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Addition of a potential to the Klein-Gordon equation to determine ‘fireball’ size. HBT Pion Correlations. Laniece Miller – Clarkson University Dr. Ralf Rapp – Texas A&M University, Cyclotron Institute. The Project.

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Addition of a potential to the Klein-Gordon equation to determine ‘fireball’ size

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Addition of a potential to the Klein-Gordon equation to determine ‘fireball’ size

HBT Pion Correlations

Laniece Miller – Clarkson University

Dr. Ralf Rapp – Texas A&M University, Cyclotron Institute


The Project

My project is to look at the optical potential in the Klein-Gordon equation and attempt to determine a more exact form.

Included is:

  • A physical overview

  • A look at HBT interferometry

  • A few details of the project

  • A look at where the project currently stands


The RHIC Experiment

Au

Au


Quark Gluon Plasma

  • Result from some Au-Au collisions

  • Restores chiral symmetry

  • Quarks and gluons become unbound and do not ‘know’ which nucleon they belong to

  • Allows other particles to form which posses a shorter lifetime


Current Ideas


What is HBT Interferometry?

  • Often called two particle correlation

  • Initially discovered by Robert Hanbury-Brown and Richard Twiss in the 1950’s

    • They used HBT to determine the size of stars using photons

    • Photons (and pion) tend to arrive in pairs, so the source size can be determined


HBT

1

a

2

b


What is HBT interferometry?

  • Goldhaber, Goldhaber, Lee, and Pais applied the same idea (independently) to pions

    • In 1960, they discovered angular correlation between identical pions


Determining the Radii

  • The ‘fireball’ is assumed to be cylindrically symmetric

    • Allows the number of integrals to be greatly reduced (8 to 2)

  • From the correlation function, the individual radii can be determined


Current Ideas

  • The standard idea has been not to include an optical potential (plane-wave)

    • This gives smaller radii than is experimentally observed

  • Recently the idea of adding an optical potential to match theoretical and experimental data better

    • The current optical potential possesses some other problems with parameters being inconsistent


Our Idea

  • Write code to calculate the radii and graph it

  • Determine parameters to get correct radii

  • Determine is parameters are consistent

    • Temperature and chemical potential were most inconsistent on the Miller model


Current State

  • At the moment we’re in the process of writing the computer code to calculate the correlation function and the resulting radii.

    • We ran across several issues with the code and the math slowing progress.

      • We are beginning to find some of the solutions to the problems we have come across so the code is beginning to make a little headway


Where to Now?

  • Get the code completely working and completely program the necessary equations

  • Determine a new form for the optical potential

    • Determine what the parameters need to be

    • Determine the reasonableness of the parameters

    • Try a new potential if the parameters are not realistic


References

J.G. Cramer, G.A. Miller, J.M.S. Wu, J.H.Yoon, Quantum Opacity, the RHIC Hanbury Brown-Twiss Puzzle, and the Chiral Phase Transition, Phys. Rev. Left. 94, 102302 (2005)


Special Thanks

Dr. Ralf Rapp, my mentor this summer

Dr. Hendrik van Hees, Dr. Rapp’s post-doc who has spent a lot of time helping me sort out the computer code

Cyclotron Institute at Texas A&M University

The Department of Energy

The National Science Foundation


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