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

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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

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

Au

Au

- 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

- 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

1

a

2

b

- Goldhaber, Goldhaber, Lee, and Pais applied the same idea (independently) to pions
- In 1960, they discovered angular correlation between identical pions

- 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

- 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

- 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

- 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

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

- 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

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)

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