Electric Dipole Response Neutron Skin and Symmetry Energy

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Electric Dipole Response, Neutron Skin, and Symmetry Energy Atsushi Tamii Research Center for Nuclear

Electric Dipole Response, Neutron Skin, and Symmetry Energy Atsushi Tamii Research Center for Nuclear Physics (RCNP) Osaka University, Japan CNS Summer School 2013 August 28 – September 3, 2013 1

Outline of the lecture 1. Symmetry energy • mass formula • nuclear density distribution

Outline of the lecture 1. Symmetry energy • mass formula • nuclear density distribution • nuclear equation of state (EOS) 2. Determination the neutron skin thickness and the symmetry energy by using • weak interaction • strong interaction • electro-magnetic interaction

Mass Formula What is the origin or the asymmetry term? Bethe-Weizsäcker semi-empirical mass formula

Mass Formula What is the origin or the asymmetry term? Bethe-Weizsäcker semi-empirical mass formula

Asymmetry (Symmetry) Energy Origin of the asymmetry term Stronger attraction in a pn pair

Asymmetry (Symmetry) Energy Origin of the asymmetry term Stronger attraction in a pn pair than nn (pp) Maximum number of pn-pairs when N=Z for a fixed A. p n T=0 Stronger attraction due to tensor force T=1 charge symmetry isospin symmetry T=1 Fermi-particle (Pauli exclusion) effect Higher orbits must be occupied when N≠Z. Z = N Z ≠ N

Charge Density Distribution of Nuclei Charge density Measured by electron elastic scattering Charge density

Charge Density Distribution of Nuclei Charge density Measured by electron elastic scattering Charge density distribution Sugimoto and Sugiyama, Nuclear Structure 5

Nuclear Density Distribution Schematic Illustration Why the nuclear density distribution has this kind of

Nuclear Density Distribution Schematic Illustration Why the nuclear density distribution has this kind of shape? Density distribution of 208 Pb, studied by proton and electron elastic scatterings. J. Zenihiro et al. , Phys. Rev. C 82, 044611 (2010).

Nuclear Density Distribution of typical heavy nuclei 1. constant inner density (saturation density) independent

Nuclear Density Distribution of typical heavy nuclei 1. constant inner density (saturation density) independent of A 2. surface diffuseness independent of A Schematic Illustration Why the nuclear density distribution has this kind of shape? 3. very small difference of the radius between p and How the difference (neutron skin thickness) is made?

Saturation of Density ~0. 16 fm-3 Nucleon-nucleon interaction 1 S 0 Channel Symmetric nuclear

Saturation of Density ~0. 16 fm-3 Nucleon-nucleon interaction 1 S 0 Channel Symmetric nuclear matter N=Z Short range interaction 1 -2 fm A nucleon only interacts with neighboring nucleons and the volume energy is independent on A. Attraction due to pion-exchange Energy increase at higher-density: 1. density dependence of the tensor interaction. 2. exchange interaction 3. short range repulsive core of the NN interaction and 3 NF…

Infinite nuclear matter Nuclear Matter SHF Symmetric (N=Z) E/A RMF -16 Me. V 0.

Infinite nuclear matter Nuclear Matter SHF Symmetric (N=Z) E/A RMF -16 Me. V 0. 16 fm-3 Courtesy of H. Sagawa

Nuclear Density Distribution of typical heavy nuclei 1. constant inner density (saturation density) independent

Nuclear Density Distribution of typical heavy nuclei 1. constant inner density (saturation density) independent of A 2. surface diffuseness independent of A Schematic Illustration Why the nuclear density distribution has this kind of shape? 3. very small difference of the radius between p and How the difference (neutron skin thickness) is made?

diffuseness tunneling Surface diffuseness is created 1. mainly by the tunneling effect of the

diffuseness tunneling Surface diffuseness is created 1. mainly by the tunneling effect of the bound nucleons in the nuclear potential 2. and by the zero-point oscillation of the nuclear shape.

Nuclear Density Distribution of typical heavy nuclei 1. constant inner density (saturation density) independent

Nuclear Density Distribution of typical heavy nuclei 1. constant inner density (saturation density) independent of A 2. surface diffuseness independent of A Schematic Illustration Why the nuclear density distribution has this kind of shape? 3. very small difference of the radius between p and How the difference (neutron skin thickness) is made?

Equation of State (EOS) Thermodynamics Pressure in the equilibrium condition is expressed as a

Equation of State (EOS) Thermodynamics Pressure in the equilibrium condition is expressed as a function of other state variables, e. g. volume, temperature, mol number. The equation depends on the system. EOS of the ideal gas Nuclear Equation of State Energy per nucleon of nuclear matter in the equilibrium condition is expressed as a function of nucleon density (r), asymmetry parameter (d), and temperature (T).

Nuclear Equation of State (EOS) EOS for energy per nucleon (at T=0, no Coulomb)

Nuclear Equation of State (EOS) EOS for energy per nucleon (at T=0, no Coulomb) EOS of symmetric nuclear matter Saturation Density ~0. 16 fm-3 Symmetry energy originates from 1. stronger attraction in a pn pair than an nn or pp pair. 2. Fermi particle nature. larger number of particles -> occupation of higher orbit.

E/A (Me. V) Neutron Matter (d=1) 核子当たりのエネルギー E/N (Me. V) Nuclear Equation of State

E/A (Me. V) Neutron Matter (d=1) 核子当たりのエネルギー E/N (Me. V) Nuclear Equation of State (EOS) Neutron Density (fm-3) Neutron Matter (d=1) Symmetry Energy (and Coulomb) Nuclear Matter (d=0) Nucleon Density (fm-3) Steiner et al. , Phys. Rep. 411 325(2005) Prediction of the neutron matter EOS is much model dependent.

My “simple explanation” of the correlation between the neutron skin thickness and the slope

My “simple explanation” of the correlation between the neutron skin thickness and the slope parameter (L) Density distribution of protons and neutrons in a nucleus Neutron density Proton density Neutron rms radius Proton rms radius

A naive explanation of the correlation between the neutron skin thickness and the slope

A naive explanation of the correlation between the neutron skin thickness and the slope parameter (L) ignoring Coulomb Smaller Sd 2 at higher r Larger Sd 2 at lower r larger skin

A naive explanation of the correlation between the neutron skin thickness and the slope

A naive explanation of the correlation between the neutron skin thickness and the slope parameter (L) ignoring Coulomb Larger Sd 2 at higher r Smaller Sd 2 at lower r smaller skin

A naive explanation of the correlation between the neutron skin thickness and the slope

A naive explanation of the correlation between the neutron skin thickness and the slope parameter (L) ignoring Coulomb Larger Sd 2 at higher r Smaller Sd 2 at lower r smaller skin Neutron skin thickness Density dependence of the symmetry energy Energy minimization = equilibrium condition

Correlation between the Neutron Skin Thickness of 208 Pb and the Slope Parameter (L)

Correlation between the Neutron Skin Thickness of 208 Pb and the Slope Parameter (L) X. Roca-Maza et al. , PRL 106, 252501 (2011) 208 Pb

Neutron Density (fm-3) E/A (Me. V) Neutron Matter (d=1) 核子当たりのエネルギー E/N (Me. V) Nuclear

Neutron Density (fm-3) E/A (Me. V) Neutron Matter (d=1) 核子当たりのエネルギー E/N (Me. V) Nuclear Equation of State (EOS) Neutron Matter (d=1) Symmetry Energy (and Coulomb) Nuclear Matter (d=0) Nucleon Density (fm-3) Steiner et al. , Phys. Rep. 411 325(2005)

Type II Supernova Langanke and Martinez-Pinedo Supernova Cycle

Type II Supernova Langanke and Martinez-Pinedo Supernova Cycle

Determination of the Symmetry Energy Term in EOS. Neutron Star Mass and Radius Core-Collapse

Determination of the Symmetry Energy Term in EOS. Neutron Star Mass and Radius Core-Collapse Supernova K. Sumiyoshi, Astrophys. J. 629, 922 (2005) Nucleosynthesis Langanke and Martinez-Pinedo Neutron Star Cooling Lattimer et al. , Phys. Rep. 442, 109(2007) Neutron Star Structure Accreting neutron star/white dwarf, X-Ray burst, Superburst http: //www. astro. umd. edu/~miller/nstar. html

Neutron Star Fundamental Questions: How large and stiff is a neutron star? How is

Neutron Star Fundamental Questions: How large and stiff is a neutron star? How is the inner structure? How much content of protons and electrons? Do meson-condensed states or hyperons exist? For answering to the questions, precise knowledge is required for the EOF of nuclear and neutron rich matter. http: //www. astro. umd. edu/~miller/nstar. html

X. Roca-Maza et al. , PRL 106, 252501 (2011)

X. Roca-Maza et al. , PRL 106, 252501 (2011)

Summary of the part 1 I have discussed the followings. • origin of the

Summary of the part 1 I have discussed the followings. • origin of the symmetry energy • how the nuclear density distribution is created • relation between the neutron skin thickness and the symmetry energy • nuclear equation of state

Electric Dipole Response Neutron Skin and Symmetry EnergyElectric Dipole Response Neutron Skin and Symmetry Energy
Electric Dipole Radiation The image shows electric dipoleElectric Dipole Radiation The image shows electric dipole
Selection Rules Electric Dipole Selection Rules Electric DipoleSelection Rules Electric Dipole Selection Rules Electric Dipole
The Hertz Antenna Dipole Dipole Fundamentals A dipoleThe Hertz Antenna Dipole Dipole Fundamentals A dipole
Symmetry Line Symmetry n Shape has line symmetrySymmetry Line Symmetry n Shape has line symmetry
3 1 Symmetry Symmetry All Around Us Symmetry3 1 Symmetry Symmetry All Around Us Symmetry
Plane Symmetry Plane Symmetry A plane of symmetryPlane Symmetry Plane Symmetry A plane of symmetry
Symmetry Monarch butterfly bilateral symmetry mirror symmetry WheneverSymmetry Monarch butterfly bilateral symmetry mirror symmetry Whenever
Symmetry Concept 39 symmetry line of symmetry rotationalSymmetry Concept 39 symmetry line of symmetry rotational
Symmetry Monarch butterfly bilateral symmetry mirror symmetry 153Symmetry Monarch butterfly bilateral symmetry mirror symmetry 153
symmetry line of symmetry rotational symmetry center ofsymmetry line of symmetry rotational symmetry center of
SYMMETRY LINE SYMMETRY A line symmetry occurs inSYMMETRY LINE SYMMETRY A line symmetry occurs in
Symmetry Line Symmetry A figure has line symmetrySymmetry Line Symmetry A figure has line symmetry
Symmetry Ahhhh Isnt symmetry wonderful Symmetry is allSymmetry Ahhhh Isnt symmetry wonderful Symmetry is all
ELECTRIC POTENTIAL ENERGY ELECTRIC ENERGY ELECTRIC POTENTIAL VELECTRIC POTENTIAL ENERGY ELECTRIC ENERGY ELECTRIC POTENTIAL V
Electric Potential Electric Potential Energy Electric Potential EnergyElectric Potential Electric Potential Energy Electric Potential Energy
Electric Dipole Moment of Neutron and Neutrinos JenChiehElectric Dipole Moment of Neutron and Neutrinos JenChieh
Neutron and electron electric dipole moments Ben SauerNeutron and electron electric dipole moments Ben Sauer
Improved search for the neutron electric dipole momentImproved search for the neutron electric dipole moment
Neutron Electric Dipole Moment Rajan Gupta Los AlamosNeutron Electric Dipole Moment Rajan Gupta Los Alamos
The neutron electric dipole moment experiment at PSIThe neutron electric dipole moment experiment at PSI
Neutron Electric Dipole Moment Sham Chun Hong SpinDressingNeutron Electric Dipole Moment Sham Chun Hong SpinDressing
Full QCD Calculation of Neutron Electric Dipole MomentFull QCD Calculation of Neutron Electric Dipole Moment
4 quark operator contributions to neutron electric dipole4 quark operator contributions to neutron electric dipole