1. 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

2. 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

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

4. 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

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

6. 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, (2010).

7. 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?

8. 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…

9. -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

10. 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?

11. 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.

12. 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?

13. 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).

14. 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.

15. 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 (2005)
Prediction of the neutron matter EOS is much model dependent.

16. 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

17. 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

18. 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

19. 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

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

21. 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 (2005)

22. Type II Supernova
Langanke and Martinez-Pinedo
Supernova Cycle 22

23. 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

24. 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.

25. X. Roca-Maza et al., PRL106, (2011)

26. 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