Nuclear Thermometers

1
Nuclear Thermometers

• Theresa B. Conway
• Honors Thesis
• Presentation and Defense
• April 19, 2001

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What Does Nuclear Temperature Mean?

• We know that temperature in general is related to
  the kinetic energy of particles 3/2KT1/2mv2avg.
• A nucleus has particles like protons and neutrons
  bumping around it with some average Kinetic
  Energy.
• Nuclear temperature is related to the Kinetic
  Energy of nuclear particles.

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Nuclear Collisions

• If two nuclei collide, the energy from the
  collision can go into the production of particles
• High energy collisions allow heavy particles to
  be made
• Low energy nuclear collisions cannot generate
  heavy particles

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The Central Idea...

• At a given energy, more light particles are made
  and relatively fewer heavy particles are
  produced.
• Therefore, looking at the ratio of particles
  generated can give us an idea of the nuclear
  temperature.

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Why Find the Temperature?
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Nuclear Phase Diagram

• How can we reproduce a system that exhibits the
  quark-gluon plasma phase?
• With a nuclear collision, of course!!

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How do we find the temperature?

• We use a ratio of particles--A ratio of four
  particle densities allows us to cancel out
  systematic effects
• The individual Particle Density, nA, is a
  function of spin, s, chemical potential, ?, mass,
  m, and temperature, T. (non-relativistic limit)

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Particles used in the ratio
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Is the (p ?-)/(? ?) double-yield ratio
reasonable?

• Why isnt the ratio (p K-)/(? ?0)?
• The actual reaction channels are
  p?0 ? ?0 ? and p?0 ? p ? ?-
• Based on these decay modes one would expect ?0 to
  be used in the ratio
• Experimentally, it is difficult to detect the
  uncharged ?0
• We detect ? ? particles and approximate the
  number of ? 0

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• Mass difference
  ?m(mK-mp) (m?m?) 176.8 MeV
• This mass difference is much larger than previous
  double yield-ratio thermometers
• Conserved Quantities
• The particles strangeness and baryon numbers
  allow the chemical potentials to cancel out of
  the ratio since the quantities are conserved.

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The ratio of particles is a function of
temperature

• R (np nK-)/(n? n??) ? exp(-?m/T)
• The non-relativistic expression can be solved for
  T
• Note the temperatures sensitivity to change in
  the ratio

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First test of the (p ?-)/(? ?) thermometer

• A thermal model was used to generate particles
• Input parameters included temperature and baryon
  chemical potential
• The model also includes decay of unstable
  particles
• After the particles were generated, we counted
  the number of protons, ?-, ?, ? to calculate the
  ratio R(number of p)(number of ?-)/(number of
  ?)/(number of ? )
• The ratio was then numerically inverted to derive
  the temperature

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Results for First Test

• Input parameters
• chemical potential 400 MeV
• Result
• The thermometer is only reliable up to 70 MeV.

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Complications

• Decays!
• Experimentally, some particles will decay before
  they are detected
• Our program assumed that if a particle decays
  through the weak interaction, then it will live
  long enough to be detected.
• Conversely, particles decaying via the Strong and
  EM forces are too short-lived to be detected.

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Why does the graph bend over?

• Branching ratios indicate that decays must give
  the same fractional loss of particles independent
  of the temperature
• Remember that the ratio R ? exp(-?m/T)
• Therefore T ? - ?m/ln R
• This means that a fractional ?R will not cause a
  large ?T for low temperatures.
• At high temperatures, the same ?R will cause a
  more drastic ?T .

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That pesky chemical potential!

• Mathematically, the chemical potential should
  cancel out
• But our program depends on the ?B to thermally
  generate particles.
• We dont know how to resolve this problem!

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Second test of the (p ?-)/(? ?) thermometer

• The URQMD AuAu Monte Carlo Simulation was used.
• This simulates a collision of two gold nuclei and
  generates particles based on kinetics
• Input parameters lab frame beam energy, impact
  parameter, number of collision events

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Results for second test

• The blue line was the first trial with 100 events
  for each beam energy
• Only 6 kaons were produced at 2 AGeV so there is
  a very large error bar.
• To reduce the error bar, we ran 2 AGeV with 500
  events as shown by the green data point
• No absolute conclusions can be made with this
  graph
• It is interesting to see that it seems the
  temperature approaches 70 MeV

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Moving onA new thermometer

• Why try a new thermometer?
• The (p ?-)/(? ?) only measured up to 70 MeV.
• We want to measure hotter nuclear temperatures
  ideally between 100 and 1000 MeV which is on the
  order of 1012 - 1014 K!

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The ?/p thermometer

• Another thermal model was used to generate
  particles
• This model included more particles that could
  decay
• Again, the number of ? and protons were counted
  and then their ratio was inverted numerically to
  derive the temperature

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Thermal Results for the ?/p thermometer

• This thermometer measured up to about 95 MeV.

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Jackpot.....well, maybe!

• A collision occurs over a certain amount of time.
• Within that time, the Deltas decay before they
  reach the detectors
• The Deltas only live for about 0.9 fm/c or 3x
  10-24 s.
• Even something traveling at the speed of light
  would only move a distance of 9 x
  10-16 m.

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?/p thermometer may not be ideal...

• In URQMD, the Deltas decay into a proton and a
  pion before they are detected.
• The decay particles are not a very unique
  signature which makes it difficult to deduce how
  many Deltas existed at an earlier point in the
  collision.
• So while the ?/p thermometer measured a higher
  temperature, it may not be practical
  experimentally.

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Conclusions

• The (p ?-)/(? ?) thermometer was only reliable
  up to a temperature of 70 MeV.
• The ?/p thermometer measured up to
  approximately 95 MeV which is an improvement over
  the (p ?-)/(? ?) thermometer
• The ?/p thermometer may not be ideal
  experimentally

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Questions to be further addressed

• It is still not obvious how the chemical
  potential affects the (p ?-)/(? ?) thermometer.
• The relationship between the beam energy and
  temperature in URQMD simulations needs further
  study.
• We would like to understand how to make the ?/p
  thermometer useful in the URQMD program.

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Acknowledgments

• Special thanks to Dr. Voytas and Dr. George for
  being the best advisors. You guys were always
  there for me and I really appreciate all your
  help!
• I would also like to thank the MSU REU program
  for introducing me to this research.
• And thanks to Mindy and Jon for making me laugh
  when I was ready to throw in the towel!