Spin%20polarization%20phenomena%20in%20dense%20nuclear%20matter

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Spin polarization phenomena in dense nuclear
matter

• Alexander Isayev
• Kharkov Institute of
• Physics and Technology
• Ukraine

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• OVERVIEW AND MOTIVATION
• The spontaneous appearance of spin polarized
  states in nuclear matter is the topic of a great
  current interest.
• Could nuclear matter, formed in heavy ion
  collisions at high and intermediate energies,
  undergo a phase transition to a spin polarized
  state?

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• OVERVIEW AND MOTIVATION
• The spontaneous appearance of spin polarized
  states in nuclear matter is the topic of a great
  current interest.
• Could nuclear matter, formed in heavy ion
  collisions at high and intermediate energies,
  undergo a phase transition to a spin polarized
  state?
• Spin correlations in the medium significantly
  influence the neutrino cross section and
  neutrino luminocity. Hence, different scenarios
  of supernova explosion and cooling of neutron
  stars can be realized, depending on whether
  nuclear matter is spin polarized or not.

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• OVERVIEW AND MOTIVATION
• Precisely Nucleons possess spin. Hence,
  nuclear matter is a paramagnetic medium and under
  lowering temperature or changing density nuclear
  matter can undergo a phase transition to the
  state with nonequal numbers of spin-up and
  spin-down nucleons spin polarized state.
  Usually majority of neutron spins are aligned in
  the same direction as majority of proton spins
  (like ferromagnetic ordering).
• Another possibility majority of neutron spins
  and majority of proton spins have the opposite
  directions (like antiferromagnetic ordering).
• Main emphasis the structure of a ground state
  of nuclear matter, whether it is spin polarized
  or not and what type of spin ordering can be
  realized.

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• OVERVIEW AND MOTIVATION
• The possibility of ferromagnetic phase transition
  in nuclear and neutron matter
• Calculations of magnetic susceptibility with
  Skyrme effective forces
• A. Viduarre, J. Navarro, and J. Bernabeu,
  Astron. Astrophys.
• 135, 361 (1984). Ferromagnetic transition occurs
  at
• The Fermi liquid criterion for the ferromagnetic
  instability in nuclear matter with Skyrme
  interaction is reached at
• being nuclear matter saturation density.
• S. Reddy, M. Prakash, J.M. Lattimer, and J.A.
  Pons, Phys. Rev. C 59, 2888 (1999).

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• In the models with realistic nucleon-nucleon (NN)
  interaction the ferromagnetic phase transition
  seems to be suppressed up to densities well above
  .

I. Vidana, A. Polls, and A. Ramos, Phys. Rev. C
65, 035804 (2002). S. Fantoni, A. Sarsa, and E.
Schmidt, Phys. Rev. Lett. 87, 181101 (2001).
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Here the study of spin polarizability of
nuclear matter with the use of effective NN
interaction (Skyrme, Gogny effective
forces). Framework for consideration Fermi
liquid (FL) description of nuclear matter,
allowing to obtain the self-consistent equations
for the order parameters, and, after solving
them, to calculate the free energy and to make
conclusions concerning thermodynamic stability of
different phases.
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Basics of Formalism
Normal states of nuclear matter are described
by the normal distribution function of nucleons
The matrix
self-consistent equation for in the state
of thermodynamic equilibrium The
single-particle energy
and
is the density matrix of the system
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Structure of the normal distribution function
and single particle energy
are the Pauli matrices in spin and isospin spaces
Normalization conditions for the distribution
functions
- the isospin asymmetry parameter
FM spin order parameter
AFM spin order parameter
In symmetric nuclear matter with FM ordering
AFM ordering
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The energy functional of the system
FL amplitudes
describe density, spin, isospin and spin-isospin
correlations in nuclear medium.
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Self-consistent equations
Set of integral equations to be solved
self-consistently. Numerical procedure
iterations on the Gaussian grid in momentum
space until convergence with required accuracy is
achieved.

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Amplitude of NN interaction for Skyrme effective
force
In numerical calculations SLy4, SkI3, SkI5
parametrizations
Amplitude of NN interaction for Gogny effective
force
Two Gaussian terms reflect the finite range
character of the Gogny interaction. In numerical
calculations D1S force.
Neutron and proton spin polarization parameters
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SLy4 1. Antiparallel ordering only! 2. Even
small admixture of protons to neutron matter
strongly decreases the onset density of spin
instability. 3. Protons become totally polarized
in a narrow density domain at strong isospin
asymmetry, unlike to neutrons.
Neutron and proton spin polarization parameters
as functions of density at zero temperature
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SkI5 1. Parallel ordering only! 2. Small
admixture of protons to neutron matter
insignificantly change the onset density of spin
instability.
Neutron and proton spin polarization parameters
as functions of density at zero temperature
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The energy gain per nucleon is decreased with
isospin asymmetry for SLy4 force while it is
increased for SkI5 force.
Total energy per nucleon, measured from its value
in the normal state, as a function of density at
T0
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SkI3 1. Transient behavior from antiparallel
ordering to parallel ordering under increasing
density. 2. There are no long tails in the
density profile of neutrons at strong isospin
asymmetry. 3. The energy gain is increasing
function of isospin asymmetry at the given
density.
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Symmetric nuclear matter
AFM spin polarization parameter as a function of
density at zero temperature for D1S Gogny force
and SkM, SGII Skyrme forces.
For D1S force only AFM spin ordering is realized
and there are no solutions, corresponding to FM
spin ordering.
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Total energy per nucleon, measured from its
value in the normal state, for the AFM spin
state as a function of density at zero
temperature for D1S Gogny force and SkM, SGII
Skyrme forces.
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CONCLUSIONS

• Thus, modern effective nuclear forces being
  relevant for calculations at wide range of
  isospin asymmetries and high densities provide us
  with different possible scenarios of a phase
  transition to a spin polarized state in dense
  nuclear matter
• a) nuclear matter with SLy4 Skyrme and D1S Gogny
  interactions undergoes at some critical density a
  phase transition to a spin polarized state with
  the oppositely directed spins of neutrons and
  protons
• b) for SkI5 interaction, a spin polarized state
  with the like-directed neutron and proton spins
  is formed
• c) nuclear matter with SkI3 interaction under
  increasing density, at first, undergoes a phase
  transition to the state with the opposite
  directions of neutron and proton spins, which
  goes over at larger density to the state with the
  same direction of nucleon spins.

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The different behavior at high densities of the
interaction amplitudes, describing spin-spin and
spin-isospin correlations, lays behind this
divergence in calculations with different
effective potentials. These results clearly
indicate the necessity to construct a new
generation of the energy functionals with the
properly constrained time-odd part. Probably,
these constraints will be obtained from the data
on the time decay of magnetic field of isolated
neutron stars. S.B. Popov and M.E. Prokhorov,
Surveys in High Energy Physics 15, (2001) 381.