From atomic nuclei to neutron stars

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From atomic nuclei to neutron stars
Atomic nucleus

• Piotr Magierski
• (Warsaw University of Technology)

5th International Student Conference of Balkan
Physical Union
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Nuclear Landscape
126
Stable nuclei
82
r-process
known nuclei
Terra incognita
50
protons
82
rp-process
neutron stars
28
20
50
8
28
neutrons
2
20
8
2
3
What are the basic degrees of freedom of a
nuclear system?
It depends on the energy scale we are interested?
LOW ENERGY NUCLEAR PHYSICS- - PHYSICS OF ATOMIC
NUCLEI
Collective degrees of freedom 1MeV
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Nucleon-nucleon (N-N) interaction is an effective
interaction
N-N force can be determined (except for the
three-body term) from the proton-proton and
proton-neutron scattering experiments.
Results of solving Schroedinger eq. with N-N
potential. Blue only two-body terms
included. Red two-body and three-body
terms. Green experiment.
3-body interaction is important!
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Can we solve Schroedinger eq. for medium or heavy
nuclei? Can we calculate the wave function for
medium and heavy nuclei?
How many points inside the volume V do we need?
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Not possible now and never will be!!!
Nuclear wave function contains too much
information
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Why now? What nuclear theorists have been doing
for more than half century?
Short history of nuclear theory
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• Further work on the theory
• of N-N interaction (60s-70s)
• Semiphenomenological potentials
• Bonn potential, Paris potential.
• Calculations for deuteron, triton, helium.
• -Problems with short range.

• 60s-70s
• - More accurate average potentials
• have been introduced Nilsson potential,
• Woods-Saxon potential.
• - Liquid drop formula has been improved
• - more terms added (more parameters).
• First attempts to derive the average potential
• from some phenomenological N-N interaction
• (density dependent, no hard core)
• Hartree-Fock method
• Many successes in interpreting experimental
• spectroscopic data in terms of single-nucleon
• excitations, rotations of the whole nucleus,
• vibrations and mutual coupling between these
• modes.

• 70s-80s
• Quantum Chromodynamics (QCD)
• is born strong interaction is mediated
• by gluons (8) between quarks.
• Meson theory is an effective low
• energy theory.
• Problem QCD is nonperturbative at low
• energies

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80s-90s The shell model and liquid drop formula
reached the limit of their usefulness too many
parameters, too much phenomenology, too little
physical insight. - More sophisticated
phenomenological interactions were used not only
to generate an average potential, but also to
calculate properties of excited states of heavy
nuclei (effective many-body methods
RPA,GCM,TDHF). Problem how to link this
phenomenological N-N interaction with real N-N
interaction?
Effective field theory (EFT) is developed
(80s-90s) Allows to consistently
formulate the effective quantum theory at low
energies using the experimental information as
well as information from more fundamental
theory (symmetries). Progress in
computational abilities Properties of heavier
nuclei (Alt10) were calculated using EFT input.
EFT provides a missing link between real N-N
interaction and phenomenological N-N
interaction! Eventually it will help to construct
the Universal Energy Density Functional for
nuclear systems
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Neutron star discovery

• The existence of neutron stars was predicted by
  Landau (1932), Baade Zwicky (1934) and
• Oppenheimer Volkoff (1939).
• On November 28, 1967, Cambridge graduate student
  Jocelyn Bell (now Burnell) and her advisor,
• Anthony Hewish discovered a source with an
  exceptionally regular pattern of radio flashes.
  These
• radio flashes occurred every 1 1/3 seconds like
  clockwork. After a few weeks, however, three more
  
• rapidly pulsating sources were detected, all
  with different periods. They were dubbed
  "pulsars."

Nature of the pulsars
Pulsar in the Crab Nebula
pulse rate 30/second slowing down rate 38
nanoseconds/day
Calculated energy loss due to rotation of a
possible neutron star
Energy radiated
Conclusion the pulses are produced by rotation!
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Basic facts about neutron stars
Radius 10 km Mass 1-2 solar
masses Average density Magnetic field
G Magnetars
G Rotation period 1.5 msec. 5 sec.
Number of known pulsars gt 1000 Number of pulsars
in our Galaxy
Gravitational energy of a nucleon at the
surface of neutron star
100 MeV
Binding energy per nucleon in an atomic nucleus
8 MeV
Neutron star is bound by gravitational force
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Thermal evolution of a neutron star
Temperature 50 MeV 0.1 MeV URCA
process
g
g
Crust
Temperature 0.1 MeV 100eV MURCA
process
ne
What are the basic degrees of freedom of nuclear
matter at various densities?
URCA MURCA
ne
ne
Energy transfer between core and surface
Core
T
core
ne
g
T
For t lt 100 years
g
surf
Tcore lt Tsurf
Cooling wave
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Why the neutron star is made of neutrons?
Lets assume that the star consists of 3 types of
noninteracting Fermi gases
Energy
Since electron are about 2000 lighter than
nucleons the density of states of electron gas
is much smaller.
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Structure of the neutron star
The stability of the neutron star is a result of
the balance between the gravitational attraction
and the pressure of the matter forming the star.
Hydrostatic stability condition
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Ideal Fermi gas nonrelativistic (T0K) Ideal
ultrarelativistic Fermi gas (T0K)
The equation of state
determines the size and the mass of the star
through the requirement
The equation of state of nuclear matter for
the density range up to 10 nuclear densities is
needed!
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What information do we need from physics of
atomic nuclei?
Let us consider the simplest version of the
liquid drop formula
Which terms are important in the context of
neutron stars?
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Crystalline solid
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Nuclei
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Electrons
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Nuclei
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Outer crust
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Inner crust
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Core
Uniform nuclear matter
Neutrons
Exotic nuclear shapes pasta phase
Quark-gluon plasma?