1. Neutron Stars
Aree Witoelar

2. What is a neutron star? A collapsed core of a massive star
Composed entirely from neutron
Incredibly high density

3. Creation of a neutron star
Fusion from H to Fe in the core of stars
No more fuel -> core reaches tremendous density and explodes (Supernova)
Inverse ß–decay takes place:

4. Properties Mass = 1.3-1.5 Msun (3.1030 kg) Radius = 10 km
Density = 1014g/cc
Magnetic field = 1012 Gauss

5. Interior
Increasing pressure inwards creates ‘Pasta’ layers

6. Nuclear Physics of Neutron Stars
Neutron stars are like giant neutron supernuclei
Testing models of Nuclei-Nuclei Interaction on neutron stars
Estimating Neutron Star radius:
Binding Energy
Fermi Gas model
Nuclei-Nuclei Interaction (first principles)

7. Binding Energy Binding energy for a nucleus
Assumptions for a huge ‘neutron nucleus’:
No Coulomb energy
Neglect pairing energy
Neglect surface term with respect to volume term

8. Binding Energy (2) Simplified Binding energy
Bound state exist if binding energy is positive
Filling the constants, the result is
A = 5 x 1055
R = 4.3 km
M = solar mass
Same order of magnitude as observations

9. Fermi Gas model
Treat neutron stars as degenerate Fermi gases (of neutrons) held by gravity
Assume
Constant density: average pressure
No nucleon-nucleon interaction
Number of possible states
Integrate to Fermi momentum pF

10. Fermi Gas model (2)
Calculate <Ekin/N> from Fermi momentum and <Epot /N> from gravitational energy
Minimize total of kinetic and potential energy
The results are
R = 12 km
 = 0.25 nucleons/fm3 (nucleus = 0.17 nucleons/fm3 )
Close to experimental values: gravitational pressure compensated by Fermi pressure and nucleon-nucleon repulsion

11. Nucleon-Nucleon Interaction
Nuclear force is an interaction between colourless nucleons with range of the same order of magnitude as the nucleon diameter
It is not possible to extract n-n potential directly from structure of nucleus
Different models with different parameterization

12. General form of n-n potential
Quantities to determine interaction
Separation of nucleons x
Relative momenta p
Total orbital angular momentum L
Relative orientation of spins s1 and s2
Potential is scalar
Symmetric under exchange of the two nuclei
central
spin-spin
Tensor
spin-orbit

13. -meson theory
Nucleons are surrounded by field of massive (virtual) particles called -mesons (pions)
Pion could be absorbed by another nucleon in its lifetime
Momentum transfer -> akin to force (but attractive)
Direct analogy of EM force but photons have no mass, pion have mass of 140 MeV/c2 -> finite range
Heisenberg uncertainty principle

14. Covalent and Meson exchange
Covalent bonds (direct q-exchange) are suppressed by color restriction
Meson exchange: color-neutral
Yukawa potential:

15. Equation of State
The relations between the density and temperature to its pressure and internal energy, specific heats, etc.
Pure neutron matter is unbound

16. Many-Body Theory Hamiltonian:
Four-body and higher order interaction are neglected

17. Neutron Star Radius
Different models have different parameterizations of vijR

18. Summary Neutron stars are interesting!
Nuclear Physics: Approximate Neutron Star radius with Binding Energy, Fermi Gas model, or Nucleon-Nucleon interaction
Nucleon-Nucleon interaction is caused by meson exchange (virtual particles)
Different n-n models predict different radii of neutron stars