JDiener_SKA09II
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Transcript JDiener_SKA09II
Ferromagnetism in neutron matter
...and how it could apply to neutron stars
JPW Diener1 , FG Scholtz1,2, HB Geyer1, GC Hillhouse3
1 Institute
of Theoretical Physics, Stellenbosch University
2 National Institute for Theoretical Physics, Stellenbosch
3 New York Institute of Technology, Nanjing, China
Introduction
We are investigating pulsar/neutron star
matter.
• One of the densest states of matter.
Aiming to better understand the magnetic
field of these stars.
Pulsars are made up (in part at least) of
nuclear matter.
We are investigating the spontaneous
magnetisation of neutron matter.
Ferromagnetism
Unmagnetised matter
(Ferro)magnetised matter
Ferromagnetism is a property of any system
that can undergo a phase transition from an
unmagnetised to a magnetised state.
Neutrons
Neutrons are neutral particles,
Neutron with the
magnetic dipole moment
with spin ±½.
Dipole moment reacts to a external magnetic
field.
Aligned dipole moments induce a magnetic
field.
Spontaneous magnetisation will occur if a
stable, lower energy (magnetic) configuration
is available.
Relativity
Relativistic description of ferromagnetism.
Relativity: Albert Einstein’s most famous
equation:
E = mc 2
More general form: E 2 = p2c 2 + m2c 4
Considering plane waves solution and natural
2
2
2
units (ћ = c = 1)
E = k +m
Non-relativistic energy-momentum
2
relationship:
k
E=
2m
Neutron matter dispersion relationship
Magnetic neutron matter
Including the magnetic field in a relativistic
fashion, the energy-momentum relationship is
2
modified: 2
E = kz 2 + k2 + m2 ± bz
For zero momentum:
E = m ± bz
(External) magnetic field introduces a specific
direction, breaking spherical symmetry.
Neutron matter dispersion relationship (2)
Magnetised vs unmagnetised system
Ferromagnetic state
External magnetic field makes a lower energy
state available.
If lower energy state is favoured, a magnetic
field is induced.
Ferromagnetic state would be stable if the
induced magnetic field is equal to the external
field.
Conclusions and way forward
Have shown that lower energy state exists.
Strength of induced magnetic field as function
of density still unknown.
• To be calculated.
Compare to experimental known properties of
the neutron to determine accuracy.
If there is agreement, then we would be able
to predict at what densities a ferromagnetic
phase would present itself.
Acknowledgements
This research is support by the
SA SKA project,
and,
Stellenbosch University.