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

Outline of the lecture Symmetry energy mass formula nuclear density distribution nuclear equation of state (EOS) 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

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

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

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

Nuclear Density Distribution of typical heavy nuclei 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?

Symmetric nuclear matter Saturation of Density ~0.16 fm-3 Nucleon-nucleon interaction 1S0 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 3NF…

-16 MeV 0.16 fm-3 Infinite nuclear matter SHF RMF E/A Nuclear Matter Symmetric (N=Z) E/A -16 MeV 0.16 fm-3 Courtesy of H. Sagawa 9

Nuclear Density Distribution of typical heavy nuclei 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 bound nucleons in the nuclear potential 2. and by the zero-point oscillation of the nuclear shape.

Nuclear Density Distribution of typical heavy nuclei 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 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) EOS of symmetric nuclear matter Saturation Density ~0.16 fm-3 Symmetry energy 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.

Nuclear Equation of State (EOS) Neutron Matter (d=1) Neutron Matter (d=1) 核子当たりのエネルギー E/N (MeV) E/A (MeV) Symmetry Energy (and Coulomb) Nuclear Matter (d=0) Neutron Density (fm-3) 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 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 parameter (L) ignoring Coulomb Smaller Sd2 at higher r Larger Sd2 at lower r larger skin

A naive explanation of the correlation between the neutron skin thickness and the slope parameter (L) ignoring Coulomb Larger Sd2 at higher r Smaller Sd2 at lower r smaller skin

A naive explanation of the correlation between the neutron skin thickness and the slope parameter (L) ignoring Coulomb Larger Sd2 at higher r Smaller Sd2 at lower r smaller skin Neutron skin thickness Energy minimization = equilibrium condition Density dependence of the symmetry energy

Correlation between the Neutron Skin Thickness of 208Pb and the Slope Parameter (L) X. Roca-Maza et al., PRL106, 252501 (2011) 208Pb

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

Type II Supernova Langanke and Martinez-Pinedo Supernova Cycle 22

Determination of the Symmetry Energy Term in EOS. Neutron Star Mass and Radius Core-Collapse Supernova K. Sumiyoshi, Astrophys. J. 629, 922 (2005) Nucleosynthesis Lattimer et al., Phys. Rep. 442, 109(2007) Langanke and Martinez-Pinedo Neutron Star Cooling 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 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., PRL106, 252501 (2011)

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