Nuclear Symmetry Energy and its Density Dependence. Chang Xu Department of Physics, Nanjing University. Wako, Japan

Transcription

1 Nuclear Symmetry Energy and its Density Dependence Chang Xu Department of Physics, Nanjing University Wako, Japan

2 Outline 1. Brief Review: Nuclear symmetry energy 2. What determines the symmetry energy? A modelindependent theorem and symmetry energy formula 3. New/direct way to determine the symmetry energy and its slope at saturation density: Global optical potential (I) and Cluster radioactivity (II) 4. Why the symmetry energy at high-density is so uncertain? 5. A brief summary

3 Nuclear symmetry energy (finite nuclei) The density dependence of nuclear symmetry energy ----an important issue in both nuclear physics and astrophysics Liquid drop model of finite nuclei Properties of neutron stars

4 Nuclear symmetry energy (nuclear matter) The density dependence of nuclear symmetry energy ----an important issue in both nuclear physics and astrophysics symmetry energy Isospin asymmetry ρn ρp E( ρn, ρp) = E0 ( ρn = ρp) + Es ym( ρ) ο δ ( ) 1 ρ 2 Energy 1per 3 nucleon 1 in symmetric nuclear 8matter 8 Energy per nucleon in asymmetric nuclear matter

5 A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. 411, 325 (2005). n/p γ π - /π + t/ 3 He K + /K 0 Isospin physics in Terrestrial Labs isodiffusion isotransport isocorrelation isofractionation isoscaling

6 Recent progress: 1 Experimentally, some constraints on E sym at subsaturation densities (ρ< ρ 0 ) have been obtained recently from analyzing nuclear reaction data. 2 E sym at normal nuclear density is known to be around 30MeV from analyzing nuclear masses and other data. 3 At supra-saturation densities (ρ> ρ 0 ), however, the situation is much less clear because of the very limited data available.

7 Questions: Is there a general principle at some level, independent of the interaction and many-body theory, telling us what determines the symmetry energy and its slope? Is there new and direct way to determine the symmetry energy and its slope at saturation density? Why the symmetry energy at high-density is so uncertain?

8 The HVH theorem

9 Q1: Theoretical Formulism Starting from the Hugenholtz Van Hove theorem that is a fundamental relation among the Fermi energy, the average energy per particle E and the pressure of the system P at the absolute temperature of zero. The nucleon single-particle potentials can be expanded as a power series isoscalar isovector (Lane potential)

10 Xu et. al, Phys. Rev. C 82, (2010) Xu et. al, Phys. Rev. C 81, (2010) Xu et. al, Phys. Rev. C 81, (2010) Xu et. al, Nucl. Phys. A 865, 1 (2011) Xu et. al, Nucl. Phys. A 913 (2013) 236 Xu et. al, Eur. Phys. J. A 50 (2014) 21 Xu et.al,phys. Rev. C 90, (2014)

11 Theoretical Formulism Comparing the coefficient of each term then gives the symmetry energy of any order Symmetry energy: kinetic energy part isoscalar potential part + isovector potential part (most

12 Connections between the symmetry energy and isoscalar and isovector parts of single-particle potential is explicitly shown. BUU: The Momentum dependent Interaction (MDI)

13 Theoretical Formulism The quadratic term E sym,2 is the most important. Microscopic calculations : higher-order terms are usually negligible, less than 1 MeV at ρ 0. At supra-saturation densities : modify the proton fraction in neutron stars and the cooling mechanism of proto-neutron stars

14 Density slope of symmetry energy The symmetry energy can be characterized by using the value of E sym (ρ 0 ) and the slope parameter L Density dependence L is important for : the size of the neutron skin in heavy nuclei, location of the neutron drip line, corecrust transition density and gravitational binding energy of neutron stars Momentum dependence

15 Q2: Symmetry energy and its slope at saturation density Method I and Method II Systematics based on world data accumulated since 1969: (1) Single particle energy levels from pick-up and stripping reaction (2) Neutron and proton scattering on the same target at about the same energy (3) Proton scattering on isotopes of the same element (4) (p,n) charge exchange reactions Method I

16 Constraining the symmetry energy near saturation density using global nucleon optical potentials C. Xu, B.A. Li and L.W. Chen, PRC 82, (2010).

17 Density slope of the symmetry energy L: particularly important for determining several critical quantities Xu et. al Nucl. Phys. A 913 (2013) 236 Xu et. al Eur. Phys. J. A 50 (2014) 21

18 Effect of the second-order symmetry potential U sym,2 in asymmetric nuclear matter on the slope parameter L Li et al. / Physics Letters B 721 (2013) Xu et. al Nucl. Phys. A 913 (2013) 236 Xu et. al Eur. Phys. J. A 50 (2014) 21

19 Cluster radioactivity Method II Alpha cluster emission Superheavy island Spontaneous fission Heavier cluster emission Chart of Nuclides

20 Importance of cluster radioactivity Ø Alpha decay/cluster radioactivty: an old problem but renewed interest in recent years Ø Superheavy nuclei Ø Nuclear properties: energy, lifetime, and nuclear spin and parity, nuclear interactions, deformation, clustering effect, shell effect. Ø Symmetry energy Ø Phenomenological Formulas: Ø The Geiger-Nuttall law, Viola-Seaborg formula, Other forms of decay formulas Ø Theoretical Approaches : Ø Shell model, Cluster model, Fission-like model, A mixture of shell and cluster model configurations.

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22 212 Po Pb +α Neutron skin Strong correlation Measured data Symmetry Energy

23 Symmetry energy and density slope extracted from cluster radioactivity

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27 Density slope of symmetry energy extracted from cluster radioactivity

28 Q3: Symmetry energy at supra-saturation density Some indications of a supersoft E sym at high densities have been obtained from analyzing the π + /π ratio data. Experiments have now been planned to investigate the highdensity behavior of the E sym at the CSR in China, GSI in Germany, MSU in the United States, and RIKEN in Japan. Possible physical origins of the very uncertain E sym at suprasaturation densities?

29 U U U + U 3 1 = = u + u U U 1 1 = = u u 2δ 4 4 n p 0 T1 T0 n p sym T1 T0 Effects of the spinisospin dependent three-body force U 0 : relatively well determined U sym :isosinglet vs isotriplet channels, However, the U sym is very poorly known especially at high momenta. Effects of the inmedium tensor force and nucleon correlation

30 Effects of the spin-isospin dependent three-body force Symmetry energy with different spin dependence x 0 and density dependence α in the three-body force (Gogny force) Qualitative analysis

31 Effects of short-range correlations induced by tensor force Symmetry energy with different values of the BRS parameter α BR = 0, 0.05, 0.10, 0.15, 0.20 using different values for the tensor correlation parameter. Qualitative analysis

32 Tensor correlation : high-momentum tail in the single nucleon distribution in symmetric nuclear matter (SNM) Predictions: Average kinetic energy in SNM: increased largely Kinetic energy part of nuclear symmetry energy: very small even negative

33 Support from the experimental side: high energy electron scattering with nuclei Jefferson Lab CLAS Collaboration

34 Support from the experimental works

35 Chang Xu et.al, Jour. of Phys: Conf. Seri., 420, (2013) Science paper data: E kin : 35 ~ 43MeV

36 Support from the experimental works Jefferson Lab CLAS Collaboration

37 Summary General expressions are derived for E sym and L by using the HVH theorem. E sym and L at normal density: extracted from the global optical potential [reaction] E sym and L at normal density: cluster radioactivity [decay] The reason why the E sym and L at supra saturation density so uncertain: isospin-dependence of the three-body force, tensor force and nucleon-nucleon correlation.

38 Thanks!

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41 Example from theoretical side: long paper 论 书 该论 观 补 动 对 质 [39-41]. 论 观计 证实 SRC 对对 动 应 们 论 论证实 论证实

42 Decay theory in textbooks (1) Preformation probability (2) Frequency (Pre-exponential factor) (3) Exponential factor

43 Decay theory in textbooks (1)Preformation probability (most difficult) This is not true for shell region nuclei!

44 Decay theory in textbooks (2) Frequency (Pre-exponential factor)

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46 Frequency Vs Well defined pre-factor

47 Decay theory in textbooks (3) Exponential factor

48 Alpha-decay half-lives of even-even nuclei of ground-state transitions (Z=52-104) Circles : Experiment Stars : Theory

49 The factor of agreement for odd nuclei of ground-state transitions (Z=52-105) Circles : HF=Texp / Tcal between experiment and theory

50 The experimental and calculated alpha-decay halflives of nuclei with Z= Deformation: the macroscopicmicroscopic model (MM) Deformation: the relativistic meanfield model (RMF) with a TMA force parameter

51 A constant alpha preformation factor is OK for open shell nuclei, but not for shell region nuclei! How to calculate the preformation factor and penetration factor microscopically? One must first test the theory for alpha decay of 212 Po

52 1. Single-nucleon potential: constrained by reaction data 2. Cluster-core potential: constrained by radioactivity data 3. Density slope of symmetry energy