of contents:

More information

Probing the Nuclear Symmetry Energy and Neutron Skin from Collective Excitations. N. Paar

Probing the Nuclear Symmetry Energy and Neutron Skin from Collective Excitations. N. Paar Calcium Radius Experiment (CREX) Workshop at Jefferson Lab, March 17-19, 2013 Probing the Nuclear Symmetry Energy and Neutron Skin from Collective Excitations N. Paar Physics Department Faculty of Science

More information

Nature of low-energy dipole states in exotic nuclei

Nature of low-energy dipole states in exotic nuclei Nature of low-energy dipole states in exotic nuclei Xavier Roca-Maza Università degli Studi di Milano, Via Celoria 16, I-133, Milano SPES One-day Workshop on "Collective Excitations of Exotic Nuclei" December

More information

Pb, 120 Sn and 48 Ca from High-Resolution Proton Scattering MSU 2016

Pb, 120 Sn and 48 Ca from High-Resolution Proton Scattering MSU 2016 Dipole Polarizability and Neutron Skins in 208 Pb, 120 Sn and 48 Ca from High-Resolution Proton Scattering MSU 2016 Equation of State of neutron matter and neutron skin Proton scattering at 0 and electric

More information

Parity violating asymmetry, dipole polarizability, and the neutron skin thickness in 48 Ca and 208 Pb

Parity violating asymmetry, dipole polarizability, and the neutron skin thickness in 48 Ca and 208 Pb Parity violating asymmetry, dipole polarizability, and the neutron skin thickness in 48 Ca and 208 Pb Xavier Roca-Maza Università degli Studi di Milano and INFN Via Celoria 16, I-20133, Milano (Italy)

More information

Parity violating asymmetry, dipole polarizability, and the neutron skin thickness in 48 Ca and 208 Pb

Parity violating asymmetry, dipole polarizability, and the neutron skin thickness in 48 Ca and 208 Pb Parity violating asymmetry, dipole polarizability, and the neutron skin thickness in 48 Ca and 208 Pb Xavier Roca-Maza Università degli Studi di Milano and INFN Via Celoria 16, I-20133, Milano (Italy)

More information

arxiv: v2 [nucl-th] 19 May 2010

arxiv: v2 [nucl-th] 19 May 2010 Analysis of bulk and surface contributions in the neutron skin of nuclei M. Warda 1,2, X. Viñas 1, X. Roca-Maza 1, and M. Centelles 1 1 Departament d Estructura i Constituents de la Matèria and nstitut

More information

Nuclear symmetry energy and Neutron star cooling

Nuclear symmetry energy and Neutron star cooling Nuclear symmetry energy and Neutron star cooling Yeunhwan Lim 1 1 Daegu University. July 26, 2013 In Collaboration with J.M. Lattimer (SBU), C.H. Hyun (Daegu), C-H Lee (PNU), and T-S Park (SKKU) NuSYM13

More information

Symmetry energy and the neutron star core-crust transition with Gogny forces

Symmetry energy and the neutron star core-crust transition with Gogny forces Symmetry energy and the neutron star core-crust transition with Gogny forces Claudia Gonzalez-Boquera, 1 M. Centelles, 1 X. Viñas 1 and A. Rios 2 1 Departament de Física Quàntica i Astrofísica and Institut

More information

Structure properties of medium and heavy exotic nuclei

Structure properties of medium and heavy exotic nuclei Journal of Physics: Conference Series Structure properties of medium and heavy exotic nuclei To cite this article: M K Gaidarov 212 J. Phys.: Conf. Ser. 381 12112 View the article online for updates and

More information

Dipole Polarizability, parity violating asymmetry and the neutron skin thickness Xavier Roca-Maza Università degli Studi di Milano and INFN

Dipole Polarizability, parity violating asymmetry and the neutron skin thickness Xavier Roca-Maza Università degli Studi di Milano and INFN Dipole Polarizability, parity violating asymmetry and the neutron skin thickness Xavier Roca-Maza Università degli Studi di Milano and INFN Institute of Theoretical Physics Chinese Academy of Sciences

More information

Nuclear symmetry energy deduced from dipole excitations: comparison with other constraints

Nuclear symmetry energy deduced from dipole excitations: comparison with other constraints Nuclear symmetry energy deduced from dipole excitations: a comparison with other constraints G. Colò June 15th, 2010 This work is part of a longer-term research plan. The goal is: understanding which are

More information

Theory of neutron-rich nuclei and nuclear radii Witold Nazarewicz (with Paul-Gerhard Reinhard) PREX Workshop, JLab, August 17-19, 2008

Theory of neutron-rich nuclei and nuclear radii Witold Nazarewicz (with Paul-Gerhard Reinhard) PREX Workshop, JLab, August 17-19, 2008 Theory of neutron-rich nuclei and nuclear radii Witold Nazarewicz (with Paul-Gerhard Reinhard) PREX Workshop, JLab, August 17-19, 2008 Introduction to neutron-rich nuclei Radii, skins, and halos From finite

More information

The Nuclear Equation of State and the neutron skin thickness in nuclei

The Nuclear Equation of State and the neutron skin thickness in nuclei The Nuclear Equation of State and the neutron skin thickness in nuclei Xavier Roca-Maza Università degli Studi di Milano e INFN, sezione di Milano Physics beyond the standard model and precision nucleon

More information

Heavy-ion reactions and the Nuclear Equation of State

Heavy-ion reactions and the Nuclear Equation of State Heavy-ion reactions and the Nuclear Equation of State S. J. Yennello Texas A&M University D. Shetty, G. Souliotis, S. Soisson, Chen, M. Veselsky, A. Keksis, E. Bell, M. Jandel Studying Nuclear Equation

More information

Gianluca Colò. Density Functional Theory for isovector observables: from nuclear excitations to neutron stars. Università degli Studi and INFN, MIlano

Gianluca Colò. Density Functional Theory for isovector observables: from nuclear excitations to neutron stars. Università degli Studi and INFN, MIlano Density Functional Theory for isovector observables: from nuclear excitations to neutron stars Gianluca Colò NSMAT2016, Tohoku University, Sendai 1 Outline Energy density functionals (EDFs): a short introduction

More information

Towards a universal nuclear structure model. Xavier Roca-Maza Congresso del Dipartimento di Fisica Milano, June 28 29, 2017

Towards a universal nuclear structure model. Xavier Roca-Maza Congresso del Dipartimento di Fisica Milano, June 28 29, 2017 Towards a universal nuclear structure model Xavier Roca-Maza Congresso del Dipartimento di Fisica Milano, June 28 29, 217 1 Table of contents: Brief presentation of the group Motivation Model and selected

More information

Symmetry Energy within the Brueckner-Hartree-Fock approximation

Symmetry Energy within the Brueckner-Hartree-Fock approximation Symmetry Energy within the Brueckner-Hartree-Fock approximation Isaac Vidaña CFC, University of Coimbra International Symposium on Nuclear Symmetry Energy Smith College, Northampton ( Massachusetts) June

More information

Volume and Surface Components of the Nuclear Symmetry Energy

Volume and Surface Components of the Nuclear Symmetry Energy NUCLEAR THEORY, Vol. 35 (2016) eds. M. Gaidarov, N. Minkov, Heron Press, Sofia Volume and Surface Components of the Nuclear Symmetry Energy A.N. Antonov 1, M.K. Gaidarov 1, P. Sarriguren 2, E. Moya de

More information

Finite Range Force models for EOS

Finite Range Force models for EOS 1 / 30 Finite Range Force models for EOS INT 2012-2a Core-collapse supernova Yeunhwan Lim 1 (in collaboration with Prof. James M. Lattimer 1 ) 1 SUNY STONY BROOK, NY 11794 July 11, 2012 2 / 30 Table of

More information

Dipole Polarizability, parity violating asymmetry and the neutron skin thickness Xavier Roca-Maza Università degli Studi di Milano and INFN

Dipole Polarizability, parity violating asymmetry and the neutron skin thickness Xavier Roca-Maza Università degli Studi di Milano and INFN Dipole Polarizability, parity violating asymmetry and the neutron skin thickness Xavier Roca-Maza Università degli Studi di Milano and INFN Department of Physics. Peking University. January 19th 2016.

More information

Density dependence of the symmetry energy and the nuclear equation of state : A dynamical and statistical model perspective

Density dependence of the symmetry energy and the nuclear equation of state : A dynamical and statistical model perspective Density dependence of the symmetry energy and the nuclear equation of state : A dynamical and statistical model perspective D. V. Shetty, S. J. Yennello, and G. A. Souliotis The density dependence of the

More information

Discerning the symmetry energy and neutron star properties from nuclear collective excitations

Discerning the symmetry energy and neutron star properties from nuclear collective excitations International Workshop XLV on Gross Properties of Nuclei and Nuclear Excitations Hirschegg, Kleinwalsertal, Austria, January 15-21, 2017 Discerning the symmetry energy and neutron star properties from

More information

Nuclear Equation of State from ground and collective excited state properties of nuclei

Nuclear Equation of State from ground and collective excited state properties of nuclei Nuclear Equation of State from ground and collective excited state properties of nuclei arxiv:1804.06256v1 [nucl-th] 17 Apr 2018 X. Roca-Maza 1 and N. Paar 2 1 Dipartimento di Fisica, Università degli

More information

An empirical approach combining nuclear physics and dense nucleonic matter

An empirical approach combining nuclear physics and dense nucleonic matter An empirical approach combining nuclear physics and dense nucleonic matter Univ Lyon, Université Lyon 1, IN2P3-CNRS, Institut de Physique Nucléaire de Lyon, F-69622 Villeurbanne, France E-mail: j.margueron@ipnl.in2p3.fr

More information

Constraining the symmetry energy based on relativistic point coupling interactions and excitations in finite nuclei

Constraining the symmetry energy based on relativistic point coupling interactions and excitations in finite nuclei 7 th International Symposium on Nuclear Symmetry Energy, GANIL (France) 4-7.9.2017 Constraining the symmetry energy based on relativistic point coupling interactions and excitations in finite nuclei N.

More information

Relativistic Radioactive Beams as a Tool for Nuclear Astrophysics

Relativistic Radioactive Beams as a Tool for Nuclear Astrophysics Relativistic Radioactive Beams as a Tool for Nuclear Astrophysics Thomas Aumann December 11 th 2013 27 th Texas Symposium on Relativistic Astrophysics Dallas, Texas Supported by the BMBF under contract

More information

Pygmies, Giants, and Skins: Reaction Theory Informing Nuclear Structure

Pygmies, Giants, and Skins: Reaction Theory Informing Nuclear Structure Pygmies, Giants, and Skins: Reaction Theory Informing Nuclear Structure Reactions and Structure of Exotic Nuclei INT Workshop March, 2015 Cassiopeia A (circa 1675) Giant (Hercules) Awakes and Drives off

More information

Equation of State of Dense Matter

Equation of State of Dense Matter Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University April 25, 2017 Nuclear Astrophysics James.Lattimer@Stonybrook.edu Zero Temperature Nuclear Matter Expansions Cold, bulk, symmetric

More information

Clusters in Dense Matter and the Equation of State

Clusters in Dense Matter and the Equation of State Clusters in Dense Matter and the Equation of State Excellence Cluster Universe, Technische Universität München GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt in collaboration with Gerd Röpke

More information

Crust-core transitions in neutron stars revisited

Crust-core transitions in neutron stars revisited Crust-core transitions in neutron stars revisited X. Viñas a, C. González-Boquera a, B.K. Sharma a,b M. Centelles a a Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos, Universitat

More information

An empirical Equation of State for nuclear physics and astrophysics

An empirical Equation of State for nuclear physics and astrophysics An empirical Equation of State for nuclear physics and astrophysics Collaborators: Debarati Chatterjee LPC/ENSICAEN, caen, france Francesca Gulminelli Jerome Margueron Adriana Raduta Sofija Antic Debora

More information

An extended liquid drop approach

An extended liquid drop approach An extended liquid drop approach Symmetry energy, charge radii and neutron skins Lex Dieperink 1 Piet van Isacker 2 1 Kernfysisch Versneller Instituut University of Groningen 2 GANIL, Caen, France ECT,

More information

arxiv: v1 [nucl-th] 18 Jan 2012

arxiv: v1 [nucl-th] 18 Jan 2012 Electric dipole polarizability and the neutron skin J. Piekarewicz, 1 B. K. Agrawal, 2 G. Colò, 3,4 W. Nazarewicz, 5,6,7 N. Paar, 8 P.-G. Reinhard, 9 X. Roca-Maza, 4 and D. Vretenar 8 1 Department of Physics,

More information

Reactions of neutron-rich Sn isotopes investigated at relativistic energies at R 3 B

Reactions of neutron-rich Sn isotopes investigated at relativistic energies at R 3 B investigated at relativistic energies at R 3 B for the R 3 B collaboration Technische Universität Darmstadt E-mail: fa.schindler@gsi.de Reactions of neutron-rich Sn isotopes have been measured in inverse

More information

Nuclear radii of unstable nuclei -neutron/proton skins and halos-

Nuclear radii of unstable nuclei -neutron/proton skins and halos- --- OUTLINE --- Introduction Situation @ stable nuclei How to measure radii? σ R / σ I measurements Transmission method Experimental setup Glauber model analysis Optical limit approximation Density distribution

More information

Parity violating electron scattering observables, and Dipole Polarizability Xavier Roca-Maza Università degli Studi di Milano and INFN

Parity violating electron scattering observables, and Dipole Polarizability Xavier Roca-Maza Università degli Studi di Milano and INFN Parity violating electron scattering observables, and Dipole Polarizability Xavier Roca-Maza Università degli Studi di Milano and INFN Neutron Skins of Nuclei: from laboratory to stars 4 7 May 2015. MITP

More information

Neutron star structure explored with a family of unified equations of state of neutron star matter

Neutron star structure explored with a family of unified equations of state of neutron star matter Neutron star structure explored with a family of unified equations of state of neutron star matter Department of Human Informatics, ichi Shukutoku University, 2-9 Katahira, Nagakute, 48-1197, Japan E-mail:

More information

Low-lying dipole response in stable and unstable nuclei

Low-lying dipole response in stable and unstable nuclei Low-lying dipole response in stable and unstable nuclei Marco Brenna Xavier Roca-Maza, Giacomo Pozzi Kazuhito Mizuyama, Gianluca Colò and Pier Francesco Bortignon X. Roca-Maza, G. Pozzi, M.B., K. Mizuyama,

More information

The isospin dependence of the nuclear force and its impact on the many-body system

The isospin dependence of the nuclear force and its impact on the many-body system Journal of Physics: Conference Series OPEN ACCESS The isospin dependence of the nuclear force and its impact on the many-body system To cite this article: F Sammarruca et al 2015 J. Phys.: Conf. Ser. 580

More information

Correlating the density dependence of the symmetry y energy to neutron skins and neutron-star properties

Correlating the density dependence of the symmetry y energy to neutron skins and neutron-star properties Correlating the density dependence of the symmetry y energy to neutron skins and neutron-star properties Farrukh J Fattoyev Texas A&M University-Commerce i My TAMUC collaborators: B.-A. Li, W. G. Newton

More information

Brief introduction Motivation and present situation: example GTR Propose new fitting protocols

Brief introduction Motivation and present situation: example GTR Propose new fitting protocols Towards the improvement of spin-isospin properties in nuclear energy density functionals Xavier Roca-Maza Dipartimento di Fisica, Università degli Studi di Milano and INFN, via Celoria 16, I-20133 Milano,

More information

Neutron skin measurements and its constraints for neutron matter. C. J. Horowitz, Indiana University INT, Seattle, 2016

Neutron skin measurements and its constraints for neutron matter. C. J. Horowitz, Indiana University INT, Seattle, 2016 Neutron skin measurements and its constraints for neutron matter C. J. Horowitz, Indiana University INT, Seattle, 2016 1 Neutron Rich Matter Compress almost anything to 10 11 + g/cm 3 and electrons react

More information

A MICROSCOPIC MODEL FOR THE COLLECTIVE RESPONSE IN ODD NUCLEI

A MICROSCOPIC MODEL FOR THE COLLECTIVE RESPONSE IN ODD NUCLEI Corso di Laurea Magistrale in Fisica A MICROSCOPIC MODEL FOR THE COLLECTIVE RESPONSE IN ODD NUCLEI Relatore: Prof. Gianluca COLÒ Correlatore: Prof.ssa Angela BRACCO Correlatore: Dott. Xavier ROCA-MAZA

More information

Relativistic versus Non Relativistic Mean Field Models in Comparison

Relativistic versus Non Relativistic Mean Field Models in Comparison Relativistic versus Non Relativistic Mean Field Models in Comparison 1) Sampling Importance Formal structure of nuclear energy density functionals local density approximation and gradient terms, overall

More information

Neutron stars at JLAB and the Pb Radius Experiment

Neutron stars at JLAB and the Pb Radius Experiment Neutron stars at JLAB and the Pb Radius Experiment PREX uses parity violating electron scattering to accurately measure the neutron radius of 208 Pb. 208 Pb This has many implications for nuclear structure,

More information

Compact star crust: relativistic versus Skyrme nuclear models

Compact star crust: relativistic versus Skyrme nuclear models Problem How do relativistic models, used to build EoS of compact stars, behave at subsaturation densities? EoS at subsaturation densities/crust of compact stars: how do relativistic and Skyrme nuclear

More information

arxiv: v1 [nucl-th] 24 Oct 2007

arxiv: v1 [nucl-th] 24 Oct 2007 February 2, 28 :28 WSPC/INSTRUCTION FILE kazi27d International Journal of Modern Physics E c World Scientific Publishing Company arxiv:71.4411v1 [nucl-th] 24 Oct 27 Cluster radioactivity of isotopes in

More information

E. Fermi: Notes on Thermodynamics and Statistics (1953))

E. Fermi: Notes on Thermodynamics and Statistics (1953)) E. Fermi: Notes on Thermodynamics and Statistics (1953)) Neutron stars below the surface Surface is liquid. Expect primarily 56 Fe with some 4 He T» 10 7 K ' 1 KeV >> T melting ( 56 Fe) Ionization: r Thomas-Fermi

More information

Inner crust composition and transition densities

Inner crust composition and transition densities Inner crust composition and transition densities W.G.Newton 1, Bao-An Li 1, J.R.Stone 2,3 M. Gearheart 1, J. Hooker 1 1 Texas A&M University - Commerce 2 University of Oxford, UK 3 Physics Division, ORNL,

More information

Symmetry energy of dilute warm nuclear matter

Symmetry energy of dilute warm nuclear matter Symmetry energy of dilute warm nuclear matter J. B. Natowitz, G. Röpke, 1 S. Typel, 2,3 D. Blaschke, 4, 5 A. Bonasera, 6 K. Hagel, T. Klähn, 4, 7 S. Kowalski, L. Qin, S. Shlomo, R. Wada, and H. H. Wolter

More information

Temperature Dependence of the Symmetry Energy and Neutron Skins in Ni, Sn, and Pb Isotopic Chains

Temperature Dependence of the Symmetry Energy and Neutron Skins in Ni, Sn, and Pb Isotopic Chains Bulg. J. Phys. 44 (2017) S27 S38 Temperature Dependence of the Symmetry Energy and Neutron Skins in Ni, Sn, and Pb Isotopic Chains A.N. Antonov 1, D.N. Kadrev 1, M.K. Gaidarov 1, P. Sarriguren 2, E. Moya

More information

Nuclear structure III: Nuclear and neutron matter. National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016

Nuclear structure III: Nuclear and neutron matter. National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016 Nuclear structure III: Nuclear and neutron matter Stefano Gandolfi Los Alamos National Laboratory (LANL) National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016

More information

Compressibility of Nuclear Matter from Shell Effects in Nuclei

Compressibility of Nuclear Matter from Shell Effects in Nuclei RIKEN Review No. 10 (March, 1999): Focused on Selected Topics in Nuclear Collective Excitations (NUCOLEX99) 1 Compressibility of Nuclear Matter from Shell Effects in Nuclei M.M. Sharma Physics Department,

More information

Study of the spin orbit force using a bubble nucleus O. Sorlin (GANIL)

Study of the spin orbit force using a bubble nucleus O. Sorlin (GANIL) Study of the spin orbit force using a bubble nucleus O. Sorlin (GANIL) I. General introduction to the atomic nucleus Charge density, nuclear orbits Shell gaps-> magic nuclei II. The spin orbit force History

More information

Dipole Response of Exotic Nuclei and Symmetry Energy Experiments at the LAND R 3 B Setup

Dipole Response of Exotic Nuclei and Symmetry Energy Experiments at the LAND R 3 B Setup Dipole Response of Exotic Nuclei and Symmetry Energy Experiments at the LAND R 3 B Setup Dominic Rossi for the LAND collaboration GSI Helmholtzzentrum für Schwerionenforschung GmbH D 64291 Darmstadt, Germany

More information

arxiv: v1 [nucl-th] 29 Jun 2009

arxiv: v1 [nucl-th] 29 Jun 2009 Neutron/proton ratio oucleon emissions as a probe of neutron skin arxiv:0906.5281v1 [nucl-th] 29 Jun 2009 X. Y. Sun a,b, D. Q. Fang a, Y. G. Ma a, X. Z. Cai a, J. G. Chen a, W. Guo a, W. D. Tian a, H.

More information

Temperature Dependence of the Symmetry Energy and Neutron Skins in Ni, Sn, and Pb Isotopic Chains

Temperature Dependence of the Symmetry Energy and Neutron Skins in Ni, Sn, and Pb Isotopic Chains NUCLEAR THEORY, Vol. 36 (17) eds. M. Gaidarov, N. Minkov, Heron Press, Sofia Temperature Dependence of the Symmetry Energy and Neutron Skins in Ni, Sn, and Pb Isotopic Chains A.N. Antonov 1, D.N. Kadrev

More information

Computational Advances in Nuclear and Hadron Physics, Kyoto, Constraining the Relativistic Nuclear Energy Density Functional

Computational Advances in Nuclear and Hadron Physics, Kyoto, Constraining the Relativistic Nuclear Energy Density Functional Computational Advances in Nuclear and Hadron Physics, Kyoto, 21.09.-30.10. 2015 Constraining the Relativistic Nuclear Energy Density Functional N. Paar Department of Physics, Faculty of Science, University

More information

13. Basic Nuclear Properties

13. Basic Nuclear Properties 13. Basic Nuclear Properties Particle and Nuclear Physics Dr. Tina Potter Dr. Tina Potter 13. Basic Nuclear Properties 1 In this section... Motivation for study The strong nuclear force Stable nuclei Binding

More information

PREX and CREX. R N from Electroweak Asymmetry in Elastic Electron-Nucleus Scattering. Neutron Skin.

PREX and CREX.   R N from Electroweak Asymmetry in Elastic Electron-Nucleus Scattering. Neutron Skin. http://hallaweb.jlab.org/parity/prex PREX and CREX 08 Pb Horowitz 48 Ca Neutron Skin R N from Electroweak Asymmetry in Elastic Electron-Nucleus Scattering R L 4 6 A ~ 10 PV Q ~ 10 R L PRL 108 (01) 1150

More information

An EOS implementation for astrophyisical simulations

An EOS implementation for astrophyisical simulations Introduction Formalism Neutron Stars CCSN An EOS implementation for astrophyisical simulations A S Schneider 1, L F Roberts 2, C D Ott 1 1 TAPIR, Caltech, Pasadena, CA 2 NSCL, MSU, East Lansing, MI East

More information

Preliminary Studies of Thermal Wavelength Approximation in 208 Pb and 91 Zr hot Nuclei

Preliminary Studies of Thermal Wavelength Approximation in 208 Pb and 91 Zr hot Nuclei PROC. ITB Eng. Science Vol. 38 B, No. 1, 006, 9-36 9 Preliminary Studies of Thermal Wavelength Approximation in 08 Pb and 91 Zr hot Nuclei R. Kurniadi Faculty of Mathematics and Natural Sciences, Institut

More information

Laboratory, Michigan State University, East Lansing, MI 48824, USA. East Lansing, MI 48824, USA. Abstract

Laboratory, Michigan State University, East Lansing, MI 48824, USA. East Lansing, MI 48824, USA. Abstract Constraints on the density dependence of the symmetry energy M.B. Tsang( 曾敏兒 ) 1,2*, Yingxun Zhang( 张英逊 ) 1,3, P. Danielewicz 1,2, M. Famiano 4, Zhuxia Li( 李祝霞 ) 3, W.G. Lynch( 連致標 ) 1,2, A. W. Steiner

More information

arxiv:astro-ph/ v2 24 Apr 2001

arxiv:astro-ph/ v2 24 Apr 2001 Neutron Star Structure and the Neutron Radius of 208 Pb C. J. Horowitz Nuclear Theory Center and Dept. of Physics, Indiana University, Bloomington, IN 47405 J. Piekarewicz Department of Physics Florida

More information

THE PYGMY DIPOLE CONTRIBUTION TO POLARIZABILITY: ISOSPIN AND MASS-DEPENDENCE

THE PYGMY DIPOLE CONTRIBUTION TO POLARIZABILITY: ISOSPIN AND MASS-DEPENDENCE TH PYGMY DIPOL CONTRIBUTION TO POLARIZABILITY: ISOSPIN AND MASS-DPNDNC V. BARAN 1, A.I. NICOLIN 1,2,, D.G. DAVID 1, M. COLONNA 3, R. ZUS 1 1 Faculty of Physics, University of Bucharest, 405 Atomistilor,

More information

Effects of n-p Mass Splitting on Symmetry Energy

Effects of n-p Mass Splitting on Symmetry Energy Effects of n-p Mass Splitting on Symmetry Energy Li Ou1,2 Zhuxia Li3 Bao-An Li1 1 Department of Physics and Astronomy Texas A&M University-Commerce, USA 2 College of Physics and Technology Guangxi Normal

More information

Effective Field Theory for Nuclear Physics! Akshay Vaghani! Mississippi State University!

Effective Field Theory for Nuclear Physics! Akshay Vaghani! Mississippi State University! Effective Field Theory for Nuclear Physics! Akshay Vaghani! Mississippi State University! Overview! Introduction! Basic ideas of EFT! Basic Examples of EFT! Algorithm of EFT! Review NN scattering! NN scattering

More information

Isospin asymmetry in stable and exotic nuclei

Isospin asymmetry in stable and exotic nuclei Isospin asymmetry in stable and exotic nuclei by Xavier Roca-Maza TESI PRESENTADA PER A OPTAR AL GRAU DE DOCTOR DATA 23 de Març del 2010 Programa de Doctorat Física Avançada del Departament d Estructura

More information

Calculations for Asymmetric Nuclear matter and many-body correlations in Semi-classical Molecular Dynamics

Calculations for Asymmetric Nuclear matter and many-body correlations in Semi-classical Molecular Dynamics Calculations for Asymmetric Nuclear matter and many-body correlations in Semi-classical Molecular Dynamics M. Papa Istituto Nazionale di Fisica Nucleare Sezione di Catania V. S.Sofia 64 9513 Catania Italy

More information

Some new developments in relativistic point-coupling models

Some new developments in relativistic point-coupling models Some new developments in relativistic point-coupling models T. J. Buervenich 1, D. G. Madland 1, J. A. Maruhn 2, and P.-G. Reinhard 3 1 Los Alamos National Laboratory 2 University of Frankfurt 3 University

More information

Evolution Of Shell Structure, Shapes & Collective Modes. Dario Vretenar

Evolution Of Shell Structure, Shapes & Collective Modes. Dario Vretenar Evolution Of Shell Structure, Shapes & Collective Modes Dario Vretenar vretenar@phy.hr 1. Evolution of shell structure with N and Z A. Modification of the effective single-nucleon potential Relativistic

More information

Nuclear matter inspired Energy density functional for finite nuc

Nuclear matter inspired Energy density functional for finite nuc Nuclear matter inspired Energy density functional for finite nuclei: the BCP EDF M. Baldo a, L.M. Robledo b, P. Schuck c, X. Vinyes d a Instituto Nazionale di Fisica Nucleare, Sezione di Catania, Catania,

More information

Constraining the nuclear EoS by combining nuclear data and GW observations

Constraining the nuclear EoS by combining nuclear data and GW observations Constraining the nuclear EoS by combining nuclear data and GW observations Michael McNeil Forbes Washington State University (Pullman) and University of Washington A Minimal Nuclear Energy Density Functional

More information

Nuclear physics input for the r-process

Nuclear physics input for the r-process Nuclear physics input for the r-process Gabriel Martínez Pinedo INT Workshop The r-process: status and challenges July 28 - August 1, 2014 Nuclear Astrophysics Virtual Institute Outline 1 Introduction

More information

Symmetry energy within the BHF approach

Symmetry energy within the BHF approach Symmetry energy within the BHF approach Isaac Vidaña 1, Constança Providência 1, A. Polls 3 and Arnau Rios 3 1 Centro de Física Computacional. Deparment of Physics, University of Coimbra, PT-34-516 Coimbra

More information

Nuclear Astrophysics

Nuclear Astrophysics Nuclear Astrophysics III: Nucleosynthesis beyond iron Karlheinz Langanke GSI & TU Darmstadt Tokyo, November 18, 2008 Karlheinz Langanke ( GSI & TU Darmstadt) Nuclear Astrophysics Tokyo, November 18, 2008

More information

Isoscalar dipole mode in relativistic random phase approximation

Isoscalar dipole mode in relativistic random phase approximation Isoscalar dipole mode in relativistic random phase approximation arxiv:nucl-th/0003041v1 20 Mar 2000 D. Vretenar 1,2, A. Wandelt 1, and P. Ring 1 1 Physik-Department der Technischen Universität München,

More information

Motivation Density functional theory H(F) RPA Skyrme, Gogny or Relativistic

Motivation Density functional theory H(F) RPA Skyrme, Gogny or Relativistic New Skyrme energy density functional for a better description of spin-isospin resonances Xavier Roca-Maza Dipartimento di Fisica, Università degli Studi di Milano and INFN, via Celoria 16, I-2133 Milano,

More information

Nuclear symmetry energy and neutron star cooling

Nuclear symmetry energy and neutron star cooling Nuclear symmetry energy and neutron star cooling Nguyen Van Giai(1), Hoang Sy Than(2), Dao Tien Khoa(2), Sun Bao Yuan(3) 2 1) Institut de Physique Nucléaire, Univ. Paris-Sud 2) VAEC, Hanoi 3) RCNP, Osaka

More information

Momentum dependence of symmetry energy

Momentum dependence of symmetry energy Momentum dependence of symmetry energy Joint DNP of APS & JPS October 7-11, 2014 Kona, HI, USA 曾敏兒 Betty Tsang, NSCL/MSU Equation of State of Asymmetric Nuclear Matter E/A (, ) = E/A (,0) + 2 S( ) = (

More information