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.

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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

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

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

The RHIC Experiment

Au

Au


Quark gluon plasma

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

Current Ideas


What is hbt interferometry

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


Addition of a potential to the klein gordon equation to determine fireball size

HBT

1

a

2

b


What is hbt interferometry1

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

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 ideas1

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

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

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

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

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

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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