Transcript Addition of a potential to the Klein

Addition of a potential to the pion-Klein-Gordon
equation to determine ‘fireball’ size
RHIC accelerated two gold ions together producing a
variety of particles that left the track pattern below
By Laniece Miller
Advisor: Dr. Ralf Rapp
Dr. Hendrik van Hees
P 2 (k 1,k 2)
C (k 1,k 2) 
 1  cos[(k1  k2 ) * ( x1  x2 )]
P1 (k1 ) P1 (k2 )
The correlation function, which employs
the wave function, gives easy rise to the
fireball radii.
My project is to look at the optical
potential in the Klein-Gordon
equation and attempt to determine
a more exact form.
2
( )*
2
( )*
(  U (b)) p (b)  p  p (b)
The pion-Klein-Gordon equation.
If the nuclei hit with high A pictorial
enough energy, then the representation
The
Klein-Gordon
equation
of bound
nucleons will overlap
quarks.
gives a differential equation Temperature vs. Chemical Potential phase diagram
enough to that the quarks
which
allows
us
to
calculate
The problem with the standard
and gluons are no longer
the
wave
function
of
pions
Klein-Gordon equation is the
bound to a particular
leaving
the
fireball.
radii do not match the
hadron, forming the quark
From the wave equations,
experimental radii. More
gluon plasma.
we can use HBT
recently, it has been suggested
Interferometry to determine to add an optical potential, but
Two atoms collide, their nucleons overlap forming
some parameters may not be
the fireball, which then expands forming the hadron the original size of the
gas before finally reaching freeze-out and
fireball.
realistic.
streaming to the detector.